Manifold based local classifiers: Linear and nonlinear approaches

Journal of Signal Processing Systems

Volumn 61, Issue 1, 2010, Pages 61-73

  Cevikalp, Hakan ^a   Larlus, Diane ^b   Neamtu, Marian ^c   Triggs, Bill ^d   Jurie, Frederic ^e  

^a ESKISEHIR OSMANGAZI UNIVERSITY   (Turkey)

^b INRIA   (France)

^c VANDERBILT UNIVERSITY   (United States)

^d UNIV GRENOBLE ALPES   (France)

^e UNIVERSITÉ DE CAEN   (France)

Author keywords

Affine hull; Common vector; Convex hull; Distance learning; Image categorization; Local classifier; Manifold learning; Object recognition

Indexed keywords

AFFINE HULL; COMMON VECTORS; CONVEX HULL; IMAGE CATEGORIZATION; LOCAL CLASSIFIER; MANIFOLD LEARNING;

DISTANCE EDUCATION; FACE RECOGNITION; IMAGE SEGMENTATION; OBJECT RECOGNITION;

SUPPORT VECTOR MACHINES;

EID: 78650309274     PISSN: 19398018     EISSN: 19398115     Source Type: Journal    
DOI: 10.1007/s11265-008-0313-4     Document Type: Article

References (35)

1. Simard, P., Le Cun, Y., Denker, J., & Victorri, B. (1998). Transformation invariance in pattern recognition-tangent distance and tangent propagation, lecture notes in computer science (vol. 1524, pp. 239-274). Berlin: Springer.
2. Peng, J., Heisterkamp, D. R., & Dai, H. K. (2003). LDA/SVM Driven Nearest Neighbor Classification. IEEE Trans Neural Netw, 14, 940-942. doi:10.1109/TNN.2003.813835.
3. Hastie, T., & Tibshirani, R. (1996). Discriminant adaptive nearest neighbor classification. IEEE Trans. PAMI, 18(6), 607-616. (Pubitemid 126773896)
4. Vincent, P., & Bengio, Y. (2001). K-local hyperplane and convex distance nearest neighbor algorithms. Adv Neural Inf Process Syst, 14, 985-992.
5. Domeniconi, C., & Gunopulos, D. (2002). Efficient local flexible nearest neighbor classification. In Proceedings of the 2nd SIAM International Conference on Data Mining.
6. Zhang, H., Berg, a. C., Maire, M., & Malik, J. (2006). SVM-KNN: discriminative nearest neighbor classification for visual category recognition, in CVPR 2006 (pp. 2126-2136).
7. Peng, J., Heisterkamp, D. R., & Dai, H. K. (2004). Adaptive quasiconformal kernel nearest neighbor classification. IEEE Trans Pattern Anal Mach Intell, 28, 656-661. doi:10.1109/TPAMI.2004. 1273978.
8. Domeniconi, C., Peng, J., & Gunopulos, D. (2002). Locally adaptive metric nearest-neighbor classification. IEEE Trans Pattern Anal Mach Intell, 24, 1281-1285. doi:10.1109/TPAML 2002.1033219.
9. Olkun, O. (2004). Protein fold recognition with K-local hyperplane distance nearest neighbor algorithm. In Proceedings of the 2nd European Workshop on data Mining and Text Mining in Bioinformatics, pp. 51-57.
10. Hinton, G. E., Dayan, P., & Revow, M. (1997). Modeling the manifolds of images of handwritten digits. IEEE Trans Neural Netw, 18, 65-74. doi:10.1109/72.554192. (Pubitemid 127767781)
11. Roweis, S. T., & Saul, L. K. (2000). Nonlinear dimensionality reduction by locally linear embedding. Science, 290, 2323-2326. doi:10.1126/science.290.5500.2323. (Pubitemid 32041578)
12. Verbeek, J. (2006). Learning non-linear image manifolds by global alignment of local linear models. IEEE Trans PAMI, 28, 1236-1250.
13. Cevikalp, H., Neamtu, M., & Wilkes, M. (2005). Discriminative common vectors for face recognition. IEEE Trans PAMI, 27, 4-13. (Pubitemid 40195893)
14. Kim, T.-K., & Kittler, J. (2005). Locally linear discriminant analysis for multimodally distributed classes for face recognition with a single model image. IEEE Trans PAMI, 27, 318-327. (Pubitemid 40377325)
15. Fitzgibbon, A. W., & Zisserman, A. (2003). Joint manifold distance: a new approach to appearance based clustering. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition.
16. Zhang, J., Marszalek, M., Lazebnik, S., & Schmidt, C. (2006). Local features and kernels for classification of texture and object categories: a comprehensive study. In Proceedings of the Computer Vision and Pattern Recognition Workshop.
17. Tenenbaum, J. B., Silva, V., & Langford, J. C. (2000). A global geometric framework for nonlinear dimensionality reduction. Science, 290, 2319-2323. doi:10.1126/science.290.5500.2319. (Pubitemid 32041577)
18. Gulmezoglu, M. B., Dzhafarov, V., & Barkana, A. (2001). The common vector approach and its relation to principal component analysis. IEEE Trans Speech Audio Process, 9(6), 655-662. doi:10.1109/89.943343. (Pubitemid 32945712)
19. Boyd, S. (2004). Convex optimization pp. 399-401. Cambridge, UK: Cambridge University Press.
20. Schölkopf, B., Smola, A. J., & Muller, K. R. (1998). Nonlinear component analysis as a kernel eigenvalue problem. Neural Comput, 10, 1299-1319. doi: 10.1162/089976698300017467. (Pubitemid 128463674)
21. Cevikalp, H., Neamtu, M., & Wilkes, M. (2006). Discriminative common vector method with kernels. IEEE Trans Neural Netw, 17, 1550-1565. doi:10.1109/TNN.2006.881485. (Pubitemid 44824267)
22. Xu, J., & Zikatanov, L. (2002). The method of alternating projections and the method of subspace corrections in hilbert space. JAm Math Soc, 15, 573-597. doi:10.1090/S0894-0347-02-00398-3.
23. Fei-Fei, L. Fergus, R., & Perona, P. (2004) Learning generative visual models from few training examples: an incremental Bayesian approach tested on 101 object categories. In Proceedings of the IEEE CVPR Workshop of Generative Model Based Vision.
24. USPS dataset of handwritten characters created by the US Postal Service. Retrieved from ftp://ftp.kyb.tuebingen.mpg.de/pub/bs/data.
25. Keysers, D., Dohmen, J., Theiner, T., & Ney, H. (2000). Experiments with an extended tangent distance. In Proceedings of the 15th International Conference on Pattern Recognition, vol. 2, pp. 38-42.
26. C codes for computing tangent distances. Retrieved from http:// www-i6.informatik.rwth-aachen.de/~keysers/td/.
27. Golub, G. H., & Loan, C. F.-V. (1996). Matrix computations (3rd ed.). Baltimore, MD: Johns Hopkins University Press.
28. UCI-benchmark repository-a huge collection of artificial and real world data sets. University of California Irvine. Retrieved from http://www.ics.edu/ ~mlearn/MLRepository.html.
29. Csurka, G., Dance, C., Fan, L., Willamowski, J., Bray, C. (2004). Visual categorization with bags of keypoints. In Proceedings of the ECCV Workshop on Statistical Learning for Computer Vision.
30. Lazebnik, S., Schmid, C., & Ponce, J. (2005). A sparse texture representation using local affine regions. IEEE Trans PAMI, 27(8), 1265-1278. (Pubitemid 41245056)
31. Fowlkes, C., Belogie, S., Chung, F., & Malik, J. (2004). Spectral grouping using the Nystrom method. IEEE Trans PAMI, 26, 1-12.
32. Saul, L. K., & Roweis, S. T. (2003). Think globally, fit locally: unsupervised learning of low dimensional manifolds. J Mach Learn Res, 4, 119-155.
33. Levina, E., & Bickel, P. J. (2005). Maximum likelihood estimation of intrinsic dimension. In L. K. Saul, Y. Weiss, & L. Bottou (Eds.), Advances in neural information processing system, 17 (pp. 777-784). Cambridge, MA: MIT Press.
34. Camastra, F., & Vinciarelli, A. (2002). Estimating the intrinsic dimension of data with a fractal-based method. IEEE Trans Pattern Anal Mach Intell, 24(10), 1404-1407. doi:10.1109/ TPAMI.2002.1039212.
35. Fukunaga, K., & Olsen, D. R. (1971). An algorithm for finding intrinsic dimensionality of data. IEEE Trans Comput, C-20, 176-183. doi:10.1109/T-C.1971.223208.