Geometric Metric Learning for Multi-Output Learning

Due to its wide applications, multi-output learning that predicts multiple output values for a single input at the same time is becoming more and more attractive. As one of the most popular frameworks for dealing with multi-output learning, the performance of the k-nearest neighbor (kNN) algorithm mainly depends on the metric used to compute the distance between different instances. In this paper, we propose a novel cost-weighted geometric mean metric learning method for multi-output learning. Specifically, this method learns a geometric mean metric which can make the distance between the input embedding and its correct output be smaller than the distance between the input embedding and the outputs of its nearest neighbors. The learned geometric mean metric can discover output dependencies and move the instances with different outputs far away in the embedding space. In addition, our objective function has a closed solution, and thus the calculation speed is very fast. Compared with state-of-the-art methods, it is easier to explain and also has a faster calculation speed. Experiments conducted on two multi-output learning tasks (i.e., multi-label classification and multi-objective regression) have confirmed that our method provides better results than state-of-the-art methods.