Joseph St.Amand (University of Kansas);Jun Huan (University of Kansas)
Mahalanobis distance metric learning becomes an especially challenging problem as the dimension of the feature space p is scaled upwards. The number of parameters to optimize grows with O (p 2 ) complexity, making storage infeasible, interpretability poor, and causing the model to have a high tendency to overfit. Additionally, optimization while maintaining feasibility of the solution becomes prohibitively expensive, requiring a projection onto the positive semi-definite cone after every iteration. In addition to the obvious space and computational challenges, vanilla distance metric learning is unable to model complex and multi-modal trends in the data.
Inspired by the recent resurgence of Frank-Wolfe style optimization, we propose a new method for sparse compositional local Mahalanobis distance metric learning. Our proposed technique learns a set of distance metrics which are composed of local and global components. We capture local interactions in the feature space, while ensuring that all metrics share a global component, which may act as a regularizer. We optimize our model using an alternating pairwise Frank-Wolfe style algorithm. This serves a dual purpose, we can control the sparsity of our solution, and altogether avoid any expensive projection operations. We conduct an empirical evaluation of our technique on 5 separate datasets and find that in some cases our proposed technique is capable of outperforming current state of the art methods.