# Stability of Feature Selection in Multi-Omics Data Analysis
###### Abstract  
In the rapidly evolving field of multi-omics data analysis, understanding the stability of feature selection is critical for reliable biomarker discovery and clinical applications. This study investigates the stability of feature-selection methods across various cancer types by utilizing 15 datasets from The Cancer Genome Atlas (TCGA). We employed classifiers with embedded feature selection, including Support Vector Machines (SVM), Logistic Regression (LR), and Lasso regression, each incorporating L1 regularization. Through a comprehensive evaluation using five-fold cross-validation, we measured feature-selection stability and assessed the accuracy of predictions regarding TP53 mutations, a known indicator of poor clinical outcomes in cancer patients. All three classifiers demonstrated optimal feature-selection stability, measured by the Nogueira metric, with higher regularization (fewer selected features), while lower regularization generally resulted in decreased stability across all omics layers. Our findings indicate differences in feature stability across the various omics layers; _mina_ consistently exhibited the highest stability across classifiers, while the _mutation_ and _rnu_ layers were generally less stable, particularly with lower regularization. This work highlights the importance of careful feature selection and validation in high-dimensional datasets to enhance the robustness and reliability of multi-omics analyses. multi-omics; high-dimensional data; cancer genomics; feature selection; stability; L1 regularization +
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the International Cancer Genomics Consortium repository, a global initiative to build a comprehensive catalog of mutational abnormalities in the major tumor types [9, 10]. Due to the dispersion of dataset publishing spaces, indexing services have been developed, e.g., the Omics Discovery Index, that participate in the discovery and linking of public omics datasets [11, 12]. Security policies have gained importance as well [13]. Multi-omics data have put new force into biomedical research, especially by allowing systematic modeling and a comprehensive understanding of mechanisms behind disease progression and associated risk management [14, 15, 16]. Naturally, we cannot imagine these applications without machine-learning (ML) and artificial-intelligence (AI) support, as deriving conclusions from these data is one of the most demanding tasks [17, 18]. Recently, deep learning (DL) has gained high interest due to its performance and the capability of capturing nonlinear and hierarchical features [14, 19, 20, 21]. In the field of machine learning, classification tasks, data mining, and exploration often require effective feature extraction and selection to improve model performance. Feature selection becomes particularly important in multi-omics data analysis, where the number of features (e.g., genes, proteins, metabolites) far exceeds the number of observations (samples or instances). This imbalance between the dimensionality of the data and the available observations necessitates a careful selection of features, as using all available features can lead to overfitting and reduce the model's ability to generalize. In classification tasks, especially when dealing with datasets where the number of features exceeds the number of observations, it is not feasible for the model to make decisions based on all features; instead, it relies on a subset of features that are selected during the learning process. This subset is selected to maximize predictive power while minimizing complexity and overfitting, representing a trade-off between model accuracy and the risk of overfitting. By selecting a smaller set of relevant features, the model is better able to generalize to unseen data, but this comes at the cost of potentially losing some predictive power if too many features are excluded. The process of selecting features as part of the model training is known as embedded feature selection and is often referred to as an \"intrinsic\" or \"embedded\" method [22].