关键词: 主成分分析, 稀疏化方法, fused惩罚, 手写数字识别, 可解释性

Abstract: This paper mainly studies sparse principal component analysis with fused penalty, so as to solve problems with features which are naturally ordered or variables which are related or even equal to their neighbors. First, we propose a simple approach to obtain sparse PCs from the perspective of regression. A new generalized sparse PCA model is introduced, namely generalized sparse PCA (GSPCA), and the corresponding algorithm is offered. Also, we prove that the solution of GSPCA is equivalent to that of SPC, an existing sparse PCA model, when the penalty is 1-norm. Next, we propose combining the fused penalty and sparse PCA to get a fused sparse PCA method, and introduce the corresponding model with two forms on the basis of PMD and regression. After theoretical derivation, we find that the solutions of the two model forms are consistent, so we call the model FSPCA without discrimination. The simulation reveals that FSPCA has a good performance on datasets where variables are related or even equal to their neighbors. At last, we apply the FSPCA to handwritten numeral recognition. It turns out that compared with SPC, FSPCA can extract PCs which have better interpretability, and this makes FSPCA of higher practical value.

Key words: Principal Component Analysis, Sparsity Method, Fused Penalty, Handwritten Numeral Recognition, Interpretability