# Harnessing Machine Learning and Deep Learning Approaches for Laser-Induced Breakdown Spectroscopy Data Analysis: A Comprehensive Review

P. Dehbozorgi, Ludovic Duponchel, V. Motto-Ros, T. Bocklitz

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P. Dehbozorgi, Ludovic Duponchel, V. Motto-Ros, T. Bocklitz. Harnessing Machine Learning and Deep Learning Approaches for Laser-Induced Breakdown Spectroscopy Data Analysis: A Comprehensive Review. Analysis & Sensing, 2025, Anal. Sens., 00, pp.e202500106. 10.1002/anse.202500106. hal-05319010

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# Harnessing Machine Learning and Deep Learning Approaches for Laser-Induced Breakdown Spectroscopy Data Analysis: A Comprehensive Review

Pegah Dehbozorgi, Ludovic Duponchel, Vincent Motto-Ros, and Thomas Bocklitz*

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Laser-induced breakdown spectroscopy (LIBS) is a rapid, accurate technique for material analysis, offering real-time, minimally destructive, and in situ detection capabilities with broad application potential. LIBS extends its applications across various fields, from geology to biomedicine. However, barriers like matrix effects, reproducibility, self-absorption, and spectral noise often restrict the proper interpretation of the spectra. This review paper examines literature from 2015 to 2025, focusing on the evolution of machine learning (ML) and deep learning (DL) techniques, in LIBS analysis. It evaluates the advancement of these techniques, assessing both the qualitative and quantitative performance of LIBS analysis. These observations support the complementary

roles of ML and DL methodologies. ML captures general patterns, while DL, through convolutional neural networks (CNNs), excels at identifying high-level features. This literature review reveals that no single ML or DL tool consistently provides optimal solutions for LIBS applications. The analysis pipeline needs to be tailored based on the LIBS data and the goal of the study. Designing such a framework requires the incorporation of preprocessing techniques to enhance the quality of raw signals. This step should then be followed by integrating the data into predictive models, whether ML or DL, to accomplish tasks like classification or concentration prediction.

# 1. Introduction

Laser-induced breakdown spectroscopy (LIBS) is a form of atomic emission spectroscopy (AES) that has profoundly influenced the field of analytical science.[1] LIBS has been effectively utilized for both quantification and classification purposes, using microscopes,[2] handheld devices,[3,4] and standoff instruments.[5] Recent advancements in this technique allow for elemental imaging, which refers to spatially resolved surface analysis. There has been increasing emphasis on analytical techniques for performing spatially resolved surface analyses, driven by the advancing needs in industrial, nanotechnology, geology, and biomedical applications. Depending on the application, spatially resolved measurements are essential for gaining a more detailed understanding of the sample's composition, offering significant advantages over conventional bulk analysis. LIBS functionality as a powerful imaging technique for elemental characterization in

analytical chemistry, enables the detection of major, minor, and trace elements with a high dynamic range, low limits of detection, and rapid acquisition rates.[6] LIBS-based imaging has emerged as a significant extension of conventional LIBS, sharing its core measurement principles while adding the capability of spatially resolved chemical analysis, thus offering deeper insights into the elemental distribution across complex surfaces.[7] These advancements, combined with the technique's inherent ease of use, have led to the development of systems capable of performing fast, multielement analyses across large sample surfaces.

High-quality LIBS spectra are now routinely captured, and diverse data processing and modeling strategies are needed to achieve optimal analytical performance.[8] Therefore, extracting meaningful insights from complex LIBS datasets quickly and accurately becomes a hot research focus.[9] In this regard, chemometrics has emerged as a powerful solution to address the challenges of LIBS data processing.[10-12] By integrating chemistry, mathematics, and computer science, it enables efficient analysis and interpretation of complex spectral data from analytical instruments. Recently, various ML and DL techniques have been integrated into chemometrics to enhance the reliability of outcomes, whether addressing qualitative or quantitative challenges.[13-17] By employing supervised or unsupervised ML algorithms and DL models, combined with appropriate LIBS data preprocessing techniques, a robust framework can be established to achieve more accurate and precise outcomes in shorter times.

The following subsections will explain the process of generating LIBS and its application to various types of samples, including liquids, gases, and particularly solids. Next, we will explore the advantages and disadvantages associated with the technique, as well as the increasing trend of incorporating machine learning ML and DL techniques. The necessity and benefits of these technologies will also be highlighted.

## 1.1. LIBS Plasma Formation

LIBS enables the detection and quantification of elemental composition, encompassing both heavy and light elements, across solid, liquid, and gaseous states.[18] However, its application to

P. Dehbozorgi, T. Bocklitz
Leibniz Institute of Photonic Technology
Member of Leibniz Health Technologies, Member of the Leibniz Centre for Photonics in Infection Research (LPI)
Albert Einstein Strasse 9, Jena 07745, Germany
E-mail: Thomas.bocklitz@uni-jena.de

P. Dehbozorgi, T. Bocklitz
Institute of Physical Chemistry (IPC) and Abbe Center of Photonics (ACP)
Member of the Leibniz Centre for Photonics in Infection Research (LPI)
Friedrich Schiller University Jena, Member of the Leibniz Centre for Photonics in Infection Research (LPI)
Helmholtzweg 4, Jena 07743, Germany

L. Duponchel
Univ. Lille, CNRS, UMR 8516 - LASIRE - Laboratoire de Spectroscopie pour Les Interactions, La Réactivité et L'Environnement
Univ. Lille, CNRS
Lille F-59000, France

V. Motto-Ros
Institut Lumière Matière
UMR5306 Université Lyon 1-CNRS
Université de Lyon
Villeurbanne cedex 69622, France

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© 2025 The Author(s). Analysis & Sensing published by Wiley-VCH GmbH. This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.
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gaseous and liquid samples remains less common compared to solid samples. This section primarily discusses plasma formation from solid samples, though some studies also explore plasma formation in gases<sup>[19,20]</sup> and liquids.<sup>[21,22]</sup>

The analysis of solid samples involves precisely directing a laser beam onto the material's surface for accurate spectroscopic examination. However, a laser is not just one device. Instead, it represents a broad category that includes many types, each with unique characteristics. Different lasers differ in their wavelengths and operational qualities, which are tailored to specific uses.[23] A variety of lasers, spanning wavelengths from infrared (IR) to ultra-violet (UV), have been employed in LIBS. These laser types include solid-state lasers, gas lasers, and excimer lasers. Nd:YAG lasers, operating at a fundamental wavelength of 1064 nanometers in the IR range, with pulse durations of 5–10 ns, are among the most commonly adopted in LIBS measurements.[24]

Considering the often-employed nanosecond IR pulses on a solid sample, plasma formation can be structured through the following procedures.

As soon as the laser pulse reaches the sample, the absorption of photons rapidly elevates the temperature of the material at the focal point. In less than a nanosecond (ns), the temperature rises to the boiling point, initiating the ejection of sample vapor, fragments, and particles, a process referred to as laser ablation.[25,26] The laser continues to heat the ablated material, driving its temperature to an exceptionally high level, generally between 8000 and 10,000 K. This intense heat is sufficient to thermally atomize, excite, and ionize the plume material, transforming it into a plasma. These processes, recognized as laser-induced optical breakdown, are responsible for generating the microplasma and forming the foundation of LIBS. After laser irradiation, the initially hot and dense plasma emits mostly continuum radiation due to Bremsstrahlung and recombination processes.[23] As the

microplasma evolves, it begins to emit a strong radiation signature at distinct wavelengths indicative of its chemical composition. Once the laser pulse terminates, the plasma continues to expand and rapidly cools down due to the absence of additional energy input. During the cooling and expansion of the plasma plume, the material within it condenses and redeposits onto the sample surface in the form of micro and nanodroplets or particles. This process leaves behind a small crater on the sample surface, with a diameter slightly larger than the laser spot size and a shallow depth, typically on the order of a few tens of micrometers.[26] These processes are schematically illustrated in Figure 1.

Considering the conditions outlined above, a typical, conventional laboratory-based LIBS instrument comprises the following key elements: 1) laser source that emits high-intensity, short-duration laser pulses, ideally at a wavelength strongly absorbed by the sample; 2) focusing optics designed to concentrate the laser beam into a small spot either on or within the sample, achieving the optical power density necessary to induce laser-induced breakdown; 3) a sample stage that securely holds the sample and enables precise movement to target specific analytical locations; 4) light collection optics to capture the emitted radiation; 5) a fast triggerable, sensitive spectrometer capable of recording the UV-Vis-NIR emission spectrum with a spectral resolution of at least 100 picometers (pm) and an integration time in the µs range; and 6) fast electronics, which ensure synchronized operation of the spectrometer and incoming laser pulse with sub-µs precision.

As an example, a microscope can be seamlessly integrated into the LIBS instrumental setup to facilitate high-resolution LIBS imaging.[27–29] This standardized configuration is depicted in Figure 2. It is important to note that alongside this stated configuration, a diverse array of LIBS setups exists, with variations in

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Pegah Dehbozorgi received her B.Sc. in Nuclear Physics (2011) from the University of Mazandaran and her M.Sc. in Photonics (2015) from the Institute for Advanced Studies in Basic Sciences, Zanjan. She is currently pursuing a Ph.D. with the Photonic Data Science Group at the University of Jena, supervised by Prof. Dr. Thomas Bocklitz. Her research integrates image analysis, machine learning, and spectral data analysis to advance computer vision, medical diagnostics, and analytical performance, driving innovative solutions in these fields.

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Ludovic Duponchel earned his Ph.D. in Physical Chemistry in 1997, focusing on a portable near-infrared spectrometer for agrifood analysis. He then spent 2 years at Horiba Jobin-Yvon. In 2000, he became Assistant Professor at the University of Lille, where he joined the Infrared and Raman Spectroscopy Laboratory (LASIR). He advanced to Full Professor in 2008. From 2013 to 2022, he chaired the French Chemometrics Society. His current research develops advanced chemometric methodologies for complex spectral datasets, emphasizing spectroscopic imaging.

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Vincent Motto-Ros is Associate Professor at the University Claude Bernard Lyon 1 and researcher at the Institut Lumière Matière (ILM). He obtained his Ph.D. in Physics in 2005 in Lyon, followed by postdoctoral stays at the Canadian Space Agency (Montréal) and the LIPhy laboratory (Grenoble). Since 2008, his research has focused on the development of Laser-Induced Breakdown Spectroscopy (LIBS), with recognized expertise in instrumentation, quantification, experimental training, and elemental imaging.

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Thomas Bocklitz received a Diploma in theoretical physics (2007), a Ph.D. in chemometrics (2011), and a degree in physics and mathematics from Friedrich Schiller University Jena. He leads the “Photonic Data Science” department at Leibniz-Institut of Photonic Technology and a research group at the Institute of Physical Chemistry. Passionate about solving problems with mathematical methods, his research focuses on machine learning for photonic image data, chemometrics for spectral data, correlation of measurement methods, and data fusion.
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<figure><img src="image_13.png" /><figcaption>**Figure 1.** Overview of laser-induced breakdown of a solid sample under atmospheric conditions. A simplified depiction of the time evolution and key processes involved in the laser-induced breakdown of a solid sample under atmospheric conditions. The indicated time ranges serve as approximate references. The color gradient of the ablation plume represents its temperature variations. Laser beam targets the surface of a solid sample, which is followed by initiating laser-matter interactions leading to microplasma formation. The laser pulse strikes the sample, rapidly raising its temperature and triggering laser ablation, which leads to the formation of a high-temperature plasma. This plasma emits radiation, forming the basis for spectral analysis. The cooling and expansion of the plasma leads to the formation of a crater and the emission of LIBS spectra, which are used for chemical composition analysis. In the illustration, ns stands for nanoseconds, and µs refers to microseconds. Reproduced with permission.[26] under a granted STM PG license and with permission from Springer Nature and the Copyright Clearance Center.</figcaption></figure>

<figure><img src="image_14.png" /><figcaption>**Figure 2.** Schematic illustration of a standard LIBS experimental setup.</figcaption></figure>

system component specifications and geometrical arrangements that are tailored to optimize performance for specific applications or experimental requirements.

LIBS offers several advantages over traditional analytical techniques, which encourage its use. However, it also has certain limitations that restrict its applicability. In the following section, we will briefly review both the benefits and the drawbacks of LIBS spectra.[30]

## 1.2. Advantages and Disadvantages of LIBS

As a well-established analytical atomic emission spectroscopic technique, LIBS presents both distinct advantages and disadvantages. Below, we outline the key points within each category.

### 1.2.1. Advantages

Reduced sample preparation process is a key advantage of LIBS measurements.[31] In LIBS, sample preparation is typically minimal and, in some instances, entirely unnecessary. Sample preparation might often be expensive, considering time estimations, and may inadvertently modify the composition of the sample at hand over time, negatively compromising the integrity of the analysis.[32]

LIBS can also be regarded as a microdestructive method.[33,34] The physical impact on the sample is limited to a small spot where the laser hits, with the mass of the evaporated material ranging from nanograms (in micro-LIBS) to micrograms. Accordingly, LIBS can be regarded as a microdestructive method, preserving the structural integrity of the sample to a significant extent while providing detailed compositional insights.[35]

LIBS allows swift elemental analysis across diverse applications.[36] Classic LIBS setups typically operate at frequencies of 10–20 Hz. Meanwhile, modern kHz imaging systems are emerging and significantly enhancing analysis speed.[37] The lack of sample preparation and the inherent simplicity of LIBS make it an excellent choice for real-time analysis. Due to the short plasma duration, quick collection of spectral data, and the minimal processing time needed, each LIBS measurement can be considered fast.[38]

Additionally, LIBS facilitates efficient in situ elemental analysis.[39] In traditional AES methods, the process starts by bringing the sample to the device, where it is introduced into a vaporizing or atomizing source for the analysis. With LIBS, the approach is
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reversed. Using focused laser light to generate a plasma, materials can be analyzed directly, often right where they are, simply by pointing the laser pulse at the target. LIBS flips the conventional methodology by bringing the analysis source directly to the sample, rather than the other way around.[38]

LIBS can be integrated with other spectroscopic techniques to improve analytical accuracy, combining its unique elemental insights with complementary data from additional methods. While LIBS is beneficial for multielemental analysis of well-characterized matrices, it is not effective for molecular analyses. However, LIBS can be effectively integrated with other techniques such as Raman spectroscopy,[40,41] IR spectroscopy,[42,43] and luminescence,[44] leveraging the complementary strengths of these methods alongside the capabilities LIBS provides. For example, while no single method can achieve both molecular and elemental analysis simultaneously with high efficacy, LIBS and Raman spectroscopy can provide complementary information about both molecular and elemental compositions.

Given these characteristics, the application range of LIBS has continued to expand. However, there are several disadvantages associated with LIBS that limit its further application.[45]

### 1.2.2. Disadvantages

LIBS exhibits so-called matrix effects.[46,47] These effects occur when the physical properties and chemical composition of a sample, as well as the measurement conditions, influence the signal of a target element. This can cause variations in the signal even when the concentration of the element remains constant. For example, the signal intensity for silicon in water, steel, and soil can vary significantly despite having similar concentrations, as different matrices interact uniquely with the laser pulse. In general, the matrix effect influences the characteristics of laser-induced plasma, including plasma temperature, total number density, and electron number density.[48]

LIBS also suffers from the effect of self-absorption.[49,50] Self-absorption is a common phenomenon in emitting sources, which can lower the maximum intensity of a spectral line, resulting in an intensity that is typically lower than expected.[51] Basically, the spectrochemical analysis of materials involves establishing a relationship between the spectral signal and the analyte concentration.[52] In a LIBS spectrum, the intensity of emission lines for each species' spectrum correlates with its concentration in the sample, forming the basis for quantitative analysis.[50,52] This relationship can be complex, but from an analytical perspective, it is highly desirable to achieve a linear correspondence between sample concentration and spectral intensity. The relationship between the intensity of spectral lines and sample concentration in LIBS measurements is not always linear. This nonlinearity can occur due to the self-absorption effect, where emitted radiation is reabsorbed by the same species that emitted it. This effect is especially pronounced for strong spectral lines or at high concentrations, which can lead to nonlinear intensity-concentration relationships. The degree of self-absorption experienced by each spectral line varies based on the conditions of the plasma

and the composition of the elements involved. This factor might highlight the necessity of a nonlinear model within the ML and DL framework to explore the LIBS spectra.

LIBS is often criticized for its poor shot-to-shot signal repeatability.[53] This characteristic arises from the complex interactions between the laser and the sample, as well as the laser and the plasma. The observed phenomenon is transient and inhomogeneous, making it sensitive to the sample's physical and chemical properties and to atmospheric conditions. As a result, the experimental data can be inconsistent and widely dispersed unless the experimental settings are optimized to minimize potential sources of noise.[54,55] Noise sources in LIBS can be categorized into four main types: source noise, stemming from fluctuations in laser-sample or laser-plasma interactions; shot noise, caused by variations in the number of photons reaching the detector; detector noise; and instrumental (thermal) drift.[54] The limited reproducibility of LIBS, combined with multiple potential noise sources, poses significant challenges, especially in single-shot applications like LIBS imaging. However, certain instrumental designs can achieve a shot-noise-limited setup, making noise mitigation more feasible. Consequently, depending on the specific configuration and the objective of the investigation, different levels of noise may need to be addressed.

Furthermore, monitoring a single spectral line in atomic emission analyses can be hindered by spectral interferences, which occur when two or more elements emit at the same or closely overlapping wavelengths. This overlap can compromise the accurate detection and measurement of the target element's emission line.[56] In LIBS, the elemental analysis begins with the assignment of spectral lines; however, this line assignment can be affected by potential spectral interferences.[57] Elements like transition metals, such as iron (Fe), titanium (Ti), molybdenum (Mo), and nickel (Ni), exhibit numerous emission lines across a wide wavelength range, from ultraviolet to near-infrared.[58] If a sample contains one or more of these elements, the corresponding spectra will be very dense from a spectral perspective. Consequently, significant spectral interferences may occur, impacting the signal extraction of other elemental lines, including some of the most interesting and valuable ones. Additionally, interference effects can sometimes lead to a significant decrease in sensitivity performance. This occurs when the number of available lines for the elements of interest is reduced due to interference, resulting in the most sensitive line not always being accessible.[58] Spectral broadening, another source of spectral interference, can also further limit accurate interpretation and characterization of LIBS spectra.[59] During real LIBS experiments, spectral lines from the plasma are broadened, partly due to the finite resolution of the spectrometer and partly due to intrinsic physical causes. The primary broadening mechanism in a LIBS plasma, driven by its physical cause, is the Stark effect,[60] resulting from the high initial density of free electrons and ions. In LIBS, the emission line profile is typically well-represented by a Lorentzian function. However, as the radiation propagates through the plasma, the line shape often deviates from the ideal Lorentzian profile, exhibiting reduced peak intensity and increased broadening.[61] Besides Stark broadening, another key factor that affects the width of spectral lines is
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instrumental broadening. This happens when the spectrometer's resolution is comparable to the line's width, making the effect of the instrument significant. Because of limitations in the spectrometer's optics, the recorded line shape differs from the actual one. Instrumental broadening is typically represented as a Gaussian curve, since the combined impact of components like the slit, grating, and detector creates a response that closely resembles a Gaussian distribution.[61,62] Consequently, the broadening of spectral lines increases the likelihood of spectral interference with adjacent lines.

Despite the aforementioned advantages and disadvantages, LIBS has continued to be implemented in various fields, including archaeology and cultural heritage, biomedical applications, industry, and the analysis of geological samples. This has resulted in the generation of a substantial amount of data.[63–66] This data must be analyzed and processed expeditiously, yet with precision and reliability, to address a particular inquiry within a related scientific domain. This necessitates the implementation of a proper preprocessing approach to enhance LIBS data quality, thereby suppressing or removing the limitations of LIBS previously discussed. However, in order to proceed with further analysis, it is necessary to integrate the clean, enhanced LIBS spectral data with an ML or DL computational tool. The subsequent section will provide a concise justification for the implementation of artificial intelligence (AI)-based analytical methodologies within the framework of LIBS.

## 1.3. LIBS Analysis Approach

With its minimal sample preparation requirements, combined with the ability to perform real-time, multielement, and remote analysis, LIBS has become a versatile tool applicable to a diverse array of scenarios, ranging from deep ocean exploration to Mars surface analysis.[67] As a unique identifier of a sample, LIBS spectra support a wide range of qualitative and quantitative applications.[68–70] In practical LIBS, qualitative analysis usually entails material identification, classification, sample comparison, diagnostics, and monitoring. On the other hand, quantitative analysis focuses on measuring the concentrations of chemical components present in the sample being studied.

However, despite the wide variety of advantages it offers, the analysis of LIBS spectra can often be challenging. These challenges primarily arise from matrix effects, self-absorption phenomena, spectral interference, and limitations in reproducibility, all of which can complicate accurate spectral interpretation and significantly undermine the precision, and overall reliability of the analytical results. Diverse applications of LIBS require advanced multivariate data analysis techniques, combined with robust statistical methods, to fully unlock the data's potential for accurate investigations.

ML algorithms represent an emerging interdisciplinary approach capable of extracting the maximum amount of valuable and meaningful information from LIBS data. While various ML techniques have been applied to LIBS spectra analysis,[71–74] selecting the appropriate methods remains crucial for achieving

specific research objectives. No single ML technique is universally effective, as their performance varies significantly depending on the experimental goals and application context.

Beyond traditional ML techniques, DL, a subset of ML, has gained significant attention in spectral data analysis owing to its proven success and promising potential across diverse applications. DL is particularly effective at automatically and efficiently learning complex underlying features from large and intricate datasets. This capability makes it well-suited for analyzing complex LIBS data to uncover hidden patterns and relationships.[75–78]

There are some fields of investigation where integrating LIBS with computational techniques is critical. For instance, one of the most rapidly evolving aspects of LIBS applications is LIBS imaging, a technique with high potential for elemental imaging across various domains, including biology, medicine, geology, and industry.[79] However, the large number of spectra (over a million in some cases) within an imaging dataset and the complexity of the spectra make this task challenging, especially when certain elements, such as Fe or Ti, are present. It becomes a crucial issue when high-throughput analysis is expected at high speed. Indeed, analyzing such huge data typically demands considerable time and a high level of expertise in emission spectroscopy to ensure that spectral interferences or any other unforeseen issues do not compromise the results.[80] This is where optimized ML or DL models and algorithms can play an effective role, not only in making the analysis more precise and reliable but also in accelerating the entire process and delivering unbiased results.

In situ analysis is another domain where ML and DL methodologies can provide significant benefits. Due to known limitations in the reproducibility of LIBS measurements caused by factors such as minimal sample preparation, no surface cleaning, high spectral variability, and laser stability issues, there is a clear need for advanced computational approaches. ML and DL can be effectively utilized to compensate for these challenges, enhancing the consistency and interpretability of the analytical outcomes.

Given the wide range of applications for LIBS and the associated advantages and disadvantages of LIBS measurement data, as well as the significance of incorporating ML and DL techniques for enhanced analysis, the following subsections will provide an overview of important signal preprocessing techniques applicable to LIBS. These techniques are essential for refining the data before it is input into predictive ML or DL models.

## 2. Preprocessing of LIBS Spectral Data

LIBS spectral data is inherently complex and often contains a high degree of redundancy.[81] These variabilities have the potential to compromise the consistency of the LIBS data collected, thereby restricting the establishment of a reliable yet accurate analysis.[82] In this context, preprocessing can significantly enhance the quality of raw data, as it represents the initial step in minimizing spectral noise, variations, and uncertainties. As illustrated in **Figure 3**, the quality of LIBS signals can be enhanced using several techniques, such as baseline correction, filtering out noise, and normalizing LIBS spectra to a specific range, with each method
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<figure><img src="image_18.png" /><figcaption>**Figure 3.** Schematic illustration of the key preprocessing methods adopted in the LIBS analysis pipeline. This figure presents the preprocessing techniques discussed in this review. Each category targets a specific limitation or drawback of LIBS measurement data.</figcaption></figure>

designed to address specific data limitations. The selection of an appropriate technique and the required level of preprocessing depends on the specific quality of the data being examined.

## 2.1. Baseline Correction

A major source of error in LIBS data originates from the baseline,[83] a varying shift in spectral intensity across wavelengths, which can distort the true signal and complicate accurate elemental analysis. The baseline in LIBS arises mainly from continuous radiation emitted by free electrons and recombination processes within the plasma. Consequently, identifying and removing the baseline from the analytical signal is essential prior to conducting further analysis to ensure accurate and reliable results. Several methods exist for estimating the baseline, with the most widely adopted approaches relying on these primary techniques: polynomial fitting algorithms,[84] Asymmetric Least Squares (ALS),[84,85] Statistics-Sensitive Non-Linear Iterative Peak-Clipping (SNIP),[86] Top Hat (TH),[87] Median,[84] Rolling Balls (RB),[87] and 4S Peak Filling (PF).[87]

Polynomial fitting correction algorithm utilizes high-order polynomial functions to estimate the baseline in LIBS spectra. The method works by dividing the spectrum into N distinct regions, within which it identifies local minima and points of lowest intensity and selects a specific subset of minor minima corresponding to pixels with the smallest intensities. These minor minima are classified as if their values fall within three standard deviations of the more prominent major minima. A polynomial curve is then fitted through the major minima across all segments using a least-squares approach, and a standard deviation is calculated to ensure the fit closely aligns with the minor minima, minimizing discrepancies. The algorithm is then optimized

through an iterative process that identifies the optical parameters involving the polynomial power order, the number of divisions, and the number of major minima in each group. Ultimately, the polynomial function, derived from both major and minor minima, represents the continuum background or so-called baseline.[88]

Turning to the next correction method, ALS employs a smoothing algorithm with asymmetric weighting of deviations to derive a robust baseline estimator. By assigning different weights to deviations, ASL effectively prioritizes the correction of baseline drift while preserving the integrity of signal peaks.

In addition to the latter two approaches, the SNIP method can also be used to determine the baseline within the LIBS signal. SNIP's core principle involves replacing data points within a defined window with the minimum value found within that window, iteratively. This effectively eliminates features broader than the window, thus removing the baseline while preserving sharper peaks.[89]

Another technique for baseline correction is TH, which utilizes the Fourier transform of spectral intensity to extract fine details and small features from spectral data. TH prioritizes these features over adjacent noise. TH uses a user-defined sliding window to process the data; the size of the window determines the level of detail captured.[87]

As a straightforward solution for establishing a baseline correction in LIBS measurement data, the median method employs local averaging to adjust spectral information. This process involves replacing each data point with the average of its neighboring points within a user-defined local window, which can be strategically placed around spectral peaks or in noise regions. This sliding window approach iterates across the entire dataset, effectively completing the baseline correction.[87]

Adding to the baseline correction techniques adopted within the LIBS analysis framework, RB is a method originally developed for processing X-ray spectroscopy data. RB is based on the concept of a rolling sphere with a fixed radius that moves along the spectrum.[90] The algorithm has three main steps. The process entails identifying the minima within a designated window, subsequently locating the maxima among these minima, and finally, applying an averaging technique to smoothen the data over the identified maxima. As the sphere rolls, it creates a smooth line that helps extract the baseline from the spectrum.[91]

The list of baseline correction techniques continues with the application of PF as an iterative method for baseline suppression.[92] This technique also relies on data being averaged within local windows. Based on the assumption that the baseline follows a monotonically decreasing trend, it uses the second derivative of the spectrum for initial smoothing. This technique is based on several key parameters, including the size of the data window, how many windows are used, and how many iterations are executed in the baseline suppression process. This method calculates the average for each local window across iterations and selects the minimum value as the updated baseline.[87]

These methods effectively adjust the baseline of the spectra, eliminating undesirable variations and enhancing the accuracy of subsequent data analysis. However, LIBS spectra are often compromised by noise and unwanted artifacts. These artifacts must be removed or suppressed by applying different filtering techniques.
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## 2.2. Filtering

Data filtering methods can theoretically separate spectra into "signal" and "noise," subsequently removing the "noise" component to enhance the signal-to-noise ratio (SNR) and improve the reproducibility of both the LIBS plasma and its resulting spectra. Accurate LIBS analysis is often hindered by noise interference, making it essential to develop effective filtering methods to prevent noise from being mistaken for meaningful key features.[93] Upgrading hardware facilities can reduce noise, but such upgrades are often expensive. Therefore, denoising through data preprocessing framework is a more cost-effective and efficient alternative.

One example of a noise reduction technique in signal preprocessing is adaptive filters.[94] These filters feature coefficients that can vary over time, enabling them to adjust dynamically.[95] They are employed when the optimal filter response for a specific task is unknown beforehand or when the operating environment is expected to change.[96,97] The filter continuously modifies its parameters based on an optimization algorithm that minimizes an error signal. This error is typically the difference between the filter's output and a desired signal (or reference). The ultimate goal is to maximize the suppression of unwanted noise while preserving the integrity of the target signal to the greatest possible extent.

The Kalman filter can also be used to denoise LIBS spectral data. This filter is a model that uses estimations from previous states to predict future states of processes. One of its main advantages is that it employs a recursive approach. Whenever it predicts a new state, it attempts to correct it using the estimation from the previous state. As a result, this method significantly reduces the mean square error.[98,99]

Alongside the previously discussed techniques, the Savitzky-Golay filter (SGF)[27] is a commonly used method for data smoothing based on local least-squares polynomial approximation.[100,101] The smoothing can be controlled with two parameters, the window size and the polynomial degree. Small window sizes and high polynomial degrees may yield noisy signals, whereas large window sizes and low polynomial degrees may yield distorted signals.[102] LIBS analysis can be improved by properly incorporating this simple, low-cost technique into its framework.[103,104]

The denoising of signals frequently involves the implementation of filters such as the Kalman and median filters, which are designed to target noise in either the time or frequency domain. A single-scale representation of noisy signals is often inadequate for extracting meaningful information. Wavelet threshold denoising (WTD)[27,105,106] is superior to aforementioned noise reduction algorithms since it combines both scales. Wavelets offer time-scale information about a signal, enabling the extraction of time-varying features. It not only effectively localizes features in LIBS data across multiple scales but also retains essential signal components while eliminating noise.[107]

Last but not least, another common issue encountered in almost all spectroscopic techniques, including LIBS, is signal saturation. This phenomenon occurs when detected signals exceed the detector's dynamic range, resulting in distorted data and compromised spectral analysis accuracy. It is important to

address this phenomenon because ignoring saturation can lead to a biased understanding of a sample's chemical composition. On the other hand, removing simply the saturated data points may result in significant loss of relevant information needed for the task. Treating saturated signals as missing values and using statistical imputation proves to be an effective method for reconstructing accurate spectral information. This enhances the reliability of chemical distribution mapping for various applications.[108]

While baseline correction and filtering are essential for a robust analytical pipeline, the predictive model can be severely compromised if normalization is not applied. Data points that are far from each other are brought closer by normalization operation, so that the effectiveness of the algorithm is increased and the computation process is sped up. Scaling the data allows the model to better understand and solve the problem.

## 2.3. Normalization

One effective method for mitigating the impact of laser energy fluctuations across measurements is the application of normalization techniques.[109] Normalization typically is about adjusting intensity values to a consistent, common scale and was introduced to ensure the stability and independence of the analysis results from the variations in the LIBS collection systems. However, there is no universally recognized best normalization method.[110] There are several widely used techniques that are the main normalization strategies.[111] For example, when employing max intensity normalization, each spectrum is normalized by dividing all data points, that is, the intensity value at each pixel, by the maximum peak intensity value.[112] Utilizing total intensity normalization,[110,113] the intensity values can be scaled by dividing each spectrum by the sum of all intensity values.[112] Internal standard or reference line normalization[113] is a method in which each spectrum is normalized using the intensity value of a peak from the matrix element, typically the sample's major element. The standard normal variate transformation[114] subtracts the intensity mean from every data point and divides the result by the standard deviation.[115]

Ultimately, the choice between employing a single preprocessing technique or designing a multistep approach for LIBS data enhancement depends entirely on the specific characteristics of the dataset and the precise scientific objectives of the research. Figure 4 illustrates the transformation of a LIBS spectrum through various preprocessing techniques. For demonstration purposes, the spectrum was randomly generated and does not represent real-world elemental data. Its only purpose is to provide a visual illustration. Figure 4a displays the raw, unnormalized spectrum with a simulated baseline (dashed red line) and noise. Figure 4b,c,d shows the results after applying baseline correction, filtering, and normalization, respectively. In a typical LIBS workflow, the preprocessing strategy, whether a single step or a multistep sequence, is chosen based on data quality and the analytical objective. A multistep approach allows for the targeted correction of specific artifacts within the spectral data.
<figure><img src="image_20.png" /></figure>

<figure><img src="image_21.png" /><figcaption>**Figure 4.** Illustration of a randomly generated LIBS spectrum after preprocessing. These figures are created using randomly generated data and do not represent real-world LIBS spectra or any elemental signatures.</figcaption></figure>

a) Random LIBS spectrum exhibiting baseline, noise, and no normalization.

b) The transformation after baseline correction. c) The effect of filtering on the noise removal or suppression. d) The normalized spectrum.

Data preprocessing lays the foundation for successful data analysis and modeling by ensuring data quality, enhancing feature representation, handling data complexity, and improving computational efficiency. Although investing in robust data preprocessing pipelines requires time and effort to begin with, it pays off in the form of more accurate predictions, deeper insights, and better decision-making. The decision-making process involves selecting proper ML algorithms or DL models to learn from preprocessed data and generalize well on unseen data. The next section will provide an overview of the most commonly used ML or DL methodologies for quantitative or qualitative analysis of LIBS.

## 3. Machine Learning: Overview

A machine learning algorithm is a computational framework that uses input data to perform a specific task, adapting and optimizing its performance without requiring explicit, predefined programming (i.e., “hard-coded” instructions) to generate a particular result.[116,117] These algorithms are, in essence, “soft-coded,” meaning they dynamically adjust or refine their structure through iterative processes, progressively enhancing their ability

to accomplish the intended task.[118] The process of adaptation, termed training, involves supplying input data samples alongside their corresponding outputs to refine and optimize the model’s performance. The algorithm then adjusts its configuration to effectively generate the desired output for the training inputs while also achieving generalization, enabling it to produce accurate outcomes for new, previously unseen data. This training is the “learning” phase of machine learning. Learning is not confined to an initial adaptation within a fixed time frame, but rather, it can extend beyond such limitations. As with humans, a good algorithm can practice “lifelong” learning as it encounters and processes new data and learns from its mistakes.[119]

The fundamental concept of ML is to mimic the way humans learn to interpret data. ML can be mainly classified into two distinct categories based on its learning approaches: supervised learning, and unsupervised learning. Supervised learning is an approach wherein each training example consists of input data paired with its corresponding known classification label, enabling the model to learn from these labeled instances to make accurate predictions, classifications, or generally any decisions.[120] This approach enables the learner to address similarities and differences among objects to be analyzed, particularly when these objects exhibit a wide range of variable properties within their respective classes while still retaining core characteristics that define their identity. Most importantly, an effective learner must hold the capability to accurately identify an unknown instance it has not previously encountered.[119]

Another type of ML is unsupervised learning, where the algorithm operates on its own, without being passed labeled data or clear instructions about what it’s supposed to achieve.[120] Rather than depending on preset instructions or direct links between inputs and expected outcomes, the learner or machine independently uncovers patterns, structures, or connections within the data it’s given. The algorithm refines its understanding by iteratively processing the data, adjusting internal parameters only based on the inherent characteristics of the input data. This independent approach lets the algorithm adjust to new or varying situations, which makes it especially useful for tasks where it needs to search for hidden patterns or make sense of new scenarios without labeled examples.

The following explores the widely adopted supervised and unsupervised ML techniques used to develop predictive models in LIBS analysis.

### 3.1. Supervised ML Methods

The often applied supervised ML methods in LIBS spectral analysis include Partial Least Squares (PLS),[121] Support Vector Machines (SVM),[122] Random Forest (RF),[123] K-nearest neighbors (K-NN),[124] and Linear Discriminant Analysis (LDA).[125]

#### 3.1.1. Partial Least Squares

PLS regression is a statistical-based ML method that has been widely used in many areas of analytical chemistry. PLS considers
<figure><img src="image_22.png" /></figure>

the information in matrix Y, a response variable, while describing
the information of matrix X, set of predictor variables. PLS finds
the key patterns in X that best predict Y, simplifying data while
keeping essential information. This process reduces complexity
while preserving the most relevant information. Essentially, it
connects sample data with their corresponding labels or catego-
ries, enabling regression modeling, simplification of data struc-
tures, and analysis of variable correlations. As a supervised
pattern recognition method, PLS can build models to automate
sample recognition and classification.[126] PLS is popular for quan-
titative LIBS investigations, especially for analyzing samples with
multiple elements and predicting the concentrations of chemical
components. While PLS has certain theoretical advantages for
addressing multivariate analysis,[127,128] it fundamentally relies
on statistical correlation and curve fitting. This can sometimes
lead to overlooking the physical principles underlying LIBS meas-
urements.[129] In ref. [130], the authors developed predictive mod-
els using PLS as the base regression method, incorporating a
range of PLS components to predict the concentrations of the
existing elements within the rock sample. The objective was to
evaluate the stability and reliability of PLS against variations in
the plasma temperature and electron number density. The results
demonstrated that PLS can yield accurate predictions; however,
there remains potential for improvement through the implemen-
tation of more advanced techniques. In a study by Blanchette
et al.,[131] the researchers investigated the integration of LIBS with
ML techniques to detect and diagnose bacterial pathogens in
urine samples. They developed and tested a rapid diagnostic
method using partial least squares discriminant analysis (PLS-
DA). The PLS-DA model demonstrated promising performance
with 98.3% sensitivity and 97.9% specificity for single-shot spec-
tra, showing the great potential of LIBS measurements for disease
detection tasks.

3.1.2. Support Vector Machines

SVM is a powerful supervised ML method effective for both clas-
sification and regression problems, with Support Vector
Regression (SVR) being a specific application of SVM for regres-
sion tasks. SVM demonstrates strong adaptability to high-dimen-
sional, complex, and nonlinear data.[129] SVM uses a separating
line or hyperplane to classify data points, namely features.
These closest points are referred to as support vectors.[14] In sim-
ple terms, SVM predicts by determining which side of the bound-
ary a new data point lies on. For regression tasks, it adapts this
concept by fitting a line that remains as close as possible to all
data points within a specified margin. Rehan et al.[132] demon-
strated the efficacy of combining LIBS spectroscopy with an
SVM-based classification approach for the noninvasive detection
of diabetes mellitus. Deploying an SVM algorithm, the disease
detection process successfully distinguished between diseased
and healthy samples, yielding an accuracy of 90.4%. This research
highlights the effectiveness of LIBS and SVM for clinical diagnos-
tics. Additionally, Wang et al.,[105] combined LIBS spectral data
with an SVM algorithm to develop predictive models for

distinguishing between normal and cancerous cells. The use of
SVM proved highly effective in extracting meaningful information
from the LIBS data, achieving an impressive accuracy of 97.7%. It
is critical to note that the discussion of LIBS within the medical
domain, particularly in cancer diagnosis, both here and through-
out this review, is intended exclusively to present the potential of
the technique. It is not indicative of methods that have been vali-
dated through controlled clinical testing.

3.1.3. Random Forest

RF belongs to the ensemble learning algorithms, which integrate
multiple predictors with low learning efficacy to improve the
learning procedure and deliver better predictions compared to
a single model, applicable to both classification and regression
tasks.[133] RF builds on the concept of decision trees by creating
an ensemble or “forest” of many trees, each trained on a random
subset of the data and features. In RF, each tree has nodes that
make simple decisions such as yes/no or high/low, based on the
value of a specific data feature, guiding the data to a final node
that assigns a class for classification or a value for regression. For
classification, RF uses majority voting across trees to determine
the final prediction. For regression, it averages the outputs of
all trees to produce the final result.[134] The RF algorithm offers
several advantages, including high accuracy, resistance to over-
fitting, and strong adaptability to high-dimensional data.
However, RF is primarily employed to address classification prob-
lems. Since decision trees produce discontinuous predicted val-
ues, they often exhibit significant prediction errors when applied
to regression tasks. Additionally, RF may struggle with the extrap-
olation, as it depends heavily on the distribution of the training
data rather than incorporating strong assumptions about under-
lying trends and correlations.[134] In this study,[74] Lin et al. dem-
onstrated the effectiveness of integrating RF with LIBS spectral
data to differentiate between lung tumors and boundary tissues.
By implementing RF in the analysis workflow, the authors
achieved an impressive classification performance, with an accu-
racy of 98.9%. The research conducted by Jin et al.[135] highlighted
the use of the RF method alongside LIBS data for geological anal-
ysis. Combining RF with LIBS spectral information, the authors
achieved a discrimination accuracy of 97.7% for rock samples
from the Dajianggang and Chaihe areas. This work further
emphasized the role of RF in improving LIBS classification effi-
ciency and accuracy for geological research.

3.1.4. K-Nearest Neighbors

The K-NN algorithm is a versatile, multivariate statistical method applicable to classification and regression tasks. As a nonparametric supervised learning classifier, the K-NN employs proximity to make decisions regarding the grouping of individual data points.[136] K-NN predicts a data point's value or class by looking at its closest neighbors in a feature space, assuming similar items are nearby. For classification, it assigns the most common label among the k nearest neighbors. For regression, it utilizes the
<figure><img src="image_23.png" /></figure>

average of their values. While K-NN algorithm can be applied to both regression and classification problems, it is mainly preferred for classification with discrete values. For regression, while K-NN averages neighbor values to predict continuous outcomes, this approach may oversimplify complex or noisy data, where overlooking subtle changes or outliers can hinder the accuracy of the method. The authors in ref. [137] investigated the significance of the K-NN technique in LIBS analysis for brain tumor identification. The findings demonstrated that K-NN improved diagnostic accuracy from 89% to 100% for distinguishing glioma and infiltrating boundary tissues, indicating its adaptability to subtle spectral differences. Zhang et al.[138] studied the critical role of the K-NN technique in LIBS for rapid indoor air quality analysis. They revealed that when LIBS spectral data are combined with the power of the K-NN algorithm, the classification of air compositions across scenarios like burning carbon, incense, and indoor air can be achieved with an outstanding accuracy of 99.2%. This high precision highlights K-NN's effectiveness in handling complex, multiscenario spectral data, enabling automated identification of aerosols and elemental differences.

### 3.1.5. Linear Discriminant Analysis

LDA is a widely used method to classify data into a finite number of distinct categories (classes) by analyzing their features. LDA operates by identifying a straight line, or a plane, that optimally separates two or more distinct groups of data. The core idea is to project high-dimensional data into a lower-dimensional space that maximizes class separation and minimizes within-class variation, ensuring optimal sample classification and reduced feature complexity. This simplifies analysis without sacrificing critical information and, equally important, lowers the computational cost for high-dimensional complex datasets. Yang et al. showcased LDA as the most efficient method, delivering high accuracy and rapid analytical speed for rice geographic origin classification.[139] Chu et al.[140] investigated the use of LDA as a ML classification tool for diagnosing blood cancer in conjunction with LIBS data. They demonstrated that LDA, when combined with the Random Subspace Method (RSM-LDA), offered significant potential for the recognition ability of blood cancer. The proposed approach delivered an accuracy of 98.3% in distinguishing the blood cancer types from healthy controls in disease detection tasks.

## 3.2. Unsupervised ML Methods

Despite what we have already covered about supervised ML methods, which depend on labeled or predefined observations, unsupervised ML methods take a different approach. These techniques function to reveal hidden patterns, structures, or relationships within the data, exploring and discovering insights without the guidance of predetermined outcomes or labels. The most common unsupervised ML methods employed in the field of LIBS analysis include principal component

analysis (PCA),[141] K-means clustering,[142] graph clustering,[143] and hierarchical cluster analysis (HCA).[144]

### 3.2.1. Principal Component Analysis

Having too many features in data can lead to issues such as overfitting, slower computation, and reduced accuracy. This phenomenon is known as the curse of dimensionality, where an increase in features significantly raises the amount of data required for the accurate results. The increase in the number of features in high-dimensional datasets complicates sampling and makes tasks like clustering and classification more challenging, slower, and less efficient. PCA simplifies complex datasets, such as those encountered in LIBS, where numerous variables, like measurements of different chemical elements, are often highly related and difficult to interpret. PCA addresses this by transforming high-dimensional data into a lower-dimensional space, creating a new set of variables called principal components (PCs). It achieves this by identifying the directions in which the data varies the most, reorienting the data along these components, and maximizing the variance or spread of the data in this new perspective, making patterns more straightforward to uncover and analyze. In the study by Fayyaz et al.,[145] the integration of PCA with LIBS proved to be instrumental in analyzing rare-earth elements (REEs) in phosphorite. PCA simplified the data by capturing 76.3% of the key spectral details in just the first three PCs, making rock samples classification easier and faster. This contribution highlighted PCA's capability to refine critical elemental patterns, enhancing both qualitative identification and quantitative accuracy. Duponchel et al.[6] emphasized the power of PCA and its ability to enhance LIBS imaging in their recent investigation. They showed that PCA allows identifying overlapping signals, or spectral interferences, in complex samples like rocks. This advantage supports the authors in correcting the data using other ML methods, leading to clearer and more accurate maps of element distribution. The study pronounced PCA as a simple yet powerful tool for improving LIBS imaging and subsequent analysis.

### 3.2.2. K-Means Clustering

K-means is a popular unsupervised ML technique widely utilized to organize data points based on their similarity without needing any prior knowledge of predefined labels. The algorithm randomly selects a set of central points, known as centroids, and then assigns each data point to the nearest centroid to form the initial clusters.[146] One fundamental requirement of K-means algorithm is specifying the number of clusters, K, in advance. Once all data points have been assigned to their respective clusters, the algorithm updates centroids by calculating the mean of each cluster's points and repeats until the centroids stop moving, creating well-defined clusters of similar data points. The aim of clustering is to divide the data points into groups where similar points are grouped together within the same cluster. Kiss et al.[147] studied how integration of LIBS in skin tumor imaging and using
<figure><img src="image_24.png" /></figure>

the K-means clustering for analysis can enhance the application of ML methodologies in interpreting LIBS data. Looking into common skin tumors with LIBS measurement, the authors employed the K-means algorithm to cluster tissue types in tumor samples. They tracked key elements in the tissue, correlating these maps to tumor progression, margins, and differences between healthy and cancerous areas. In this article,[148] Guo et al. utilized K-means clustering to classify industrial polymers based on LIBS spectral data. They proposed an approach that significantly improved classification accuracy, achieving an impressive 99.6% success rate in differentiating 20 types of industrial polymers under atmospheric conditions.

### 3.2.3. Graph Clustering

A graph is defined as a structure formed by a set of vertices, also known as nodes, and a set of edges that represent connections between pairs of nodes. Graph clustering is the process of organizing the nodes of a graph into clusters, with the objective of maximizing the within-cluster connectivity, while minimizing the between-cluster connectivity.[143] In other words, the goal of clustering with a given data set is to partition the data into clusters, ensuring that elements within a cluster are similar or connected based on predefined criteria. However, if the graph structure is uniform, with edges distributed evenly among the vertices, clustering results from any algorithm will be arbitrary and lack meaningful interpretation. Quality measures and visualizations, if feasible, will help determine whether significant clusters are present in the graph and if a given clustering reveals them.[143] In a related study, Ahmed et al.[149] employed LIBS spectral data to differentiate between various black toners of printers and photocopiers of different brands and models based on their elemental composition. Multivariate statistical analysis, employing PCA and graph clustering, was utilized to develop a discrimination model between the toners. The study demonstrated a high degree of discrimination between brand and model toners.

### 3.2.4. Hierarchical Cluster Analysis

HCA offers an alternative to k-means clustering for discovering group structures within a dataset. This method groups samples into clusters and shows their relationships in a tree-like dendrogram.[150] Hierarchical clustering can be classified into two primary approaches: agglomerative and divisive. In agglomerative clustering, initially each data point is treated as an individual cluster (a leaf). At each step, the two most similar clusters are merged to form a larger cluster (a node). This process continues until all data points are grouped into a single cluster (the root). Secondly, divisive hierarchical clustering algorithm builds clusters from the bottom up, starting with a single cluster containing all objects (the root). The algorithm identifies the most dissimilar cluster at each iteration and splits it into two subclusters. This process continues until each object forms its own individual cluster. Agglomerative clustering is good at identifying small clusters while divisive hierarchical clustering is good at identifying large

clusters.[151] The works of Costa et al.[152] and Shameem et al.[153] employed PCA as the primary method to assess the potential of the polymer classification using LIBS spectral measurement data. In addition to PCA, they considered a few other unsupervised chemometric methods, such as HCA and K-means clustering, to gain a deeper insight into the data and investigate the underlying relationships.

While conventional ML methods are common in LIBS analysis, DL potentially can offer a significant jump in accuracy. DL models use complex architectures to uncover subtle yet critical features in the data, thereby improving the performance of predictive models. The following section overviews the DL models most frequently applied to LIBS.

## 4. Deep Learning: Overview

DL represents a family of ML techniques that employs Artificial Neural Networks (ANNs) to extract and learn hierarchical feature representations from complex, high-dimensional data autonomously. Unlike traditional ML approaches that often depend on manually engineered features, DL employs multiple layers of interconnected nodes, mimicking the structure of the human brain, to efficiently capture intricate details directly from raw inputs. LIBS struggles with the nonlinear response of spectroscopic signal since its inception.[154] This nonlinearity can be effectively addressed by applying advanced DL methods. To enhance the efficacy of data analysis in LIBS spectral analysis, several DL techniques have been introduced, such as ANNs,[155] Convolutional Neural Networks (CNNs),[156] Recurrent Neural Networks (RNNs),[157] Generative Adversarial Networks (GANs),[158] self-organizing map (SOM),[159] and autoencoders (AEs). The following subsections will concisely review these methods, highlighting their key principles and features.

### 4.1. Artificial Neural Networks

ANNs are computer systems that mimic the human brain's ability to process information. Inspired by biological neurons, ANNs use artificial neurons to analyze data, detect patterns, and make predictions. In an ANN, a neuron processing unit can represent various entities, such as features, characters, concepts, or meaningful abstract patterns. These processing units are categorized into three types: input units, which receive data; output units, which produce results; and hidden units, which perform intermediate computations to map input into output.[160] The input unit receives and processes signals and data from external sources.[161] The output unit delivers the results of the system's processing. Hidden units, situated between the input and output units, perform internal computations and are not directly observable from outside the system.[162] During the learning and training process conducted within hidden layers, each neuron's output is calculated as the weighted sum of its inputs plus a bias term. Activation functions then determine which neurons are activated and pass their output to the next hidden layer.[163] Therefore, the
<figure><img src="image_25.png" /></figure>

strength of connections between neurons is determined by the weights assigned to these connections. The two main processes associated with ANNs are Feedforward and Backpropagation. Feedforward neural networks are defined by their unidirectional flow of information, where data moves sequentially from the input layer through one or more hidden layers to the output layer, without any cycles or feedback loops.[164] On the other hand, backpropagation works by calculating the difference, or error, between the predicted output of the network and the actual output. This error is then propagated backward through the network's layers, from the output layer to the input layer. As the error moves back, the algorithm adjusts the weights and biases of each connection to reduce the error in future predictions.[165] The iterative process of Feedforward and Backpropagation is how the network learns. ANNs are valuable computational tools with great strength in revealing hidden patterns applicable in various fields, including both quantitative and qualitative LIBS spectral analysis. Babos et al.[166] in their recent study, explored the use of LIBS for the rapid quantification of total carbon in Brazilian soil samples. Among the implemented methods, their developed ANN model demonstrated superior performance by achieving the lowest prediction error equals 0.5 wt%. Ni et al.[167] explored an industrial application of LIBS combined with a back-propagation ANN for the quantitative analysis of trace elements such as Ni, chromium (Cr), and Ti in stainless steel. Their methodology incorporated data preprocessing strategies to enhance spectral quality before feeding the data into the ANN model. This integrated approach led to a significant improvement in the accuracy and reliability of elemental quantification.

## 4.2. Convolutional Neural Networks

CNN is a type of ANN composed of multiple hidden layers designed to automatically extract and recognize characteristic features at various scales. In the context of LIBS, where input data can consist of thousands of spectral points, CNNs effectively reduce this high-dimensional input into a compact set of meaningful features. These extracted features can then be used to predict elemental concentrations through a training process similar to that of conventional ANNs. CNNs rank among the most dominant DL models, integrating components such as convolutional blocks, pooling layers, and fully connected layers. The convolution block in CNN handles feature extraction and data compression by implementing convolution layers and pooling layers to create a compact yet deep feature vector that efficiently captures the essence of the raw input data. Adjusting the convolutional kernel size enables CNN models to process diverse data forms, including 1D spectra, 2D grayscale images, and 3D data points.[168] Finally, the fully connected network component maps the extracted features to the desired output. Generally, as the data passes through successive convolutional and pooling layers, the network progressively learns more abstract and complex features. Ultimately, these learned features are used by the network to make predictions, such as classification labels or probability scores, depending on the specific task.[169] Building upon the

basic CNN framework, well-known models like, GoogLeNet,[170] VGG,[171] and ResNet,[172] along with their variants, have emerged as robust tools for LIBS analysis, each contributing to its advancement with distinctive strengths.[173] Dehbozorgi et al.[130] explored the application of DL through the implementation of CNNs to enhance the predictive accuracy and stability of LIBS analysis acquired from a rock sample. The study aimed to address plasma temperature and electron number density variations, which significantly impact LIBS spectra. The findings highlighted CNNs as a powerful tool for LIBS-based elemental analysis, offering significant improvements over traditional PLS regression technique. In the study conducted by Xing et al.,[174] a methodology integrating LIBS with CNN was introduced for the quantitative analysis of lithium (Li) in brine samples. The authors proposed two CNN-based strategies to address challenges posed by non-linear spectral interferences. The results underlined the potential of advanced DL techniques in LIBS analysis by providing superior predictive accuracy and robustness against matrix interferences.

## 4.3. Recurrent Neural Networks

RNNs are a class of ANNs particularly well-suited for processing sequential data, making them highly applicable in the context of LIBS, where spectral data can be treated as sequences. RNNs have an internal memory that captures information about previous inputs in the sequence, enabling them to model temporal or sequential dependencies effectively.[175] In simpler terms, RNNs process sequences of data one element at a time, maintaining a memory of what they've seen so far. In conventional feedforward neural networks, inputs and outputs are considered independent entities. However, in RNNs, the output from the previous step is incorporated into the network as an input for the subsequent step. This process is repeated for each element in the sequence, thereby enabling the network to accumulate information over time.[176] However, standard RNNs can struggle with long-term dependencies due to issues like vanishing or exploding gradients during training. To address these limitations, more advanced variants such as Long Short-Term Memory (LSTM) networks[177] have been developed.[178] This network tackles the issue by selectively capturing and retaining relevant information through multiple gating mechanisms.[173] The authors in ref. [179] studied the effectiveness of combining RNNs with LIBS spectral information for the quantitative analysis of aluminum alloys. The primary challenge in LIBS elemental analysis is the accurate prediction of elemental concentrations despite spectral variations due to plasma fluctuations and matrix effects. To handle these issues, the study utilized various RNN architectures, including simple RNN, LSTM, Gated Recurrent Units (GRU), and Convolutional Recurrent Networks (CRNs). The observations demonstrated that among all the RNN-based approaches, SimpleRNN and ConvSimpleRNN yielded the highest prediction accuracy for aluminum alloy concentrations, outperforming classical ML models. In the study performed by Zeng et al.,[180] a hybrid DL model was introduced for accurate quantitative analysis in a portable LIBS system. The approach utilized CNN for spectral feature extraction while
<figure><img src="image_26.png" /></figure>

integrating a convolutional block attention module to refine rel-
evant spectral features. In the proposed model, employing the
LSTM component to manage sequential dependencies in spectral
data further enhanced quantitative analysis. The study under-
scored the potential of LSTM when combined with other power-
ful techniques in optimizing quantitative predictions in LIBS
applications.

4.4. Generative Adversarial Networks

GANs are a class of neural networks designed to automatically
learn patterns from input data, enabling them to generate
new examples that closely resemble the original dataset. The
architecture of a GAN consists of two main distinct neural net-
works and operates based on differentiable generator networks:
1) Generator: creates synthetic data from random noise to pro-
duce data so realistic that the discriminator cannot distinguish
it from real data. 2) Discriminator: It evaluates whether the data
it receives is genuine or fake.

The generator and discriminator are trained at the same time. The generator learns to create realistic data, while the discriminator is tasked with distinguishing between real data and the data produced by the generator. As the generator and discriminator are trained, they improve at their respective tasks. Eventually, the generator becomes so proficient at creating realistic data that the discriminator can no longer distinguish between real data and the data generated by the generator.[173,181] Yan et al.[182] demonstrated that the GAN-Transformer model for detecting heavy metal anomalies in LIBS spectral data is a straightforward and reliable method for rapid on-site water quality assessment. Their proposed model employed GANs to learn the underlying spectral distribution of normal water samples, allowing for the detection of anomalous heavy metal concentrations through reconstruction errors. The authors of this study[183] proposed a semi-supervised learning model based on GAN for LIBS spectral classification, addressing the challenge of limited labeled data in industrial applications. The developed model outperformed conventional CNN and also RF classifiers, achieving a classification accuracy of 98.5% when sufficient unlabeled data were incorporated.

4.5. Self-Organizing Map

SOM is a type of unsupervised ANN that is trained to produce
low-dimensional, discretized representations of the input data.
A SOM consists of a grid of nodes, or neurons, where each neuron
represents a cluster in the input data space. These nodes are usu-
ally arranged in a 2D grid, though they can also be organized in
higher dimensions. Each node is associated with a weight vector
of the same dimensionality as the input data.[184] SOM training is
an iterative process in which the SOM adapts to the input data. At
each iteration, one object, such as a single spectrum, is selected
from the input data, and the distance of that object to each neu-
ron is calculated. The neuron that is closest to the input object is
considered the winning neuron, or the best matching unit (BMU),

and its internal weights are adjusted accordingly. Additionally,
the neighborhood of the winning neuron is adjusted with lower
weights. The rate of adjustments decreases as the iteration num-
ber increases. The training procedure is sometimes called com-
petitive-cooperative training. The competitive part involves
determining the winning node, and the cooperative part involves
adjusting neighboring neurons.[184] SOM as an AI-based tool
reduces data dimensionality while preserving the topological
structure for clustering and data exploration.[185] The study by
Holub et al.[186] involved studying of the LIBS data transition
between two well-described matrices. The authors' objective
was to cluster the obtained characteristic spectra and to provide
Supplementary Information regarding the composition and dis-
tribution of individual matrices on the sample surface. Employing
a carefully designed experiment, several Fe:Al ratios were ablated
and analyzed by PCA, SOM, and standard data metrics. In a recent
study, Yang et al.[187] employed SOM as a key part of their model
development process. The goal was to identify the presence of
heavy metals in mulberry leaves using data from LIBS measure-
ments. Their proposed methodology effectively reduced the
number of variables involved while also improving the model's
accuracy and robustness.

4.6. Autoencoders

AEs are commonly employed in unsupervised learning tasks. They are designed to learn efficient data representations by compressing and reconstructing input data. This makes them an ideal technique for simplifying the process of feature learning in ML-based studies.[188] An AE consists of two key components: an encoder, which transforms the input into a compact, deep feature representation (often in a lower-dimensional space), and a decoder, which reconstructs the original input from this representation. By training the network to minimize reconstruction error, AEs capture the underlying structure of the data without requiring labeled examples.[173,189] Lv et al. in their recent work[190] suggested a robust approach for quantitative elemental analysis of ceramic raw materials (silicon (Si), aluminum (Al), magnesium (Mg), Fe, and Ti) using LIBS combined with advanced ML and DL techniques. Their approach involved a hybrid method combining linear regression (LR), sparse and undercomplete autoencoder (SUAC), and a Back Propagation Neural Network (BPNN). LR served as a linear dimension reduction step. SUAC further transformed the data into compact, high-level feature representations. The abstract features were then input into the BPNN for regression modeling. The results demonstrated that the model significantly outperformed PLS and LR + PLS, achieving R² values above 0.93 for all key elements. Zhou et al.[191] investigated the potential of extreme learning machines (ELM) and deep ELM (DELM, an ELM-auto-encoder) for calibrating the transfer of LIBS spectra. They demonstrated that both methods provided a certain level of effectiveness in transferring calibration models for two challenging scenarios: (i) LIBS spectra of samples acquired under varying conditions using the same instrument and (ii) LIBS spectra of the same sample measured by different instruments.
<figure><img src="image_27.png" /></figure>

Following the introduction of the primary ML and DL models applied to LIBS analysis, the subsequent sections present a systematic review of the literature published between 2015 and 2025. This review explores the application of LIBS measurements for tackling problems in various scientific fields, encompassing both classification and regression tasks.

## 5. Recent Advancements in LIBS Analysis through Machine Learning and Deep Learning Techniques

There are several critical steps in any analytical process, including LIBS spectral investigation, needed to follow for having a robust and reliable analysis pipeline (Figure 5). The first step is selecting the sample of interest for the experiment. Next, acquire data, specifically LIBS spectra measurement information, which is the focus of this review. The subsequent step involves applying preprocessing techniques to improve the quality of raw data, such as normalizing to a specific range, removing baselines, or suppressing noise. Once the data is cleaned, the next step is to select an ML algorithm or a DL model to develop using training data. Finally, the developed model will be deployed to make predictions for either a regression task or a classification problem.

With a solid understanding of LIBS data acquisition processes and the main preprocessing methods, as well as the predictive ML and DL models often used, we can now discuss how to effectively apply these techniques to LIBS spectral data across various

scientific fields to solve specific problems, whether they are classification tasks or regression challenges.

Regression analysis is the first approach, designed to predict continuous variables, such as the elemental concentrations present in samples at hand. Since the intensity of elemental peaks correlates closely with their concentration in a sample, regression can effectively quantify these concentrations, typically expressed as percentages. As the second strategy, classification aims to predict discrete values by sorting available samples into the corresponding categories based on the provided annotations or labels. In the sections below, we will review the recent developments and studies in the world of LIBS analysis. This exploration concerns how the powerful capabilities of ML and DL methods are implemented to enhance analysis for more accurate and reliable outcomes across various fields of investigation.

### 5.1. Regression

Regression analysis explains the relationships between variables within a dataset, quantitatively assessing the strength of these correlations and evaluating their statistical significance. A regression model helps determine if changes in the dependent variable are related to changes in one or more independent variables. It accomplishes this by identifying a best-fit line and examining how the data points are distributed around that line.

In 2015, Boucher et al.[192] conducted a comprehensive evaluation of ML regression techniques for the elemental analysis of geological samples using LIBS. Their research focused on comparing linear regression methods, such as PLS-1 and PLS-2, PCR, and linear SVR, against nonlinear approaches, including kernel principal component regression, polynomial support vector regression, and K-NN regression. Model performance was then evaluated using the Predicted Residual Sum of Squares (PRESS) on independent test sets. The results of this study demonstrated that linear models generally outperformed their nonlinear counterparts. Nonlinear methods tended to overfit, leading to reduced generalization performance. Additionally, in the same year, a study conducted by Singh et al.[193] investigated the application of LIBS for the multielemental analysis of thorium-based nuclear waste glass. The research focused on quantifying elements such as thorium (Th), Al, Fe, Cr, Ni, fluorine (F), and strontium (Sr) in simulated vitrified waste glass from a power reactor thorium reprocessing facility. To handle the challenge of overlapping emission lines in the complex spectra, the authors employed PLSR while improving its effectiveness by applying spectral truncation supported by PLSR coefficient thresholds. The enhanced accuracy and precision of the modified PLSR underscored the significant potential of LIBS as an efficient technique for the routine characterization of vitrified glass, particularly in the context of long-term storage of radioactive waste. Devangad et al.[194] in 2016 studied the quantitative analysis of manganese (Mn) in complex matrices like glass using LIBS measurement data. The authors compared univariate calibration with multivariate regression techniques, including PCR and PLSR. The univariate approach achieved an $R^2$ value of 98%. In contrast, the multivariate methods performed

<figure><img src="image_28.png" /><figcaption>**Figure 5.** General overview of the essential steps in the spectral analysis workflow. This figure illustrates the sequence of steps involved in any spectral analysis task, with an emphasis on LIBS spectral data. The initial two steps consist of selecting the sample of interest and acquiring spectral data, such as LIBS data. Data acquisition is then followed by enhancing raw spectral data through the application of preprocessing techniques. Next, an appropriate ML algorithm or DL model needs to be selected to perform the intended task, whether it concerns quantitative or qualitative analysis. Using training data, the chosen ML or DL model learns to address the proposed question within the analysis. Finally, the model makes predictions on unseen data, whether within a classification or regression scheme.</figcaption></figure>
<figure><img src="image_29.png" /></figure>

better with slightly higher R² values of 99%. In the same year, Castro et al.[111] employed LIBS for direct analysis of 80 metallic alloy and steel samples, targeting the determination of 10 key analytes: Al, Cr, copper (Cu), Fe, Mn, molybdenum (Mo), Ni, Ti, vanadium (V), and zinc (Zn). This research deployed univariate and multivariate regression techniques, with particular emphasis on PLSR. Their strategy aimed to enhance analytical precision by incorporating twelve normalization modes, seeking to reduce the interference matrix and improve the robustness of calibration models. The results revealed that both utilized approaches performed closely. It is important to note that models without normalization showed two to five times higher errors. The study showed PLS efficacy in handling complex LIBS spectra, once more proving the value of multivariate regression for alloy analysis. Moving forward to 2017, Anderson et al.[195] introduced a novel "submodel" approach to enhance the accuracy of quantitative LIBS analysis, focusing on PLSR implementation for geological samples. Unlike standard PLS, which applies a single model across the full compositional range, their method employs multiple PLS submodels, each trained on distinct, overlapping concentration ranges of major elements. Applied to ChemCam[196] data from the Mars Science Laboratory, the technique significantly reduced root mean square errors of prediction (RMSEP) for most elements compared to a full-range PLS model. Therefore, the submodel method proposed within this study can be a valuable addition to the toolbox of techniques used to derive quantitative results from LIBS data, especially in geology. In the same year, Knadel et al.[197] explored the predictive capabilities of LIBS for determining soil properties, including soil organic carbon (SOC) and particle size fractions (clay, silt, sand), in Danish agricultural soils. The study employed PLSR as the core regression technique to correlate spectral data with reference soil properties. Their work highlighted LIBS as a viable and rapid alternative to traditional methods, demonstrating that it can be as effective, or even more accurate, than the established visible near-infrared reflectance spectroscopy for determining soil properties. In 2018, Luna et al.[198] looked into the application of LIBS coupled with multivariate regression techniques for directly determining Mn, Cr, and Ni in steel samples. The research focused on comparing different PLSR strategies to optimize the analysis using a low-cost, homemade LIBS system. Three PLS-based approaches were evaluated: standard PLS, PLS with variable importance in projection, and interval PLS. The study found no significant differences among the developed models. However, PLS when using the full spectrum, yielded the lowest relative standard error of prediction. These findings emphasized PLSR as a practical chemometric approach for simplifying LIBS instrumentation. In this study,[199] Zhu et al. examined the applicability of LIBS for boron content determination, attempting to address the self-absorption limitations by building calibration with molecular emission. Following the goal of study, the authors implemented a combined genetic algorithm and PLSR (GA-PLSR) model, optimizing spectral line selection and improving calibration robustness. The results showed that the self-absorption effect was reduced and R² values were improved by employing molecular spectra. Furthermore, the developed GA-PLSR model outperformed the standalone

PLSR, confirming its efficacy in refining molecular emission studies for LIBS applications. In their 2019 study, Guo et al.[200] studied LIBS for multielement quantitative analysis of soils, focusing on 13 elements across standard soil samples with complex matrices. The study compared three regression techniques: the conventional univariate calibration curve method and two multivariate approaches, PLSR and support vector regression (SVR). The results demonstrated that the univariate method exhibited varying quantitative performance for different elements due to matrix effects. Overall, it provided inconsistent results and lacked effective quantitative capability. In contrast, multivariate methods, utilizing PCA for dimensionality reduction, demonstrated enhanced capability in managing matrix variability. PLSR excelled in predicting unknown samples, while SVR demonstrated superior robustness and predictive performance in the model development. He et al.[201] sought to address the challenge of carbon content detection in steel utilizing LIBS, focusing on the interference of the carbon lines by the adjacent Fe lines. The study proposed a hybrid regression technique combining a genetic algorithm (GA) with a back propagation (BP) neural network (GA-BP) to enhance quantitative analysis precision. Applied to carbon steel samples, the GA-BP model outperformed the standalone BP model, achieving a higher R² and a lower RMSE values. This implemented nonlinear methodology demonstrated a robust solution for handling spectral overlaps in LIBS, offering a practical advancement for carbon quantification in steel and iron-based alloys. Erler et al.[202] in their 2020 study explored the use of a handheld LIBS instrument for soil nutrient detection. To perform the analysis, three different multivariate regression methods involving PLSR, least absolute shrinkage and selection operator (Lasso), and Gaussian process regression were designed and compared for measuring soil parameters. As part of the analysis workflow, several data pretreatment methods were tested, namely variance reduction, background correction, and normalization. Results of this study showed GPR and Lasso slightly outperformed PLSR, introducing their strengths in handling complex, nonlinear relationships and sparse data. In their investigation, Ewusi-Annan et al.[203] discussed the importance of PLSR and a feed-forward ANN for the automatic preprocessing of LIBS spectra, focusing on Earth and Mars datasets from the ChemCam instrument. The authors used PLSR and ANN to transform raw LIBS spectra into preprocessed versions, handling challenges like denoising and background correction. The study indicated high correlation coefficients for both methods, though ANN showed greater consistency and fewer outliers, suggesting its superiority for handling nonlinearities in LIBS data preprocessing. In 2021, Che et al.[204] explore different regression techniques to enhance the quantitative analysis of multimetal species using LIBS, focusing on alloy steel, ferrochromium, and ferromanganese samples. The study compared three calibration methods: the basic calibration method (BCM), PLS, and least squares support vector machines (LSSVM). BCM produced poor results, indicating instability. PLS showed improvements, while LSSVM, a nonlinear regression method, outperformed both, achieving the highest performance metrics. A 2021 study[205] examined regression-based methods for quantitative LIBS analysis of plant and soil CRMs, comparing
<figure><img src="image_30.png" /></figure>

calibration-free LIBS (CF-LIBS) with PLSR. PLSR demonstrated out-
standing performance, achieving an R² close to 100%, accurately
predicting concentrations and closely aligning with CF-LIBS-
derived ratios. The authors of this study[206] proposed a small
sample ML (SSML) approach utilizing PCA-PLS regression for
quantitative LIBS analysis of coal. Concerning the challenge of
limited training data and mitigating its corresponding effect, they
successfully improved regression performance by extracting and
combining spectral subsets from the samples at hand. The pre-
sented approach reduced Absolute Relative Error (ARE) by ≈50%,
demonstrating robust regression for small datasets. Chen
et al.[207] developed a CNN coupled with LIBS for simultaneous
lithology classification and regression analysis of seven major ele-
ments in rock samples. The regression performance, when using
the predictive CNN model, demonstrated high accuracy.
Validating superiority of the proposed CNN, it was further com-
pared with the performance of other algorithms, including K-NN,
SVM, BPNN, and PLSR. The results of this research suggested that
CNNs hold significant potential for both quantitative and quali-
tative analysis of rocks. In 2023, Van den Eynde et al.[208] designed
a DL regression approach for quantitative LIBS analysis, targeting
alloying element concentrations in aluminum scrap for recycling.
They compared traditional methods, including univariate regres-
sion, RF, and logistic regression, against the performance of the
DL methodology. The CNN-based method outperformed others
by employing a multiloss function, resulting in lower prediction
errors and higher R² values. Tested on certified reference and
postconsumer scrap samples, DL demonstrated superior accuracy
and adaptability compared to traditional regression techniques.
In the study published in 2023,[209] the authors introduced an
end-to-end ensemble CNN (ECNN) framework for quantitative
regression analysis of ChemCam LIBS spectral data, focusing
on the determination of major elements in Mars exploration.
Unlike traditional methods such as PLS and extreme learning
machine (ELM), this approach achieved significant reductions
in RMSEP compared to both PLS and ELM. The results from both
the original and expanded ChemCam datasets demonstrated
superior R² values and enhanced robustness, providing a light-
weight and interpretable solution for LIBS regression tasks.
Moving to 2024, Lyu et al.[210] introduced a hybrid variable selec-
tion strategy for quantitative regression of coal ash content using
LIBS, integrating empirical knowledge with data-driven methods
and PLSR. The LASSO-PLSR model with empirical support showed
significantly improved performance after variable deselection,
leading to notable reductions in RMSEP values. Such results
revealed that using empirical knowledge as a support for data
driven variable selection can potentially be a viable approach
to improving the accuracy and reliability of LIBS quantification.
In a research conducted by Ma et al.,[211] a multielement quanti-
tative model using full-spectrum LIBS for trace element analysis in
stainless steel was developed. By utilizing multitask Lasso regres-
sion combined with a logarithmic transformation of the spectral
data, the approach achieved remarkable predictive accuracy.
Compared to PLSR and SVR, the method enhanced regression
coefficients while minimizing RMSEP, presenting robustness
and better noise handling than classic single-task models. In

2025, Fang et al.[212] presented a heterogeneous ensemble learn-
ing (HEL) model for full-spectrum LIBS quantitative regression,
combining CNN, Lasso, Boosting, and feedforward neural net-
work (FNN) submodels, enhanced by a Bayesian weighting strat-
egy. When applied to the Steel and ChemCam datasets, HEL
outperformed individual models such as CNN, Lasso, and homo-
geneous ensembles, resulting in notable RMSE reductions. In
their research work, He et al.[213] devised an Automatic Remote
LIBS (AR-LIBS) system integrated with an SVR algorithm to
improve the quantitative analysis of trace elements in alloy steel.
In comparison to univariate regression, SVR effectively mitigated
matrix effects, showcasing enhanced accuracy and precision for
remote multi-element detection.

The studies conducted from 2015 to 2025 indicate a shift
toward advanced techniques, particularly CNNs, while conven-
tional methods like PLSR and SVR remain effective for LIBS analy-
sis. CNNs show great promise in overcoming challenges related
to the variations associated with LIBS data by effectively
highlighting and extracting essential features for better analysis
and decision making.

5.2. Classification

Classification is a key area of supervised learning. A computer can
extract features from the given data and corresponding labels in
the training set by implementing ML and DL methods. It then
predicts a discrete label for each data point in the independent
test set. In LIBS, classification algorithms use the characteristics of
different sample spectra as input data and labels for learning.
Then, they use the characteristics of test sample spectra as input
data to predict the class to which the sample belongs.[134]

In 2015, Moncayo et al.[214] evaluated seven supervised chemometric methods for classifying human bone remains using LIBS data measurements. The research analyzed bone samples using techniques like PLS-DA, LDA, SVM, and ANN. Among these developed methods, SVM and ANN proved the most effective in handling complex LIBS data. This research showed the superior potential of DL in enhancing the sensitivity, generalization ability, and robustness of LIBS-based classification tasks. In this study,[215] Sheng et al. investigated the integration of LIBS with ML techniques, specifically RF and SVM, to classify 10 distinct iron ore grades based on their chemical compositions. Compared with SVM, with 96% accuracy, RF was a better approach, achieving almost perfect results with 100% prediction accuracy on the test set. As detailed in their 2016 study,[216] Yu et al. thoroughly investigated the utilization of LIBS and ML approaches for soil variety discrimination. The essence of their work lies in utilizing LIBS to capture fine spectral data from soil samples. The LIBS data measurement was then followed by implementing ML methods, namely PCA, Soft Independent Modeling of Class Analogy (SIMCA), and Least-Squares Support Vector Machine (LS-SVM), to classify soil types based on their elemental compositions. SIMCA and LS-SVM were used to build discriminant models, achieving correct 90% and 100% classification rates, respectively. Their findings revealed that LIBS technology, when coupled with
<figure><img src="image_31.png" /></figure>

chemometrics, could conduct the discrimination of soil samples. In a study published in 2016,[217] Zhang et al. explored the effectiveness of RF in classifying nine distinct steel grades based on their chemical compositions. Their study utilized LIBS to generate spectra from steel samples, which were then used for model development and validation. The RF model was also compared to PLS-DA and SVM, achieving higher classification accuracy. Throughout their work, it has been confirmed that RF was promising for automatic, reliable, and robust measurements. Moreover, the authors claimed that the developed system can be integrated into a portable form for nonspecialist users. Moving forward to 2017, Campanella et al.[218] analyzed the application of ANNs for classifying aluminum alloys using LIBS spectra, aiming to improve automotive recycling. Using a novel ANN approach, they explored real aluminum scrap samples and achieved a 74% classification accuracy with LIBS. The proposed DL-driven method outperformed traditional quantitative analysis by directly classifying alloys without the need for precise elemental concentrations. The authors of this study[219] examined the use of LIBS for differentiating oral soft and hard tissues, laying a foundation for tissue-specific laser surgery. They analyzed seven porcine tissue types using a robust LIBS setup, further supported by ML methods such as PCA and LDA. This method based on ML yielded differentiation accuracies ranging from 65 to 100%, showcasing its effectiveness despite tissue similarities. Qi et al.[220] in their study published in 2018 looked into the classifying archaeological ceramics from various Chinese dynasties integrating LIBS with RF algorithms. Their adopted workflow involved collecting LIBS spectra from ceramic samples, identifying major elements, and applying RF to classify ceramics based on spectral data preprocessed with methods like mean centering. The RF model achieved an accuracy of 94%, demonstrating robust performance despite challenges like matrix effects and spectral variability. Prochazka et al.,[221] in their research, tested the utilization of LIBS and Raman spectroscopy for the multivariate classification of bacterial strains. Their approach consisted of using PCA and SOM to enhance classification accuracy by combining elemental data from LIBS with molecular understandings from Raman spectroscopy. PCA was applied to the preprocessed LIBS and Raman data, revealing distinct clustering. The supervised SOM model achieved higher classification accuracy with merged LIBS and Raman data compared to the individual models, highlighting the efficacy of complementary spectroscopic methods. In 2019, the LIBS methodology, when combined with ANN, was examined by Cui et al.,[222] to classify four wood species. Their analysis framework involved collecting plasma emission spectra and employing PCA to select feature spectral data, which were then normalized and fed into an ANN model. ANN architecture delivered a perfect 100% accuracy, outperforming other ML methods like PLS-DA (82.5%), K-NN (95.8%), and SIMCA (51.6%). The authors in this study[223] employed ML techniques to enhance the identification of acrylonitrile butadiene styrene (ABS) plastics with different additives, leveraging LIBS spectral capabilities. They utilized PCA and LDA to process LIBS data, achieving a remarkable 100% classification accuracy. In a study performed in 2020,[224] the authors focused on the development of a 2D

CNN for lithological recognition of five rock types using LIBS. The implemented strategy involved preprocessing of LIBS spectra with Min-Max normalization and reshaping them into spectral matrices, which were then fed into the 2D CNN. This designed DL model outperformed conventional ML methods like K-NN, SVM, PLS-DA, and human-assisted ANN, with a test accuracy of 100%. Wang et al.[225] aimed to classify plastics using LIBS spectral data across various experimental conditions, including different excitation sources and time periods from 2015 to 2018. Their work emphasized the implementation of ML and DL methods, evaluating seven chemometric models, ANN, Classification and Regression Trees (CART), K-NN, LDA, PLS-DA, SVM, and SIMCA. Among the methodologies employed, the ANN model outperformed the others, with the LDA and PLS-DA models also showing strong performance. When combined with preprocessing techniques like Standard Normal Variate (SNV), ANN proved exceptional robustness and accuracy. It achieved classification rates of up to 100% for different excitation sources and an overall accuracy of 98.5%. Through the application of a residual network, the authors of this study[226] in 2021 aimed to enhance plastics classification accuracy using LIBS. They utilized LIBS data from plastic types and compressed it with a continuous wavelet-based peak searching algorithm before transforming it into characteristic images for residual network training. The suggested model achieved an impressive 100% accuracy in few-shot learning scenarios, utilizing as few as one training image. DL significantly outperformed conventional ML algorithms like K-NN (30.7%), SVM (64.1%), and BP (81.7%) under similar conditions. Dai et al.[227] performed an investigation to classify aluminum alloys using LIBS data and integration of ML tools such as PCA and LSSVM. To this end, they employed LIBS to analyze aluminum alloy types, applying PCA for data separation and reduction of dimensionality. Subsequently, they implemented SVM and LSSVM for the purpose of classification. The LSSVM model achieved a 100% identification accuracy, surpassing the standard SVM's 98.3%. In a study conducted in 2022, Chen et al.[228] explored rock lithology classification by integrating LIBS elemental imaging with DL techniques through the application of InceptionV3[229] for feature extraction. Their suggested strategy boosted the classification accuracy from 64% (using average spectrum with SVM) to 85%. Approaching 2023, Choi et al.[230] combined LIBS data with CNN to monitor the laser cleaning process of painted stainless steel specimens, with an emphasis on classifying paint removal levels under varying laser parameters. The CNN achieved a notable 94.5% accuracy, significantly enhancing the speed and precision of identifying cleaning states. In their study,[231] Chu et al. aimed to enhance the accuracy of soil classification by using LIBS spectra in conjunction with a DL method, while also comparing its performance to classical ML techniques in spectral analysis. The proposed DL methodology for establishing the classification task proved to be efficient with an initial accuracy of 75.9%, outperforming ML models like SVM, and K-NN. Further refinement of the model resulted in an increase in the model performance up to 85.5%. Mi et al.[232] studied the direct identification of bacteria using LIBS, backed by ML methods, in order to enhance classification performance while minimizing sample preparation steps.
<figure><img src="image_32.png" /></figure>

For the preprocessing step, the authors considered filtering, normalization, and PCA for dimensionality reduction. Deploying SVM with a linear kernel as the classifier resulted in an identification performance of 84.2%. The study demonstrated that bacteria can be identified directly by analyzing their LIBS spectra, providing a practical method for simple and rapid on-site bacterial identification. In 2024, Zhou et al.[233] performed a study in order to explore the effectiveness of ML methods when fed with LIBS spectral data as the input to improve the efficacy of rapid identification and classification of metal waste. Their approach utilized a self-developed LIBS system to analyze common metal waste types. PCA was applied to reduce the high-dimensional spectral data, which were subsequently classified using an optimized K-NN algorithm, achieving an impressive accuracy of 97.2%. Their work offered insights into metal waste classification. Further in 2024, Dai et al.[234] explored the potential room for enhanced analysis through the fusion of LIBS and Raman spectroscopy, supported by ML algorithms for model development. Spectral data were then preprocessed with PCA and t-SNE for dimensionality reduction and visualization. Thereafter, the authors designed the predictive models using PLS-DA and kernel extreme learning machine (K-ELM), indicating superior test accuracy of 98.4% on fused LIBS-Raman data, outperforming standalone LIBS and Raman results. Recently in 2025, Kantemiris et al.[235] analyzed the classification of soil contamination by heavy metals using LIBS when paired with ML. They analyzed soil samples from different matrices using LIBS to obtain spectral data, which was subsequently preprocessed with normalization, scaling, and PCA. For the development of predictive models, ML algorithms, including LDA, SVM, and RF, were selected for the classification of samples. Notably, the SVM with an RBF kernel presented promising performance, providing a cost-effective and efficient tool for the preliminary assessment of soil contamination. In the same year, Chen et al.[236] investigated the integration of Raman and LIBS spectroscopy for advancing the detection and classification of atmospheric microplastics. The LIBS spectra collected from microplastic samples were processed using PCA for dimensionality reduction and classified with a BPANN, resulting in a recognition accuracy of 89.3%. This study demonstrated the effectiveness of LIBS technology for the automated classification of atmospheric microplastics by employing an efficient ML strategy to extract meaningful insights from the data.

A systematic literature review from 2015 to 2025 revealed a consistent trend: scientists and researchers mostly rely on DL methods for predictive model design, while still utilizing conventional ML techniques (Table 1). Although ML and DL are complementary methods with strengths and limitations, the tendency toward the use of DL approaches is increasing. This preference arises from the ability of CNNs to more effectively capture variations within LIBS spectra, particularly in accounting for fluctuations in plasma temperature and electron number density.[130]

Nevertheless, it is crucial to reemphasize that while DL exhibits superior capacity for handling tasks with higher precision, it is not a universal solution for addressing the inherent complexity in LIBS measurement data. ML and DL are two complementary

<table><caption>**Table 1.** Examples of the established studies from 2015 to 2025 that integrate LIBS measurement data with ML and/or DL algorithms and models.</caption><thead><tr><th>Application</th><th>Example study</th></tr></thead><tbody><tr><td>Classification/ identification</td><td>Song et al.[10] Cao et al.[11] Zhao et al.[13] Ali et al.[17] Nisar et al.[69] Costa et al.[70] Ren et al.[72] Liu et al.[73] Lin et al.[74] Lin et al.[75] Guo et al.[76] Wang et al.[78] Wang et al.[105] Blanchette et al.[131] Rehan et al.[132] Jin et al.[135] Teng et al.[137] Zhang et al.[138] Yang et al.[139] Chu et al.[140] Fayyaz et al.[145] Kiss et al.[147] Yangmin et al.[148] Yan et al.[182] Wang et al.[183] Yang et al.[187] Moncayo et al.[214] Yu et al.[216] Campanella et al.[218] Qi et al.[220] Cui et al.[222] Chen et al.[224] Peng et al.[226] Chen et al.[228] Chu et al.[173] Zhou et al.[233] Kantemiris et al.[235] Sheng et al.[215] Zhang et al.[217] Rohde et al.[219] Prochazka et al.[221] Stefas et al.[223] Wang et al.[225] Dai et al.[227] Choi et al.[230] Mi et al.[232] Dai et al.[234] Chen et al.[236]</td></tr><tr><td>Regression</td><td>Képeš et al.[16] Costa et al.[70] Dehbozorgi et al.[130] Babos et al.[166] Ni et al.[167] Xing et al.[174] Rezaei et al.[179] Zeng et al.[180] Lv et al.[190] Boucher et al.[192] Devangad et al.[194] Anderson et al.[195] Luna et al.[198] Guo et al.[200] Erler et al.[202] Che et al.[204] Li et al.[206] Van den Eynde et al.[208] LYU et al.[210] Fang et al.[212] Singh et al.[193] Castro et al.[111] Knadel et al.[197] Zhu et al.[199] He et al.[201] Ewusi-Annan et al.[203] Kumar et al.[205] Chen et al.[207] Yu et al.[209] Ma et al.[211] He et al.[213]</td></tr></tbody></table>

aspects of computational tools that are required to select and tune based on the data under investigation and the ultimate goal of the analysis.

## 6. Challenges and Limitations

In this review paper, we presented how researchers integrate ML and DL methods, with LIBS spectral data to address specific challenges and enhance the efficacy of LIBS analysis. This integration mostly targets improvements in accuracy, precision, and efficiency across a wide range of fields, including industry, biomedicine, food science, agriculture, and geology. However, as explored in detail in the preceding sections, the measured LIBS spectra are subject to certain limitations, such as spectral complexity, background noise and matrix effects. These shortcomings are expected to be mitigated or ideally resolved by applying ML and DL techniques, employing their strengths in recognizing hidden underlying patterns and features. As a result, one can develop more robust and reliable elemental analysis models, with applications extending across a wide range of fields.

Although ML and DL approaches can significantly improve LIBS analysis and assist with data interpretation, they are not the ultimate solution and have certain limitations. One limitation is overfitting, which leads to overly optimistic performance metrics during training. However, the model then underperforms in real-world applications. This happens when a model is trained too well on the training dataset and cannot effectively generalize new, unseen data. In essence, the model becomes proficient at recalling the training data yet struggles when presented with new data. DL is also very demanding in terms of the availability of data during the model development and training process, also
<figure><img src="image_33.png" /></figure>

known as the learning process. The limited number of available samples diminishes the reliability of Al-based in particular DL modeling methods.

Furthermore, over time a variety of DL architectures have been developed, each with distinct structures designed to optimize influencing factors and internal parameters, ultimately improving overall model performance. Despite these efforts, determining the most suitable DL model continues to be crucial.

As another influential factor, training DL models not only can be computationally intensive but also is a demanding task when considering the hardware and significant resources required to execute the process. This advanced technology may not be accessible to all researchers or in resource-constrained environments.

Recognizing and addressing the current limitations is crucial for advancing future research, as it provides valuable insights into methodological challenges and opportunities for refinement.

## 7. Summary

Since its inception, LIBS has evolved as an all-purpose analytical tool, providing rapid, multielement analysis with minimal sample preparation across a broad range of applications. This extensive review has covered the integration of ML and DL approaches with LIBS spectral data and their transformative impact on the accuracy, precision, and reliability of elemental analysis. We demonstrated through a systematic review of the 2015–2025 literature how these computational methods are able to overcome LIBS spectra complexities in various fields of science, long known to be challenging to conventional analytical approaches.

Application of supervised ML algorithms like PLS, SVM, RF, and K-NN has been demonstrated to be effective both in regression and classification contexts, making good quantitative predictions and qualitative discriminations. Unsupervised methodologies including PCA and K-means clustering have further enriched LIBS analysis by uncovering hidden patterns and reducing data dimensionality, facilitating exploratory research. However, we also observed a notable trend toward the application of DL through the implementation of advanced tools, particularly CNNs, RNNs, GANs, and AEs. These powerful tools can often better account for fine spectral features and complex nonlinear relationships, usually outperforming conventional ML approaches in handling LIBS variability, such as fluctuations in plasma temperature and electron number density.

While LIBS is capable of offering numerous advantages, it also has some limitations that must be taken into account for an efficient analysis. Preprocessing is the key to overcoming these issues through application of various techniques, such as filtering, baseline correction, or normalization, each designed to tackle the specific problems.

According to our observations in this review, specific steps must be followed to design an analytical framework for LIBS spectral data, to address a real-world problem. Data collection marks the initial step, paving the way for data enhancement, a critical process that improves the quality of raw spectral data and enables the development of robust predictive models. With respect to the

objective of the analysis, ML or DL algorithms can assist in extracting key features from the data, enabling the uncovering of complicated patterns and the delivery of informed decision-making tailored to the task at hand. What stands out across this entire review is the absence of a one-size-fits-all solution or a consistently top-performing approach for designing qualitative or quantitative models. While DL often proves to be a stronger choice for tackling LIBS challenges, selecting the right model is heavily case- and objective-oriented. There might be scenarios where a more straightforward ML method can improve outcomes by introducing fewer affecting parameters during training and learning. On the contrary, with its many hyperparameters to optimize, control, and fine-tune, DL can add extra complexity to already complicated information, leading to low-performing models.

This review represents a dedicated effort to understand the fundamentals of LIBS. It explores the merits and drawbacks of the technique, as well as the methods used to evaluate LIBS data both quantitatively and qualitatively. By highlighting the significant progress made in the field and providing deep insights, this investigation aims to deepen the appreciation of the technology and its evolving role in real-world applications.

## Acknowledgements

This work is supported by the BMFTR, funding program Photonics Research Germany (FKZ: 13N15706 (LPI-BT2-FSU), 13N15466 (LPI-BT1-FSU), 13N15710 (LPI-BT3-FSU)) and is integrated into the Leibniz Center for Photonics in Infection Research (LPI). The LPI initiated by Leibniz-IPHT, Leibniz-HKI, UKJ and FSU Jena is part of the BMFTR national roadmap for research infrastructures.

Open Access funding enabled and organized by Projekt DEAL.

## Conflict of Interest

The authors declare no conflict of interest.

**Keywords:** classification · deep learning · elemental analysis · laser-induced breakdown spectroscopy · machine learning · regression

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