No. 956

Title:

Exploring local PCA structure for dimensionality reduction by minimizing $\beta $-divergence.

Author(s):

Mollah, M.N.H. (The Graduate University for Advanced Studies);
Sultana, N. (The Institute of Statistical Mathematics);
Mimami, M. (The Institute of Statistical Mathematics);
Eguchi,S. (The Institute of Statistical Mathematics)

Key words:

PCA; mixture model; Local PCA structure; beta-divergence; Kernel function; Initialization of parameters; Cross validation

Abstract:

    Principal component analysis (PCA) is one of the most popular technique for reducing dimensionality of multivariate data. We discuss a new learning algorithm to explore local PCA structure in which the observed data follow a mixture of several PCA models, where each model is described by a linear combination of independent and Gaussian sources. The proposed method is based on an application of the minimum $\beta $-divergence method using a local kernel function to extract all local PCA structures sequentially. This new algorithm searches the local PCA structure using a rule that sequential changes the shifting parameter and the local kernel vector. If the initial choices of the shifting parameter and local kernel vector are both close to the center of a data cluster, then all input data belonging to that cluster are transferred into a local PCA structure, considering the data in other classes as outliers. Performance of the proposed method depends on the values of tuning parameter $\beta $ and kernel parameter $\nu $, where the latter one plays the key role for local PCA. Therefore, an adaptive selection procedure for the kernel parameter $\nu $ is proposed fixing $\beta $ as $\beta _0$ throughout the simulation study.