Regularized Semi-Nonnegative Matrix Factorization Using L2,1-Norm for Data Compression

We present a robust, parts-based data compression algorithm, L21 Semi-Nonnegative Matrix Factorization (L21 SNF) for mixed-sign data. To resolve the instability issue caused by the Frobenius norm due to the effects of outliers, we utilize the noise-free L2,1 norm and a regularization parameter in our algorithm. We derive a rigorous proof of convergence of our algorithm. Based on experiments on large-scale over-determined matrices and real facial image data, L21 SNF demonstrates a significant improvement in accuracy over other classical methods. Furthermore, L21 SNF has a simple programming structure and can be implemented within data compression software for compression of highly over-determined systems encountered broadly across many general machine learning processes