Mutual neighbors and diagonal loading-based sparse locally linear embedding

In this study, a new Locally Linear Embedding (LLE) algorithm is proposed. Common LLE includes three steps. First, neighbors of each data point are determined. Second, each data point is linearly modeled using its neighbors and a similarity graph matrix is constructed. Third, embedded data are extracted using the graph matrix. In this study, for each data point mutual neighborhood conception and loading its covariance matrix diagonally are used to calculate the linear modeling coefficients. Two data points will be named mutual neighbors, if each of them is in the neighborhood of the other. Diagonal loading of the neighboring covariance matrix is applied to avoid its singularity and also to diminish the effect of noise in the reconstruction coefficients. Simulation results demonstrate the performance of applying mutual neighborhood conception and diagonal loading and their combination. Also, the results of applying the mutual neighborhood on Laplacian Eigenmap (LEM) demonstrate the good performance of the proposed neighbor selection method. Our proposed method improves recognition rate on Persian handwritten digits and face image databases.