Optimal mean two-dimensional principal component analysis with F-norm minimization

Two-dimensional principal component analysis (2DPCA) employs the squared F-norm as distance metric for feature extraction and is widely used in the field of pattern analysis and recognition, especially face image analysis. But it is sensitive to the presence of outliers due to the fact that squared F-norm remarkably enlarges the role of outliers in the criterion function. To handle this problem, we propose a robust formulation for 2DPCA, namely optimal mean 2DPCA with F-norm minimization (OMF-2DPCA). In OMF-2DPCA, distance in spatial dimensions (attribute dimensions) is measured in F-norm, while the summation over different data points uses 1-norm. Moreover, we center the data using the optimized mean rather than the fixed mean. This helps further improve robustness of our method. To solve OMF-2DPCA, we propose a fast iterative algorithm, which has a closed-form solution in each iteration. Experimental results on face image databases illustrate its effectiveness and advantages.