Manifold based local classifiers: Linear and nonlinear approaches

Manifold based local classifiers: Linear and nonlinear approaches (2007)

Cached

Download Links

[lear.inrialpes.fr]

by Hakan Cevikalp , Diane Larlus , Marian Neamtu , Bill Triggs , Frederic Jurie , H. Cevikalp , D. Larlus , M. Neamtu , B. Triggs , F. Jurie

Venue:	In Pattern Recognition in review
Citations:	3 - 1 self

BibTeX

@INPROCEEDINGS{Cevikalp07manifoldbased,
    author = {Hakan Cevikalp and Diane Larlus and Marian Neamtu and Bill Triggs and Frederic Jurie and H. Cevikalp and D. Larlus and M. Neamtu and B. Triggs and F. Jurie},
    title = {Manifold based local classifiers: Linear and nonlinear approaches},
    booktitle = {In Pattern Recognition in review},
    year = {2007}
}

Bookmark

OpenURL

Abstract

Abstract In case of insufficient data samples in highdimensional classification problems, sparse scatters of samples tend to have many ‘holes’—regions that have few or no nearby training samples from the class. When such regions lie close to inter-class boundaries, the nearest neighbors of a query may lie in the wrong class, thus leading to errors in the Nearest Neighbor classification rule. The K-local hyperplane distance nearest neighbor (HKNN) algorithm tackles this problem by approximating each class with a smooth nonlinear manifold, which is considered to be locally linear. The method takes advantage of the local linearity assumption by using the distances from a query sample to the affine hulls of query’s nearest neighbors for

Citations

2135	Convex Optimization - Boyd, Vandenberghe - 2004
1229	A global geometric framework for nonlinear dimensionality reduction - Tenenbaum, Silva, et al. - 2000
1156	Nonlinear dimensionality reduction by locally linear embedding - Roweis, Saul - 2000
775	Nonlinear component analysis as a kernel eigenvalue problem - Schölkopf, Smola, et al. - 1998
357	Visual categorization with bags of keypoints - Csurka, Dance, et al. - 2004
304	Learning generative visual models from few training examples: an incremental Bayesian approach tested on 101 object categories - Fei-Fei, Fergus, et al. - 2004
211	R.: Discriminant adaptive nearest neighbor classification - Hastie, Tibshirani - 1996
211	Local features and kernels for classification of texture and object categories: a comprehensive study - Zhang, Marszalek, et al. - 2007
196	Think globally, fit locally: unsupervised learning of low dimensional manifolds - Saul, Roweis - 2004
144	Svm-knn: Discriminative nearest neighbor classification for visual category recognition - Zhang, Berg, et al. - 2006
137	Modeling the manifolds of images of handwritten digits - Hinton, Dayan, et al. - 1997
117	Spectral grouping using the Nyström method - Fowlkes, Belongie, et al. - 2004
99	Transformation invariance in pattern recognition-tangent distance and tangent propogation - Simard, Cun, et al. - 1998
76	Maximum Likelihood Estimation of Intrinsic Dimension - Levina, Bickel - 2005
60	A sparse texture representation using local affine regions - Lazebnik, Schmid, et al. - 2005
55	D.: Locally adaptive metric nearest-neighbor classification - Domeniconi, Peng, et al. - 2002
52	DR: An algorithm for finding intrinsic dimensionality of data - Fukunaga, Olsen - 1971
48	Discriminative common vectors for face recognition - Cevikalp, Neamtu, et al.
36	Experiments with an Extended Tangent Distance - Keysers, Dahmen, et al. - 2000
31	Estimating the intrinsic dimension of data with a fractal-based method - Camastra, Vinciarelli - 2002
30	Locally linear discriminant analysis for multimodally distributed classes for face recognition with a single model image - Kim, Kittler
29	Joint manifold distance: a new approach to appearance based clustering - Fitzgibbon, Zisserman - 2003
24	K-local hyperplane and convex distance nearest neighbor algorithms - Vincent, Bengio - 2001
23	The method of alternating projections and the method of subspace corrections in Hilbert space - Xu, Zikatanov
15	H.K.: LDA/SVM driven nearest neighbor classification - Peng, Heisterkamp, et al. - 2001
11	Adaptive Quasiconformal Kernel Nearest Neighbor Classification - Peng, Heisterkamp, et al.
10	The common vector approach and its relation to principal component analysis - Gülmezoğlu, Dzhafarov, et al.
9	Discriminative common vector method with kernels - Cevikalp, Neamtu, et al.
5	Learning nonlinear image manifolds by global alignment of local linear models - Verbeek - 2006
4	Efficient local flexible nearest neighbor classification - Domeniconi, Gunopulos - 2002
3	Protein fold recognition with K-local hyperplane distance nearest neighbor algorithm - Olkun - 2004
2	Cevikalp received the B.S. and M.S. degrees from the Electrical and Electronics Engineering Department of Eskisehir Sign Process Syst (2010) 61:61–73 73 Osmangazi University, Eskisehir, Turkey in 1999 and 2001, respectively. He received a Ph.D. degree in - Hakan