Simbed: Similarity-based embedding

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 5769 LNCS, Issue PART 2, 2009, Pages 95-104

  Lee, John A ^a   Verleysen, Michel ^b  

^a Imagerie Moléculaire et Radiothérapie Expérimentale   (Belgium)

^b Machine Learning Group   (Belgium)

Author keywords

Manifold learning; Multiscale optimization; Nonlinear dimensionality reduction; Similarity measure; Stochastic gradient

Indexed keywords

MANIFOLD LEARNING; MULTI-SCALE OPTIMIZATION; NONLINEAR DIMENSIONALITY REDUCTION; SIMILARITY MEASURE; STOCHASTIC GRADIENT;

BACKPROPAGATION; COMMUNICATION CHANNELS (INFORMATION THEORY); EMBEDDED SYSTEMS; NONLINEAR ANALYSIS; STOCHASTIC SYSTEMS;

NEURAL NETWORKS;

EID: 70450179140     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/978-3-642-04277-5_10     Document Type: Conference Paper

References (21)

1. Demartines, P., Hérault, J.: Curvilinear component analysis: A self-organizing neural network for nonlinear mapping of data sets. IEEE Transactions on Neural Networks 8(1), 148-154 (1997)
2. Evans, M., Hastings, N., Peacock, B.: Statistical Distributions, 3rd edn., New York (2000)
3. François, D., Wertz, V., Verleysen, M.: The concentration of fractional distances. IEEE Transactions on Knwoledge and Data Engineering 19(7), 873-886 (2007)
4. Hérault, J., Jaussions-Picaud, C., Guérin-Dugué, A.: Curvilinear component analysis for high dimensional data representation: I. Theoretical aspects and practical use in the presence of noise. In: Mira, J., Sánchez, J.V. (eds.) Proceedings of IWANN 1999, vol. II, pp. 635-644. Springer, Alicante (1999)
5. Hinton, G., Roweis, S.T.: Stochastic neighbor embedding. In: Becker, S., Thrun, S., Obermayer, K. (eds.) Advances in Neural Information Processing Systems (NIPS 2002), vol. 15, pp. 833-840. MIT Press, Cambridge (2003)
6. Kohonen, T.: Self-organization of topologically correct feature maps. Biological Cybernetics 43, 59-69 (1982)
7. Kramer, M.: Nonlinear principal component analysis using autoassociative neural networks. AIChE Journal 37(2), 233-243 (1991)
8. Kruskal, J.B.: Multidimensional scaling by optimizing goodness of fit to a non-metric hypothesis. Psychometrika 29, 1-28 (1964)
9. Lee, J.A., Verleysen, M.: Curvilinear distance analysis versus isomap. Neurocomputing 57, 49-76 (2004)
10. Lee, J.A., Verleysen, M.: Nonlinear dimensionality reduction. Springer, Heidelberg (2007)
11. Lee, J.A., Verleysen, M.: Quality assessment of dimensionality reduction: Rank-based criteria. Neurocomputing (2009)
12. Pearson, K.: On lines and planes of closest fit to systems of points in space. Philosophical Magazine 2, 559-572 (1901)
13. Robbins, H., Monro, S.: A stochastic approximation method. Annals of Mathematical Statistics 22, 400-407 (1951)
14. Roweis, S.T., Saul, L.K.: Nonlinear dimensionality reduction by locally linear embedding. Science 290 (5500), 2323-2326 (2000)
15. Sammon, J.W.: A nonlinear mapping algorithm for data structure analysis. IEEE Transactions on Computers CC-18(5), 401-409 (1969)
16. Saul, L.K., Weinberger, K.Q., Ham, J.H., Sha, F., Lee, D.D.: Spectral methods for dimensionality reduction. In: Chapelle, O., Schoelkopf, B., Zien, A. (eds.) Semisu-pervised Learning. MIT Press, Cambridge (2006)
17. Schölkopf, B., Smola, A., Müller, K.-R.: Nonlinear component analysis as a kernel eigenvalue problem. Neural Computation 10, 1299-1319 (1998)
18. Shepard, R.N.: The analysis of proximities: Multidimensional scaling with an unknown distance function (parts 1 and 2). Psychometrika 27, 125-140, 219-249 (1962)
19. Tenenbaum, J.B., de Silva, V., Langford, J.C.: A global geometric framework for nonlinear dimensionality reduction. Science 290 (5500), 2319-2323 (2000)
20. van der Maaten, L., Hinton, G.: Visualizing data using t-SNE. Journal of Machine Learning Research 9, 2579-2605 (2008)
21. Young, G., Householder, A.S.: Discussion of a set of points in terms of their mutual distances. Psychometrika 3, 19-22 (1938)