Fusing Eigenvalues

Shahab Basiri (1) , Esa Ollila (1) , Gordana Draskovic (2) , Frédéric Pascal (2)

1 Aalto University
2 L2S - Laboratoire des signaux et systèmes

In this paper, we propose a new regularized (penalized) co-variance matrix estimator which encourages grouping of the eigenvalues by penalizing large differences (gaps) between successive eigenvalues. This is referred to as fusing eigenval-ues (eFusion), The proposed penalty function utilizes Tukey's biweight function that is widely used in robust statistics. The main advantage of the proposed method is that it has very small bias for sufficiently large values of penalty parameter. Hence, the method provides accurate grouping of eigenval-ues. Such benefits of the proposed method are illustrated with a numerical example, where the method is shown to perform favorably compared to a state-of-art method.

Keywords: eFusion; Penalized sample covariance matrix; Tuckey's biweight function; Iteratively reweighted algorithm

Domains: Computer Science [cs]; Signal and Image Processing; Statistics [stat]; Other Statistics [stat.ML]; Statistics [stat]; Applications [stat.AP]

Shahab Basiri, Esa Ollila, Gordana Draskovic, Frédéric Pascal. Fusing Eigenvalues. 2019 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP 2019), May 2019, Brighton, United Kingdom. pp.4968-4972, ⟨10.1109/ICASSP.2019.8682906⟩. ⟨hal-02186196⟩