On Kernelization of Supervised Mahalanobis Distance Learners

Details On Kernelization of Supervised Mahalanobis Distance Learners On Kernelization of Supervised Mahalanobis Distance Learners

2008-04-09

arxiv.org/abs/0804.1441v3

Computer Science

Learning

23 pages, 5 figures. There is a seriously wrong formula in derivation of a gradient formula of the "kernel NCA" in the two pre

Scientific paper

This paper focuses on the problem of kernelizing an existing supervised Mahalanobis distance learner. The following features are included in the paper. Firstly, three popular learners, namely, "neighborhood component analysis", "large margin nearest neighbors" and "discriminant neighborhood embedding", which do not have kernel versions are kernelized in order to improve their classification performances. Secondly, an alternative kernelization framework called "KPCA trick" is presented. Implementing a learner in the new framework gains several advantages over the standard framework, e.g. no mathematical formulas and no reprogramming are required for a kernel implementation, the framework avoids troublesome problems such as singularity, etc. Thirdly, while the truths of representer theorems are just assumptions in previous papers related to ours, here, representer theorems are formally proven. The proofs validate both the kernel trick and the KPCA trick in the context of Mahalanobis distance learning. Fourthly, unlike previous works which always apply brute force methods to select a kernel, we investigate two approaches which can be efficiently adopted to construct an appropriate kernel for a given dataset. Finally, numerical results on various real-world datasets are presented.

Affiliated with

Also associated with

No associations

Rating

On Kernelization of Supervised Mahalanobis Distance Learners does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with On Kernelization of Supervised Mahalanobis Distance Learners, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On Kernelization of Supervised Mahalanobis Distance Learners will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-574621