Visualizing the quality of dimensionality reduction

Neurocomputing

Volumn 112, Issue , 2013, Pages 109-123

  Mokbel, Bassam ^a   Lueks, Wouter ^b,c   Gisbrecht, Andrej ^a   Hammer, Barbara ^a  

^a BIELEFELD UNIVERSITY   (Germany)

^b UNIVERSITY OF GRONINGEN   (Netherlands)

^c RADBOUD UNIVERSITY NIJMEGEN   (Netherlands)

Author keywords

Co ranking matrix; Data visualization; Nonlinear dimensionality reduction; Quality assessment

Indexed keywords

CO-RANKING; DIMENSIONALITY REDUCTION; DIMENSIONALITY REDUCTION METHOD; EVALUATION MEASURES; INTERPRETABILITY; LOW-DIMENSIONAL REPRESENTATION; NONLINEAR DIMENSIONALITY REDUCTION; QUALITY ASSESSMENT;

DATA VISUALIZATION; VISUALIZATION;

QUALITY CONTROL;

ACCURACY; ARTICLE; CLUSTER ANALYSIS; DATA ANALYSIS; DIMENSIONALITY REDUCTION TECHNIQUE; INTERMETHOD COMPARISON; KERNEL METHOD; MATHEMATICAL ANALYSIS; MATHEMATICAL AND STATISTICAL PROCEDURES; MATHEMATICAL MODEL; MEASUREMENT ERROR; PRIORITY JOURNAL; PROBABILITY; PROCESS DEVELOPMENT; PROCESS OPTIMIZATION; QUALITY CONTROL; SYSTEMATIC ERROR;

EID: 84877627360     PISSN: 09252312     EISSN: 18728286     Source Type: Journal    
DOI: 10.1016/j.neucom.2012.11.046     Document Type: Article

References (36)

1. Lee J., Verleysen M. Nonlinear Dimensionality Reduction 2007, Springer.
2. Bunte K., Biehl M., Hammer B. A general framework for dimensionality-reducing data visualization mapping. Neural Comput. 2012, 24(3):771-804.
3. van der Maaten L., Hinton G. Visualizing high-dimensional data using t-SNE. J. Mach. Learn. Res. 2008, 9:2579-2605.
4. L. van der Maaten, E. Postma, H. van den Herik, Dimensionality Reduction: A Comparative Review, Technical Report, Tilburg University Technical Report, TiCC-TR 2009-005, 2009.
5. Schölkopf B., Smola A.J., Müller K.R. Kernel principal component analysis. Adv. Kernel Methods. Support Vector Learn. 1999, 327-352.
6. Hinton G.E., Salakhutdinov R.R. Reducing the dimensionality of data with neural networks. Science 2006, 313:504-507.
7. Gorban A., Zinovyev A. Principal manifolds and graphs in practice. from molecular biology to dynamical systems. Int. J. Neural Syst. 2010, 20(3):219-232.
8. Borg I., Groenen P. Modern Multidimensional Scaling. Theory and Applications 1997, Springer-Verlag, New York.
9. Sammon J.W. A nonlinear mapping for data structure analysis. IEEE Trans. Comput. 1969, 18(5):401-409.
10. Tenenbaum J.B., De Silva V., Langford J.C. A Global Geometric Framework for Nonlinear Dimensionality Reduction. Science 2000, 290(5500):2319-2323.
11. Kohonen T. Self-Organizing Maps 1995, Springer.
12. Bishop C.M., Svensén M., Williams C.K.I. Gtm. the generative topographic mapping. Neural Comput. 1998, 10:215-234.
13. Roweis S.T., Saul L.K. Nonlinear dimensionality reduction by locally linear embedding. Science 2000, 290:2323-2326.
14. K. Weinberger, L.K. Saul, An introduction to nonlinear dimensionality reduction by maximum variance unfolding, in: Proceedings of the National Conference on Artificial Intelligence, Boston, MA, 2006, pp. 1683-1686.
15. M. Belkin, P. Niyogi, Laplacian eigenmaps and spectral techniques for embedding and clustering, in: Advances in Neural Information Processing Systems, vol. 14, MIT Press, 2001, pp. 585-591.
16. Zhang Z., Zha H. Principal manifolds and nonlinear dimension reduction via local tangent space alignment. SIAM J. Sci. Comput. 2002, 26:313-338.
17. Hinton G., Roweis S. Stochastic neighbor embedding. Adv. Neural Inf. Process. Syst. 2003, 15:833-840.
18. Venna J., Peltonen J., Nybo K., Aidos H., Kaski S. Information retrieval perspective to nonlinear dimensionality reduction for data visualization. J. Mach. Learn. Res. 2010, 11:451-490.
19. Lee J.A., Verleysen M. Nonlinear projection with the isotop method. ICANN, Lecture Notes in Computer Science 2002, vol. 2415:933-938. Springer.
20. Bunte K., Hammer B., Villmann T., Biehl M., Wismüller A. Neighbor embedding xom for dimension reduction and visualization. Neurocomputing 2011, 74(9):1340-1350.
21. Venna J., Kaski S. Local multidimensional scaling. Neural Networks 2006, 19(6):889-899.
22. Mardia K.V., Kent J.T., Bibby J.M. Multivariate Analysis 1979, Academic Press.
23. P. Demartines, J. Herault, Curvilinear Component Analysis: A Self-Organizing Neural Network for Nonlinear Mapping of Data Sets, 1997.
24. Lee J., Verleysen M. Quality assessment of dimensionality reduction. rank-based criteria. Neurocomputing 2009, 72(7-9):1431-1443.
25. Lee J., Verleysen M. Scale-independent quality criteria for dimensionality reduction. Pattern Recognition Lett. 2010, 31:2248-2257.
26. Aupetit M. Visualizing distortions and recovering topology in continuous projection techniques. Neurocomputing 2007, 70(7-9):1304-1330.
27. A. Ultsch, H. Siemon, Kohonen's self organizing feature maps for exploratory data analysis, in: Proceedings of the INNC'90, Kluwer, 1990, pp. 305-308.
28. Sun J., Fyfe C., Crowe M. Extending sammon mapping with Bregman divergences. Inf. Sci. 2012, 187:72-92.
29. S. France, D. Carroll, Development of an agreement metric based upon the rand index for the evaluation of dimensionality reduction techniques, with applications to mapping customer data, in: Proceedings of MLDM '07, Springer-Verlag, Berlin, Heidelberg, 2007, pp. 499-517.
30. H.-U. Bauer, K. Pawelzik, T. Geisel, A topographic product for the optimization of self-organizing feature maps, in: NIPS, 1991, pp. 1141-1147.
31. Chen L., Buja A. Local multidimensional scaling for nonlinear dimension reduction, graph drawing, and proximity analysis. J. Am. Stat. Assoc. 2009, 104(485):209-219.
32. Venna J., Kaski S. Local multidimensional scaling. Neural Networks 2006, 19:889-899.
33. S.A. Nene, S.K. Nayar, H. Murase, Columbia Object Image Library (COIL-20), Technical Report, February 1996.
34. Lecun Y., Bottou L., Bengio Y., Haffner P. Gradient-based learning applied to document recognition. Proc. IEEE 1998, 86(11):2278-2324.
35. A. Gisbrecht, B. Mokbel, B. Hammer, Linear basis-function t-SNE for fast nonlinear dimensionality reduction, in: IJCNN, IEEE, 2012, pp. 1-8.
36. Radovanović M., Nanopoulos A., Ivanović M. Hubs in space. popular nearest neighbors in high-dimensional data. J. Mach. Learn. Res. 2010, 11:2487-2531.