重加权稀疏主成分分析算法及其在人脸识别中的应用

针对主成分分析（PCA）算法获取的主成分向量不够稀疏，拥有较多的非零元这一问题，使用重加权方法对PCA算法进行优化，提出了一个新的提取高维数据特征的方法，即重加权稀疏主成分分析（RSPCA）算法。首先，将重加权l₁最优化框架和LASSO回归模型引入到PCA算法数学模型中，建立新的数据降维模型；然后，使用交替最小化算法、奇异值分解算法、最小角回归算法等方式对模型进行求解；最后，使用人脸识别实验对算法效果进行了验证。在实验中使用K折交叉验证的方法针对ORL人脸数据集分别使用PCA算法和RSPCA算法进行识别实验。实验结果表明，RSPCA算法在获取更稀疏解的情况下仍拥有着不弱于PCA算法的表现，平均识别准确率达到95.1%，所提算法与表现最好的sPCA-rSVD算法相比，识别准确率提高了6.2个百分点；针对手写数字识别这一具体现实应用进行求解，获取到平均识别准确率96.4%的良好实验效果。证明了所提方法在人脸识别及书写数字识别方面的优异性。

Reweighted sparse principal component analysis algorithm and its application in face recognition

For the problem that the principal component vector obtained by Principal Component Analysis (PCA) algorithm is not sparse enough and has many non-zero elements, PCA algorithm was optimized by the reweighting method, and a new method for extracting high-dimensional data features was proposed, namely Reweighted Sparse Principal Component Analysis (RSPCA) algorithm. Firstly, the reweighted l₁ optimization framework and LASSO (Least Absolute Shrinkage and Selection Operator) regression model were introduced into PCA algorithm to establish a new dimensionality reduction model. Then, the model was solved by using alternat minimization algorithm, singular value decomposition algorithm and minimum angle regression algorithm. Finally, the face recognition experiment was carried out to verify the effectiveness of the algorithm. In the experiment, the K-fold cross-validation method was used to realize the recognition experiment on the ORL face dataset by using PCA algorithm and RSPCA algorithm. The experimental results show that RSCPA algorithm can obtain sparser vector while performs as good as PCA algorithm, has the average recognition accuracy reached 95.1%, which is increased by 6.2 percentage points compared with that of the best performing algorithm sPCA-rSVD (sparse PCA via regularized SVD). And in the experiment of the real-world specific practical application handwritten digit recognition, RSPCA algorithm has the average recognition accuracy of 96.4%, The superiority of the proposed algorithm in face recognition and handwritten digit recognition was proved.