Constructing L2-Graph For Subspace Learning and Segmentation

Construction of sparse similarity graph is a fundamental and key step of graph-oriented learning algorithms. In a similarity graph, the vertex denotes a data point and the connection weight between two points represents the similarity. Some recent works used L1-norm based sparse coefficients to build the graph for various applications, and achieved impressive results. Can we find other way to achieve sparsity with better performance and fewer limitations? This paper proposes a novel scheme to construct a sparse similarity graph by enforcing locality over a non-sparse representation, and develops an algorithm, called L2-graph, to verify the effectiveness of our scheme. Various machine learning tasks, e.g., subspace learning and subspace segmentation, are derived upon the L2-graphs. Thanks to the interesting solution of L2-graph, the proposed algorithm is more computationally efficient than its potential competitors, e.g., L1-graph, LRR and LatLRR. The experimental results demonstrate that the proposed algorithm achieves state-of-the-art results for feature extraction, data clustering and motion segmentation in accuracy, robustness and computational efficiency.