Abstract
Correlation analysis has always been a key technique for understanding data. However, traditional methods are only applicable on the whole data set, providing only global information on correlations. Correlations usually have a local nature and two variables can be directly and inversely correlated at different points in the same data set. This situation arises typically in nonlinear processes. In this paper we propose a method to visualize the distribution of local correlations along the whole data set using dimension reduction mappings. The ideas are illustrated through an artificial data example.
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References
Joshua B. Tenenbaum, Vin de Silva, and John C. Langford. A global geometric framework for nonlinear dimensionality reduction. Science, 290:2319–2323, Dec, 22 2000.
Sam T. Roweis and Lawrence K. Saul. Nonlinear dimensionality reduction by locally linear embedding. Science, 290:2323–2326, Dec., 22 2000.
Jianchang Mao and Anil K. Jain. Artificial neural networks for feature extraction and multivariate data projection. IEEE Transactions on Neural Networks, 6(2):296–316, March 1995.
David J. H. Wilson and George W. Irwin. RBF principal manifolds for process monitoring. IEEE Transactions on Neural Networks, 10(6):1424–1434, November 1999.
Teuvo Kohonen, Erkki Oja, Olli Simula, Ari Visa, and Jari Kangas. Engineering applications of the self-organizing map. Proceedings of the IEEE, 84(10):1358–1384, October 1996.
Esa Alhoniemi, Jaakko Hollmèn, Olli Simula, and Juha Vesanto. Process monitoring and modeling using the self-organizing map. Integrated Computer Aided Engineering, 6(1):3–14, 1999.
Teuvo Kohonen. Self-Organizing Maps. Springer-Verlag, 1995.
Christopher M. Bishop, Markus Svensen, and Christopher K. I. Williams. GTM: The generative topographic mapping. Neural Computation, 10(1):215–234, 1998.
M. Tipping and C. Bishop. Mixtures of probabilistic principal component analyzers. Neural Computation, 11(2):443–482, 1999.
Juha Vesanto. Som-based data visualization methods. Intelligent Data Analysis, 3(2):111–126, 1999.
Juha Vesanto and Esa Alhoniemi. Clustering of the self-organizing map. IEEE Transactions on Neural Networks, 11(3):586–600, May 2000.
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Blanco, I.D., Vega, A.A.C., González, A.B.D. (2002). Correlation Visualization of High Dimensional Data Using Topographic Maps. In: Dorronsoro, J.R. (eds) Artificial Neural Networks — ICANN 2002. ICANN 2002. Lecture Notes in Computer Science, vol 2415. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-46084-5_163
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DOI: https://doi.org/10.1007/3-540-46084-5_163
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