Structured Principal Component Analysis

Many tasks involving high-dimensional data, such as face recognition, suffer from the curse of dimensionality: the number of training samples required to accurately learn a classifier increases exponentially with the dimensionality of the data. Structured Principal Component Analysis (SPCA) reduces the dimensionality of the data by choosing a small number of features to represent larger sets of similar features. The pairwise similarity of two features is measured using the Chi-squared distance between the joint distributions of the class and the data for each feature. SPCA groups the original features of the data into clusters of similar features using the Normalized Cut algorithm. As features in a cluster are similar and thus redundant, an entire cluster can be represented by a small number of Principal Components extracted from each cluster. SPCA method was tested on two face recognition databases, the Ekman and Friesen Pictures of Facial Affect Database and the Yale Face Database, with encouraging results.