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.