CLASSIFICATION USING HIGH ORDER DISSIMILARITIES IN NON-EUCLIDEAN SPACES

Abstract: This paper introduces a novel classification algorithm named MAP-DID. This algorithm combines a maximum a posteriori (MAP) approach using the well-known Gaussian Mixture Model (GMM) method with a term that forces the various Gaussian components within each class to have a common structure. That structure is based on higher-order statistics of the data, through the use of the dissimilarity increments distribution (DID), which contains information regarding the triplets of neighbor points in the data, as opposed to typical pairwise measures, such as the Euclidean distance. We study the performance of MAP-DID on several synthetic and real datasets and on various non-Euclidean spaces. The results show that MAP-DID outperforms other classifiers and is therefore appropriate for classification of data on such spaces.