Multiple Manifolds Clustering via Local Linear Analysis

Clustering on multiple manifolds serves as an analysis of the data lying on multiple manifolds. The smoothness and local linearity of data samples are utilized to define the local linear degree which is motivated by Principal Component Analysis (PCA) and Depth First Search (DFS). Then, Multiple Manifolds Clustering (LMMC) is proposed on the base of the Local Linear Analysis (LLA) via this definition and neighbor-growing algorithm, which are especially effective under the condition of interactions. Instead of addressing problems of complex optimization and K-means operation, LMMC is simple and efficient compared with traditional manifold clustering. The algorithm can achieve superior performance on complex subspace and manifolds clustering datasets. Meanwhile, comparative experiments are given to show the effectiveness and efficiency of this algorithm.