Eigenrange: A Robust Spectral Method for Dimensionality Reduction

Malika Kharouf (1) , Tabea Rebafka (2) , Nataliya Sokolovska (3)

1 LM2S - Laboratoire Modélisation et Sûreté des Systèmes
2 LPMA - Laboratoire de Probabilités et Modèles Aléatoires
3 ICAN - Unité de Recherche sur les Maladies Cardiovasculaires, du Métabolisme et de la Nutrition = Research Unit on Cardiovascular and Metabolic Diseases

This paper addresses the problem of dimension reduction of noisy data, more precisely the challenge of determining the dimension of the subspace where the signal lives in. Based on results from random matrix theory, a novel estimator of the signal dimension is developed. Consistency of the estimator is proved in the modern asymptotic regime, where the number of parameters grows proportionally with the sample size. Experimental results show that the novel estimator is robust to noise and, moreover, it gives highly accurate results in settings where standard methods fail. The application of the new dimension estimator on several biomedical data sets in the context of classification illustrates the improvements achieved by the new method compared to the state of the art.

Mots clés: Dimensionality reduction; sample eigenvalues; random matrix theory; spiked population model

Domaines: Machine Learning [stat.ML]; Applications [stat.AP]

Malika Kharouf, Tabea Rebafka, Nataliya Sokolovska. Eigenrange: A Robust Spectral Method for Dimensionality Reduction. 2016. ⟨hal-01400952⟩