Sparse Affinity Propagation for Image Analysis

It is challenging to find a small set of data points, so-called exemplars or landmarks, that are nicely representative of itself and other data points. Affinity propagation (AP) is an effective algorithm that identifies exemplars among data points by recursively sending realvalued messages between pairs of data points. AP calculates the message using the similarity among data points. Hence, the construction of similarity graph lies in the heart of the AP algorithm. A common choice for similarity is negative Euclidean distance. However, most data points, especial high-dimensional data, lies into the non-Euclidean space such that Euclidean distance cannot capture the real structure of data. Moreover, Euclidean distance is sensitive to noise and outliers such that the performance of the algorithm will be degraded when data are grossly corrupted. In this paper, we propose an algorithm, named as Sparse Affinity Propagation (SAP), which adopts sparse representation coefficient to depict the relationship among data points. For a given data set, SAP calculates the sparse representation for each data point by solving a convex problem; and then, builds a similarity graph using the representation coefficient; after that, obtains the exemplars by performing AP over the sparse similarity graph. To verify the efficacy of our algorithm, we carried out numerous experiments in the context of data summarization. Empirical studies show that SAP is superior to AP and other baseline algorithms for image analysis in accuracy and robustness.