Learning Expected Hitting Time Distance

Most distance metric learning (DML) approaches focus on learning a Mahalanobis metric for measuring distances between examples. However, for particular feature representations, e. g. , histogram features like BOW and SPM, Mahalanobis metric could not model the correlations between these features well. In this work, we define a non- Mahalanobis distance for histogram features, via Expected Hitting Time (EHT) of Markov Chain, which implicitly considers the high-order feature relationships between different histogram features. The EHT based distance is parameterized by transition probabilities of Markov Chain, we consequently propose a novel type of distance learning approach (LED, Learning Expected hitting time Distance) to learn appropriate transition probabilities for EHT based distance. We validate the effectiveness of LED on a series of realworld datasets. Moreover, experiments show that the learned transition probabilities are with good comprehensibility.

Authors

• De-Chuan Zhan Nanjing University
• Peng Hu Sichuan University
• Zui Chu
• Zhi-Hua Zhou Nanjing University

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