Sparse Principal Components And Their Applications

Principal component analysis (PCA) is widely used in date processing and dimensionality reduction. Some interesting examples include recognitions for handwritten digits (Hastie, etc. 2001) and human face (Hancock etc.1996). Recently PCA has been used in the data analysis for genes expression. (Alter, Brown and Botstein 2000). Hastie and some others (2000) refer that the so-called "gene shaving" techniques use PCA to cluster the gene data.Even though there are many advantages of PCA: Principal components are uncorrelated and they sequentially capture the maximum variance among the columns of X, thus ensuring the minimum information loss; However, PCA also has an obvious drawback, that is, each PC is a linear combination of all pvariables and the loadings are typically nonzero. This makes it often difficult to interpret the derived PCS. Hence, many scholars put forward modified PCA, among which Zou's Spare Principal component analysis ( S-PCA ) is widely focused .This paper discuss the S-PCA and application.The main tasks of this paper are following:(1) We give a comprehensive comparative study of all kinds of spareprincipal component and point out some differences with each other.(2) We give an algorithm to solve nonnegative spare PCA based on leastangle regression algorithm. (3) We introduce various S-PCA to comprehensive evaluation and explainthe efficiency on basis of examples.