# Univariate Outlier Detection: Precision-Driven Algorithm for Single-Cluster Scenarios
## 2 Related Works  
Outlier detection in univariate data has been a well-studied area with various approaches proposed over the years. [PERSON] [11] proposed improvements for non-Gaussian data, addressing the need for robustness in skewed distributions. However, this approach might not be suitable for high-dimensional datasets. [PERSON] [12] discussed methods like [PERSON] and [PERSON]'s tests, which can handle some outliers but may struggle with complex outlier patterns or noisy data. [PERSON] et al. [13] presented an efficient algorithm based on Rough Set Theory, but its effectiveness can be limited by the quality of the knowledge base used for rule generation. [PERSON] et al. [14] proposed outlier-based initialization for K-modes clustering, highlighting the importance of accurate cluster centers. However, this method relies on the underlying clustering algorithm's ability to handle outliers itself. [PERSON] [15] investigated non-parametric approaches for survey data, which is crucial due to their inherent skewness and heavy-tailed distributions. However, such methods might not be as efficient for very large datasets. Building on this, [PERSON] [16] proposed modifications to the traditional boxplot method for better handling skewed distributions. While effective for univariate data, this approach might not extend well to multivariate outlier detection. These studies provide valuable foundations for outlier detection in univariate data. [PERSON] [PERSON] and [PERSON] and [PERSON] (2017) offered a comprehensive review comparing various methods, aiding in selecting appropriate techniques for different data characteristics. [PERSON] et al. [PERSON] et al. (2018) emphasized the importance of handling outliers in industrial process modeling, highlighting the need for robust data mining approaches. This aligns with the growing focus on robust machine learning algorithms, as exemplified by Frenay et al.'s [PERSON] et al. (2019) work on reinforced Extreme Learning Machines for robust regression. While these approaches offer diverse methodologies, they might have limitations in areas like handling complex outlier patterns, high dimensionality, or noisy data. Additionally, some methods rely on the underlying assumptions of the chosen technique. [PERSON] et al. [PERSON] et al. (2019) provide a structured overview of techniques applicable to univariate time series data, highlighting the need for the further exploration of methods for various data types and outlier scenarios.  
Recent research explores alternative approaches beyond statistical methods. Machine learning techniques like Support Vector Machines and Support Vector Data Description (SVDDs)have shown promise in outlier detection. However, SVMs might require careful parameter tuning [PERSON] et al. (2018). Additionally, deep learning approaches like autoencoders and Variational Autoencoders (VAEs) [PERSON] et al. (2019) can learn complex data representations for anomaly detection. However, their interpretability and black-box nature can be limitations compared to traditional methods [PERSON] et al. (2019).  
Our proposed algorithm addresses these limitations by prioritizing high-precision anomaly detection through a data transformation process utilizing a customized tanh function. This function enhances the separation between normal and anomalous data points, facilitating the identification of complex outlier patterns. Furthermore, compared to black-box deep learning approaches, our method offers a balance between interpretability and achieving high precision in anomaly detection.