Active metric learning for supervised classification

Abstract Clustering and classification critically rely on distance metrics that provide meaningful comparisons between data points. To this end, learning optimal functions from data, known as metric learning, aims to facilitate supervised classification, particularly in high-dimensional spaces where visualization is challenging or infeasible. In particular, the Mahalanobis default choice due simplicity interpretability a transformation of simple Euclidean using combination rotation scaling. work, we present several novel contributions both by way formulation well solution methods. Our approach motivated agglomerative clustering with certain modifications enable natural interpretation user-defined classes clusters metric. generalizes improves upon leading methods removing reliance pre-designated “target neighbors,” “triplets,” “similarity pairs.” Starting definition generalized has second order term, propose an objective function for selection does not aim isolate each other like most previous but tries distort space minimally aggregating co-class members into local clusters. Further, formulate problem mixed-integer optimization can be solved efficiently small/medium datasets approximated larger datasets. Another salient feature our method it facilitates active recommending precise regions sample improve performance. These are indicated boundary outlier points dataset defined This targeted acquisition significantly reduce computation ensuring training completeness, representativeness, economy, which could also advantages established Deep Learning Random Forests. We demonstrate computational performance through intuitive examples, followed results real image benchmark