A Sparse Principal Component Analysis Method Based On Projection Gradient

In this dissertation, we propose a sparse principal component analysis method based on projected gradient, namely PGPCA. We firstly introduce the background knowledge about principal component analysis (PCA), and discuss the importance about finding sparse loadings. Then we use the best rank-1approximation to the data matrix to turn the sparse PCA problem to an optimization problem, by adding penalty to the objective function. We discuss some properties of the e1penalty and the e0penalty, and choose to solve the problem with e0penalty since the the e1penalty doesn’t have ob-vious advantage. Furthermore we discuss how to solve the above optimization problem using projected gradient method, and prove the convergence property of the solution. We also discuss the method to choose a proper smooth parameter. Finally we test the proposed method PGPCA on real data sets and generated data sets to confirm its effec-tiveness.