Abstract
This article presents a concrete mathematical analysis on Information-Theoretic Metric Learning (ITML). The analysis provides a theoretical foundation for ITML, by supplying well-posedness, strong duality, and convergence. Our analysis suggests the correction of a typo in the original ITML article that may lead to the loss of accuracy in the metric learning. The necessity of this correction is confirmed by several numerical experiments on supervised learning.
Highlights
Many algorithms in machine learning depend on the setting of distance metric to measure similarities of data [12]
We focus on Information-Theoretic Metric Learning (ITML) suggested by Davis et al [5], which has been one of the most efficient metric learning methods
Our study reveals that there is a typo in ITML manuscript [5] that can lead to a serious flaw, and presents its correction named as an extended ITML
Summary
Many algorithms in machine learning depend on the setting of distance metric to measure similarities of data [12]. Mahalanobis distance of two points is defined by dMahal xi, xj = xi − xj T −1 xi − xj where is the covariance matrix of the data This metric measures the distance between two points, and reflects the correlation with given data sets. The main point of their work is that a metric learning procedure can be seen as LogDet divergence regularization. Davis et al [5] solved the optimization problem (2) with the iterative method based on the Bregman projection, the Bregman iteration This is an extension of the work of Kulis et al [13].
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