Phase Transitions in Unsupervised Feature Selection
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arXiv
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| Format: | Preprint |
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2026
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| author | Fiorentino, Jonathan Monti, Michele Miltiadis-Vrachnos, Dimitrios Del Tatto, Vittorio Laio, Alessandro Tartaglia, Gian Gaetano |
| author_facet | Fiorentino, Jonathan Monti, Michele Miltiadis-Vrachnos, Dimitrios Del Tatto, Vittorio Laio, Alessandro Tartaglia, Gian Gaetano |
| contents | Identifying minimal and informative feature sets is a central challenge in data analysis, particularly when few data points are available. Here we present a theoretical analysis of an unsupervised feature selection pipeline based on the Differentiable Information Imbalance (DII). We consider the specific case of structural and physico-chemical features describing a set of proteins. We show that if one considers the features as coordinates of a (hypothetical) statistical physics model, this model undergoes a phase transition as a function of the number of retained features. For physico-chemical descriptors, this transition is between a glass-like phase when the features are few and a liquid-like phase. The glass-like phase exhibits bimodal order-parameter distributions and Binder cumulant minima. In contrast, for structural descriptors the transition is less sharp. Remarkably, for physico-chemical descriptors the critical number of features identified from the DII coincides with the saturation of downstream binary classification performance. These results provide a principled, unsupervised criterion for minimal feature sets in protein classification and reveal distinct mechanisms of criticality across different feature types. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2602_00660 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Phase Transitions in Unsupervised Feature Selection Fiorentino, Jonathan Monti, Michele Miltiadis-Vrachnos, Dimitrios Del Tatto, Vittorio Laio, Alessandro Tartaglia, Gian Gaetano Biomolecules Data Analysis, Statistics and Probability Identifying minimal and informative feature sets is a central challenge in data analysis, particularly when few data points are available. Here we present a theoretical analysis of an unsupervised feature selection pipeline based on the Differentiable Information Imbalance (DII). We consider the specific case of structural and physico-chemical features describing a set of proteins. We show that if one considers the features as coordinates of a (hypothetical) statistical physics model, this model undergoes a phase transition as a function of the number of retained features. For physico-chemical descriptors, this transition is between a glass-like phase when the features are few and a liquid-like phase. The glass-like phase exhibits bimodal order-parameter distributions and Binder cumulant minima. In contrast, for structural descriptors the transition is less sharp. Remarkably, for physico-chemical descriptors the critical number of features identified from the DII coincides with the saturation of downstream binary classification performance. These results provide a principled, unsupervised criterion for minimal feature sets in protein classification and reveal distinct mechanisms of criticality across different feature types. |
| title | Phase Transitions in Unsupervised Feature Selection |
| topic | Biomolecules Data Analysis, Statistics and Probability |
| url | https://arxiv.org/abs/2602.00660 |