A Randomized Algorithm for Learning Mahalanobis Metrics: Application to Classification and Regression of Biological Data

Abstract

We present a randomized algorithm for semi-supervised learning of Mahalanobis metrics over Rn. The inputs to the algorithm are a set, U , of unlabeled points in Rn, a set of pairs of points, S = {(x, y)i};x, y ∈ U , that are known to be similar, and a set of pairs of points, D = {(x, y)i};x, y ∈ U , that are known to be dissimilar. The algorithm randomly samples S, D, and m-dimensional subspaces of Rn and learns a metric for each subspace. The metric over Rn is a linear combination of the subspace metrics. The randomization addresses issues of efficiency and overfitting. Extensions of the algorithm to learning non-linear metrics via kernels, and as a pre-processing step for dimensionality reduction are discussed. The new method is demonstrated on a regression problem (structure-based chemical shift prediction) and a classification problem (predicting clinical outcomes for immunomodulatory strategies for treating severe sepsis).