A Pairwised Specific Distance Learning from Physical Linkages

In real tasks, it is usually the case that a better classification performance can be obtained when a good distance metric is used; therefore, distance metric learning has attracted significant attention in the past few years. Typical studies of distance metric learning concern about how to construct an appropriate distance metric that is able to separate training data points from different classes or satisfy a set of constraints (e.g., must-links and/or cannot-links). It is noteworthy that this task becomes challenging when there are only limited labeled training data points and no constraints are given explicitly. Moreover, most existing approaches aim to construct a global distance metric that is applicable to all data points. However, different data points may have different properties and may require different distance metrics. We notice that data points in real tasks are often connected by physical links (e.g., people are linked with each other in social networks; personal webpages are often connected to other webpages including non-personal webpages), but these link information has not been exploited in distance metric learning. In this paper, we develop the pairwised specific distance (PSD) approach that exploits the structure of physical linkages and in particular captures the key observations that non-metric and clique linkages imply the appearance of different or unique semantics, respectively. It is noteworthy that rather than generating a global distance, PSD will generate different distances for different pairs of data points; this property is desired in applications involving complicated data semantics. We mainly present PSD for multi-class learning and further extend it for multi-label learning. Experimental results validate the effectiveness of PSD, especially in the scenarios where there are very limited labeled training data points and no explicit constraints are given.