Feature Extraction via Sparse Fuzzy Difference Embedding (SFDE) for Robust Subspace Learning

Many classical feature extraction and dimensionality reduction algorithms, such as linear algorithm principal component analysis (PCA) and nonlinear algorithm local linear embedding (LLE), have been applied to face recognition. As we all know, PCA is a global algorithm and LLE is a local algorithm. However, PCA cannot obtain the local structure of high-dimensional spatial data samples, and LLE cannot obtain the global structure of high-dimensional spatial data samples. The application effect of these algorithms is not ideal, especially when they are always affected by overlapping points (outliers) and sparse points in the data. To solve these problems, the paper proposes a new effective feature extraction and dimension reduction algorithm called sparse fuzzy difference embedding (SFDE). Firstly, SFDE algorithm tries to search an optimal projection mapping matrix, which can affect not only the local of the fuzzy local minimizing embedding obtained by LLE but also the global of the fuzzy global maximizing variance obtained by PCA. Secondly, SFDE algorithm obtains the sparse transformation matrix by using the lasso regression return. This feature makes SFDE more intuitive and powerful than PCA, LLE, and other algorithms. Finally, we estimated the proposed algorithm through experiments in Yale and AR standard face databases and added the density of "salt and pepper" noise to the Yale and AR databases to verify the robustness of SFDE algorithm. The experimental results of the SFDE algorithm were better than those of the LDA, PCA, LLE, sparse differential embedding (SDE), and fuzzy local graph embedding based on maximum margin criterion algorithms because of its sparsity and fuzzy set, which also indicates that the SFDE algorithm is an effective algorithm.