An Information Geometrical View of Stationary Subspace Analysis

Stationary Subspace Analysis (SSA) is an unsupervised learning method that finds subspaces in which data distributions stay invariant over time. It has been shown to be very useful for studying non-stationarities in various applications. In this paper, we present the first SSA algorithm based on a full generative model of the data. This new derivation relates SSA to previous work on finding interesting subspaces from high-dimensional data in a similar way as the three easy routes to independent component analysis, and provides an information geometric view.

[1]  Motoaki Kawanabe,et al.  In Search of Non-Gaussian Components of a High-Dimensional Distribution , 2006, J. Mach. Learn. Res..

[2]  Peter Schlattmann,et al.  Theory and Algorithms , 2009 .

[3]  John W. Tukey,et al.  A Projection Pursuit Algorithm for Exploratory Data Analysis , 1974, IEEE Transactions on Computers.

[4]  Motoaki Kawanabe,et al.  Learning invariances with Stationary Subspace Analysis , 2009, 2009 IEEE 12th International Conference on Computer Vision Workshops, ICCV Workshops.

[5]  Shun-ichi Amari,et al.  Differential-geometrical methods in statistics , 1985 .

[6]  Klaus-Robert Muller,et al.  Finding stationary brain sources in EEG data , 2010, 2010 Annual International Conference of the IEEE Engineering in Medicine and Biology.

[7]  K. Müller,et al.  Finding stationary subspaces in multivariate time series. , 2009, Physical review letters.

[8]  Yoshinobu Kawahara,et al.  Stationary Subspace Analysis as a Generalized Eigenvalue Problem , 2010, ICONIP.

[9]  Fabian J. Theis,et al.  Colored Subspace Analysis: Dimension Reduction Based on a Signal's Autocorrelation Structure , 2010, IEEE Transactions on Circuits and Systems I: Regular Papers.

[10]  Klaus-Robert Müller,et al.  Stationary Subspace Analysis , 2009, ICA.

[11]  Jean-Francois Cardoso,et al.  THE THREE EASY ROUTES TO INDEPENDENT COMPONENT ANALYSIS; CONTRASTS AND GEOMETRY , 2001 .

[12]  Christof Schütte,et al.  Sparse Non-Gaussian Component Analysis , 2010, IEEE Transactions on Information Theory.

[13]  F. Götze.  Differential-geometrical methods in statistics. Lecture notes in statistics - A. Shun-ichi. , 1987 .

[14]  Dinh-Tuan Pham,et al.  Blind separation of instantaneous mixtures of nonstationary sources , 2001, IEEE Trans. Signal Process..

[15]  Mark D. Plumbley.  Geometrical methods for non-negative ICA: Manifolds, Lie groups and toral subalgebras , 2005, Neurocomputing.