Sparsity induced similarity measure for label propagation

Graph-based semi-supervised learning has gained considerable interests in the past several years thanks to its effectiveness in combining labeled and unlabeled data through label propagation for better object modeling and classification. A critical issue in constructing a graph is the weight assignment where the weight of an edge specifies the similarity between two data points. In this paper, we present a novel technique to measure the similarities among data points by decomposing each data point as an L1 sparse linear combination of the rest of the data points. The main idea is that the coefficients in such a sparse decomposition reflect the point's neighborhood structure thus providing better similarity measures among the decomposed data point and the rest of the data points. The proposed approach is evaluated on four commonly-used data sets and the experimental results show that the proposed Sparsity Induced Similarity (SIS) measure significantly improves label propagation performance. As an application of the SIS-based label propagation, we show that the SIS measure can be used to improve the Bag-of-Words approach for scene classification.