Discriminant simplex analysis

Image representation and distance metric are both significant for learning-based visual classification. This paper presents the concept of k-nearest-neighbor simplex (kNNS), which is a simplex with the vertices as the k nearest neighbors of a certain point. kNNS contributes to the image classification problem in two aspects. First, a novel distance metric between a point to its kNNS within a certain class is provided for general classification problem. Second, we develop a new subspace learning algorithm, called discriminant simplex analysis (DSA), to pursue effective feature representation for image classification. In DSA, the within-locality and between-locality are both modeled by kNNS distance, which provides a more accurate and robust measurement of the probability of a point belonging to a certain class. Experiments on real-world image classification demonstrate the effectiveness of both DSA as well as kNNS based classification approach.