Abstract
The ISOMAP algorithm has recently emerged as a promising dimensionality reduction technique to reconstruct nonlinear low-dimensional manifolds from the data embedded in high-dimensional spaces, by which the high-dimensional data can be visualized nicely. One of its advantages is that only one parameter is required, i.e. the neighborhood size or K in the K nearest neighbors method, on which the success of the ISOMAP algorithm depends. However, it’s an open problem how to select a suitable neighborhood size. In this paper, we present an effective method to select a suitable neighborhood size, which is much less time-consuming than the straightforward method with the residual variance, while yielding the same results. In addition, based on the characteristics of the Euclidean distance metric, a faster Dijkstra-like shortest path algorithm is used in our method. Finally, our method can be verified by experimental results very well.
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References
Cleveland, W.S.: Visualizing Data. AT&T Bell Laboratories, Murray Hill, NJ, Hobart Press, Summit NJ (1993)
Keim, D.A.: Designing Pixel-Oriented Visualization Techniques: Theory and Applications. IEEE Transactions on Visualization and Computer Graphics 6(1), 59–78 (2000)
Inselberg, A., Dimsdale, B.: Parallel Coordinates: A Tool for Visualizing Multi-Dimensional Geometry. In: Visualization 1990, San Francisco, CA, pp. 361–370 (1990)
Kandogan, E.: Visualizing Multi-dimensional Clusters,Trends,and Outliers Using Star Coordinates. In: Proceedings of the 7th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, San Francisco, USA, pp. 107–116 (2001)
LeBlanc, J., Ward, M.O., Wittels, N.: Exploring N-Dimensional Databases. In: Visualization 1990, San Francisco, CA, pp. 230–239 (1990)
Johnson, B.: Visualizing Hierarchical and Categorical Data. Ph.D. Thesis, Department of Computer Science, University of Maryland (1993)
Tufte, E.R.: The Visual Display of Quantitative Information. Graphics Press, Cheshire (1983)
Pickett, R.M., Grinstein, G.G.: Iconographic Displays for Visualizing Multidimensional Data. In: Proceedings of IEEE Conference on Systems, Man and Cybernetics, pp. 514–519. IEEE Press, Piscataway (1988)
Mao, J.C., Jain, A.K.: Artificial Neural Networks for Feature Extraction and Multivariate Data Projection. IEEE Transactions on Neural Networks 6(2), 296–317 (1995)
Naud, A., Duch, W.: Interactive Data Exploration Using MDS Mapping. In: Proceedings of the 5th Conference on Neural Networks and Soft Computing, Zakopane, Poland, pp. 255–260 (2000)
Shao, C., Huang, H.K.: Improvement of Data Visualization Based on SOM. In: Proceedings of International Symposium on Neural Networks, Dalian, China, pp. 707–712 (2004)
Tenenbaum, J.B., de Silva, V., Langford, J.C.: A Global Geometric Framework for Nonlinear Dimensionality Reduction. Science 290(22), 2319–2323 (2000)
de Silva, V., Tenenbaum, J.B.: Unsupervised Learning of Curved Manifolds. In: Proceedings of MSRI Workshop on Nonlinear Estimation and Classification, Berkeley, USA, pp. 453–466 (2001)
Vlachos, M., Domeniconi, C., Gunopulos, D., Kollios, G., Koudas, N.: Non-Linear Dimensionality Reduction Techniques for Classification and Visualization. In: Proceedings of the 8th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, Edmonton, Canada, pp. 645–651 (2002)
Roweis, S.T., Saul, L.K.: Nonlinear Dimensionality Reduction by Locally Linear Embedding. Science 290(22), 2323–2326 (2000)
Hadid, A., Pietikäinen, M.: Efficient Locally Linear Embeddings of Imperfect Manifolds. In: Perner, P., Rosenfeld, A. (eds.) MLDM 2003. LNCS, vol. 2734, pp. 188–201. Springer, Heidelberg (2003)
Belkin, M., Niyogi, P.: Laplacian Eigenmaps for Dimensionality Reduction and Data Representation. Neural Computation 15(6), 1373–1396 (2003)
Balasubramanian, M., Schwartz, E.L., Tenenbaum, J.B., de Silva, V., Langford, J.C.: The Isomap Algorithm and Topological Stability. Science 295(5552), 7–7 (2002)
Kouropteva, O., Okun, O., Pietikäinen, M.: Selection of the Optimal Parameter Value for the Locally Linear Embedding Algorithm. In: Proceedings of the 1st International Conference on Fuzzy Systems and Knowledge Discovery (FSKD 2002), Singapore, pp. 359–363 (2002)
Bernstein, M., de Silva, V., Langford, J.C., Tenenbaum, J.B.: Graph approximations to geodesics on embedded manifolds. Technical report, Department of Psychology, Stanford University (2000)
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Shao, C., Huang, H. (2005). Selection of the Optimal Parameter Value for the ISOMAP Algorithm. In: Gelbukh, A., de Albornoz, Á., Terashima-Marín, H. (eds) MICAI 2005: Advances in Artificial Intelligence. MICAI 2005. Lecture Notes in Computer Science(), vol 3789. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11579427_40
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DOI: https://doi.org/10.1007/11579427_40
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