# Topological Machine Learning for Discriminative Spectral Band Identification in Raman Spectroscopy of Pathological Samples

Francesco Conti, Davide Moroni, Maria Antonietta Pascali

► To cite this version:

Francesco Conti, Davide Moroni, Maria Antonietta Pascali. Topological Machine Learning for Discriminative Spectral Band Identification in Raman Spectroscopy of Pathological Samples. AITA 2025 - 18th International Workshop on Advanced Infrared Technology and Applications, Sep 2025, Kobe, Japan. 10.3390/proceedings1010000. hal-05456529

HAL Id: hal-05456529

https://hal.science/hal-05456529v1

Submitted on 14 Jan 2026

HAL is a multi-disciplinary open access
archive for the deposit and dissemination of sci-
entific research documents, whether they are pub-
lished or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.

L'archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diffusion de documents
scientifiques de niveau recherche, publiés ou non,
émanant des établissements d'enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.

<figure><img src="image_1.png" /></figure>

Distributed under a Creative Commons CC BY 4.0 - Attribution - International License
Abstract

# Topological Machine Learning for Discriminative Spectral Band Identification in Raman Spectroscopy of Pathological Samples †

Francesco Conti <fnref n="1" />,<fnref n="2" />,* ID, Davide Moroni <fnref n="1" /> ID and Maria Antonietta Pascali <fnref n="1" /> ID

## Abstract

In the field of Raman spectroscopy (RS), particularly when working with biological samples, identifying the chemical compounds most involved in specific pathologies is of critical importance for pathologists. The correlation between chemical substances present in biological tissue and pathology can contribute not only to a deeper understanding of the disease itself but also to the development of novel artificial intelligence-based diagnostic methodologies. Motivated by these clinical challenges, we propose a method to identify the most discriminative spectral bands by leveraging the synergy between Topological Machine Learning (TML) and Raman spectroscopy. The intrinsic explainability of part of the TML pipeline can indeed play a key role in the detection of such spectral bands, e.g., the proteins most associated with the disease. In order to evaluate the performance of our method, we apply it to three case studies: the RS of biological tissue related to the chondrogenic bone tumors, the RS of cerebrospinal fluid associated with Alzheimer's disease and the RS of pancreatic tissue. The results obtained with our method are promising in pinpointing which spectral bands are most relevant for diagnosis, but they also highlight the need for further investigation.

**Keywords:** Raman; machine learning; topological data analysis; explainable artificial intelligence

<figure><img src="image_2.png" /></figure>

check for
updates

Academic Editor: Firstname Lastname

Published:

**Citation:** Conti, F.; Moroni, D.; Pascali, M.A. Topological Machine Learning for Discriminative Spectral Band Identification in Raman Spectroscopy of Pathological Samples. *Proceedings 2025*, 1, 0. https://doi.org/

**Copyright:** © 2025 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## 1. Introduction

Raman spectroscopy (RS) is a spectroscopic technique used to provide a structural fingerprint of a sample. It is based on the evaluation of the inelastic scattering process in which photons incident on the sample transfer energy to or from molecular vibrational modes. Since the involved energies are relatively low, RS is applicable for non-destructive analysis; hence, it is compatible with in vivo or in vitro, making it suitable for many applications in the biological realm [1–4].

In a nutshell, different bands of the Raman spectra represent specific molecular movements and rotational states, providing an insight into molecular behaviour and composition; on the other hand, despite the chemical coherence of RS, when imaging biological samples, the sources of information are always multiple, and the most prominent ones may be hidden or obscured by other spurious signals.

Consequently, advanced data filtering and processing methodologies, in conjunction with machine learning approaches, have been implemented to facilitate rapid and robust

<footnote n="1">¹ Institute of Information Science and Technologies “A. Faedo”, National Research Council, 56124 Pisa, Italy; davide.moroni@isti.cnr.it (D.M.); maria.antonietta.pascali@isti.cnr.it (M.A.P.)</footnote>

<footnote n="2">² Centre Inria at Université Côte d'Azur, 06902 Sophia Antipolis, France</footnote>

<footnote>* Correspondence: francesco.conti@inria.fr</footnote>

<footnote>† Presented at the 18th International Workshop on Advanced Infrared Technology and Applications (AITA 2025), Kobe, Japan, 15–19 September 2025.</footnote>
spectral interpretation in various application domains, as well as to enhance the understanding of RS and extract salient features. From this perspective, we aim to increase the interpretability of Topological Machine Learning (TML, [5]) models, which were trained on three distinct case studies, by conducting a band importance analysis for RS data.

## 2. Materials and Methods

A framework inspired by RISE [6], which is a post hoc AI interpretability method, has been developed to identify the most discriminative spectral bands in Raman spectroscopy data. Our approach empirically evaluates spectral band importance through the quantitative assessment of their contribution to model performance:

* **Input:** Raman spectra of biological samples;

* **Preprocessing and feature extraction:** Same as original model (when applicable);

* **Sliding window masking:** Iterative masking with 10-width window and 5 stride to identify critical spectral regions;

* **Importance estimation:** Performance drop on masked spectra indicates diagnostically relevant regions.

Figure 1 sketches the framework overview. We used a TML pipeline introduced in [5], and successfully applied in Raman spectroscopy [7,8], leveraging its input dimensionality invariance.

<figure><img src="image_3.png" /><figcaption>**Figure 1.** Identifying critical spectral regions in Raman data via sliding band masking, with band width of 10 cm⁻¹ and stride of 5 cm⁻¹. First row: classical ML pipeline for RS. Second row: masked regions causing model performance drops reveal diagnostically relevant bands.</figcaption></figure>

## 3. Results

We present the discriminative spectral band identification for our three case studies: the Alzheimer's disease detection in Figure 2, the chondrogenic cancer grading in Figure 3, and the pancreatic ductal adenocarcinoma (PDA) classification in Figure 4. For chondrogenic and pancreatic cases, we show critical regions for both binary and multi-label classification. Notably, the binary classification's critical regions remain important in multi-label scenarios (colored accordingly), demonstrating model consistency. In these figures, the results are plotted by combining the following:

* A representative Raman spectrum (intensity a.u. vs. wavenumber cm⁻¹);

* Performance drop curve (accuracy loss percentage vs. wavenumber cm⁻¹).

This dual representation links spectral features to diagnostic importance, potentially identifying relevant biomolecules. For each experiment, we set an arbitrary threshold marking significant performance degradation.

* **Alzheimer's:** Performance drop threshold: 30%. Key regions: 904–956 cm⁻¹, 1146–1198 cm⁻¹, and 1224–1313 cm⁻¹ peaks.

* **Chondrogenic:** Performance drop threshold: 3%. Primary peak: 997–1016 cm⁻¹. For 4-class: additional peaks at 725–748 cm⁻¹, 997–1072 cm⁻¹, and 1384–1394 cm⁻¹.
* PDA: Performance drop threshold: 30% (3-class) and 45% (binary). Key features: 1250–1302 cm⁻¹ peak and 958–973 cm⁻¹ valley.

Minor graphical adjustments were made for better visualization.

<figure><img src="image_4.png" /><figcaption>**Figure 2.** Discriminative spectral bands for Alzheimer's detection (904–956, 1146–1198, and 1224–1313 cm⁻¹) showing >30% performance drop when masked. Important bands are colored in red.</figcaption></figure>

<figure><img src="image_5.png" /><figcaption>**Figure 3.** Critical Raman peaks for chondrogenic cancer detection (997–1016 cm⁻¹ in binary classification, extending to 725–748 and 1384–1394 cm⁻¹ for multi-class) showing >3% performance drop when masked. Overlapping important regions are shown in binary classification colors.</figcaption></figure>

<figure><img src="image_6.png" /><figcaption>**Figure 4.** Diagnostically relevant spectral features for pancreatic adenocarcinoma classification (1250–1302 cm⁻¹ peak and 958–973 cm⁻¹ valley) showing >30% (multi-class) and >45% (binary) performance drop when masked.</figcaption></figure>
## 4. Conclusions

This preliminary study presents an AI framework for Raman spectroscopy-based disease detection, able to enhance the explainability of the classification model, assessing the band importance of RS for each case study. Unlike conventional peak analysis, our approach reveals that diagnostic information may be distributed across broad spectral regions rather than isolated peaks, suggesting complex biomolecular interactions underlying disease signatures. The consistent identification of important spectral features across different classification tasks demonstrates the robustness of the method. These findings highlight the potential of combining topological data analysis with explainability techniques to bridge the gap between machine learning predictions and clinical interpretability in spectroscopic diagnostics. While promising, further validation is needed to establish the clinical relevance of the identified spectral patterns.

**Author Contributions:** Conceptualization and methodology, all; software, F.C.; validation and data curation, all; writing, F.C. and M.A.P.; visualization, F.C.; supervision, D.M. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was partially funded by the Regione Toscana through the PRAMA Project under Grant Ricerca Salute 2018.

**Institutional Review Board Statement:** This observational study was conducted in accordance with the principles of the Declaration of Helsinki and ethical approval was obtained from CEAVNO (Comitato Etico Regionale per la Sperimentazione Clinica della Toscana—sezione AREA VASTA NORD OVEST) Committee on date 16 February 2023, Protocol Code: PANOMIC; Clinic Study: "Personalized medicine of pancreatic cancer using genomics and avatars".

**Informed Consent Statement:** Informed consent was obtained from all subjects involved in the study.

**Data Availability Statement:** Data may be shared upon request.

**Acknowledgments:** The joint laboratory BIOICT Lab, Mario D'Acunto (IBF-CNR), Gianmarco Lazzini (ISTI-CNR), Paolo Matteini (IFAC-CNR), and Marella De Angelis (IFAC-CNR) are warmly acknowledged.

**Conflicts of Interest:** The authors declare no conflict of interest.

## References

1. Haka, A.S.; Shafer-Peltier, K.E.; Fitzmaurice, M.; Crowe, J.; Dasari, R.R.; Feld, M.S. Diagnosing breast cancer by using Raman spectroscopy. *Proc. Natl. Acad. Sci. USA* **2005**, *102*, 12371-12376.

2. Eberhardt, K.; Stiebing, C.; Matthäus, C.; Schmitt, M.; Popp, J. Advantages and limitations of Raman spectroscopy for molecular diagnostics: An update. *Expert Rev. Mol. Diagn.* **2015**, *15*, 773-787. https://doi.org/10.1586/14737159.2015.1036744.

3. Polykretis, P.; Banchelli, M.; D'Andrea, C.; de Angelis, M.; Matteini, P. Raman Spectroscopy Techniques for the Investigation and Diagnosis of Alzheimer's Disease. *Front. Biosci.* **2022**, *14*, 22. https://doi.org/10.31083/j.fbs1403022.

4. Lazzini, G.; Gaeta, R.; Pollina, L.E.; Comandatore, A.; Furbetta, N.; Morelli, L.; D'Acunto, M. Raman spectroscopy based diagnosis of pancreatic ductal adenocarcinoma. *Sci. Rep.* **2025**, *15*, 13240.

5. Conti, F.; Moroni, D.; Pascali, M.A. A topological machine learning pipeline for classification. *Mathematics* **2022**, *10*, 3086.

6. Petsiuk, V.; Das, A.; Saenko, K. RisE: Randomized input sampling for explanation of black-box models. In *Proceedings of the British Machine Vision Conference 2018*, BMVC 2018, Newcastle, UK, 3-6 September 2018.

7. Conti, F.; D'Acunto, M.; Caudai, C.; Colantonio, S.; Gaeta, R.; Moroni, D.; Pascali, M.A. Raman spectroscopy and topological machine learning for cancer grading. *Sci. Rep.* **2023**, *13*, 7282.

8. Conti, F.; Banchelli, M.; Bessi, V.; Cecchi, C.; Chiti, F.; Colantonio, S.; D'Andrea, C.; de Angelis, M.; Moroni, D.; Nacmias, B.; et al. Harnessing topological machine learning in Raman spectroscopy: Perspectives for Alzheimer's disease detection via cerebrospinal fluid analysis. *J. Frankl. Inst.* **2024**, *361*, 107249.
**Disclaimer/Publisher's Note:** The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content.