Earth Mover’s Distance-Based Local Discriminant Basis
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Local discriminant basis (LDB) is a tool to extract useful features for signal and image classification problems. Original LDB methods rely on the time–frequency energy distribution of classes or empirical probability densities, with some information theoretic measure (such as Kullback–Leibler divergence) for feature selection. Depending on the problem, energy distributions may not provide the best information for classification. Further, training set sizes and accuracy in the computed empirical probability density functions (epdfs) may hinder the learning process. To improve these deficiencies and provide a more data adaptive algorithm, we propose the use of signatures and earth mover’s distance (EMD). Signatures and EMD provide a data adaptive statistic that is more descriptive than the distribution of energies and more robust than an epdf-based approach. In this chapter, we first review LDB and EMD and then outline how they can be incorporated into a fast EMD based LDB algorithm.We then demonstrate the capabilities of our new algorithm in comparison to both energy distribution and epdf-based LDB algorithms using four different classification problems using synthetic datasets.
KeywordsFeature Space Linear Discriminant Analysis Wavelet Packet Transform Discriminant Measure Empirical Probability Density Function
This research was partially supported by grants NSF DMS-0410406, ONR N00014-06-1-0615, N00014-07-1-0166, N00014-09-1-0041, and N00014-09-1-0318 as well as NSF VIGRE grant DMS-0135345. Further, support was provided from the Inhouse Laboratory Independent Research (ILIR) program at the Naval Surface Warfare Center, Panama City.
- 2.Breiman L, Friedman JH, Olshen RA, Stone C (1993) Classification and regression trees. Chapman & Hall, Inc., New YorkGoogle Scholar
- 5.Hillier FS, Lieberman GJ (1995) Introduction to mathematical programming. McGraw-Hill, San FranciscoGoogle Scholar
- 6.Levina E, Bickel P (2001) The earth mover’s distance is the mallow distance: Some insights from statistics. In: Proceedings of 8th IEEE International Conference on computer vision, pp 251–256Google Scholar
- 7.Rubner Y, Tomasi C (2000) Perceptual metrics for image database navigation. Kluwer Academic Publishers, BostonGoogle Scholar
- 9.Saito N (1994) Local feature extraction and its applications using a library of bases. Ph.D thesis. Department of Mathematics, Yale UniversityGoogle Scholar