The Translation Invariant Solution to Quadratic Metric Learning

DOI

10.2991/iwmecs-15.2015.41How to use a DOI?

Keywords

metric learning, PCA, LDA, translation invariant, image metric

Abstract

Metric learning has drawn great interests for the last decade in the field of computer vision and machine learning. In this paper, we address the importance of the translation invariance (TI) of a metric. Intuitively, translation invariance should be a fundamental requirement for any reasonable image metric, but few metric learning or subspace methods are aware of the TI property when dealing with images. We propose to solve the quadratic metric learning problem in the transform domain based on the result of [1]. The solution is guaranteed to be translation invariant. The TI assumption simplifies the optimization problems considerably. Specifically, it reduces the number of optimization parameters from of O(n2) to O(n); it turns the semi-definite constraint on a matrix to a bound constraint on a function; it applies to multi-dimensional data without having to be stacked to vectors. Experimental results show that the TI solutions are generally on par with the non-TI solutions. Specifically, the TI solutions usually favor small sample size and small reduction dimension. The framework proposed for quadratic metric learning and linear subspace method seems quite promising.

Copyright

© 2015, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - CONF
AU  - Bing Sun
AU  - Jufu Feng
AU  - Beilun Shen
PY  - 2015/10
DA  - 2015/10
TI  - The Translation Invariant Solution to Quadratic Metric Learning
BT  - Proceedings of the 2015 2nd International Workshop on Materials Engineering and Computer Sciences
PB  - Atlantis Press
SP  - 218
EP  - 223
SN  - 2352-538X
UR  - https://doi.org/10.2991/iwmecs-15.2015.41
DO  - 10.2991/iwmecs-15.2015.41
ID  - Sun2015/10
ER  -