Active Metric Learning from Relative Comparisons

This work focuses on active learning of distance metrics from relative comparison information. A relative comparison specifies, for a data point triplet $(x_i,x_j,x_k)$, that instance $x_i$ is more similar to $x_j$ than to $x_k$. Such constraints, when available, have been shown to be useful toward defining appropriate distance metrics. In real-world applications, acquiring constraints often require considerable human effort. This motivates us to study how to select and query the most useful relative comparisons to achieve effective metric learning with minimum user effort. Given an underlying class concept that is employed by the user to provide such constraints, we present an information-theoretic criterion that selects the triplet whose answer leads to the highest expected gain in information about the classes of a set of examples. Directly applying the proposed criterion requires examining $O(n^3)$ triplets with $n$ instances, which is prohibitive even for datasets of moderate size. We show that a randomized selection strategy can be used to reduce the selection pool from $O(n^3)$ to $O(n)$, allowing us to scale up to larger-size problems. Experiments show that the proposed method consistently outperforms two baseline policies.