Abstract
To cope with high-dimensional data dimensionality reduction has become an increasingly important problem class. In this paper we propose an iterative particle swarm embedding algorithm (PSEA) that learns embeddings of low-dimensional representations for high-dimensional input patterns. The iterative method seeks for the best latent position with a particle swarm-inspired approach. The construction can be accelerated with k-d-trees. The quality of the embedding is evaluated with the nearest neighbor data space reconstruction error, and a co-ranking matrix based measure. Experimental studies show that PSEA achieves competitive or even better embeddings like the related methods locally linear embedding, and ISOMAP.
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References
Abraham, A., Grosan, C., Ramos, V. (eds.): Swarm Intelligence in Data Mining. SCI, vol. 34. Springer (2006)
Bentley, J.L.: Multidimensional binary search trees used for associative searching. Communications of the ACM 18(9), 509–517 (1975)
Gieseke, F., Polsterer, K.L., Thom, A., Zinn, P., Bomanns, D., Dettmar, R.-J., Kramer, O., Vahrenhold, J.: Detecting quasars in large-scale astronomical surveys. In: International Conference on Machine Learning and Applications (ICMLA), pp. 352–357 (2010)
Herrmann, L., Ultsch, A.: The Architecture of Ant-Based Clustering to Improve Topographic Mapping. In: Dorigo, M., Birattari, M., Blum, C., Clerc, M., Stützle, T., Winfield, A.F.T. (eds.) ANTS 2008. LNCS, vol. 5217, pp. 379–386. Springer, Heidelberg (2008)
Jolliffe, I.: Principal component analysis. Springer series in statistics. Springer, New York (1986)
Kao, Y., Cheng, K.: An ACO-Based Clustering Algorithm. In: Dorigo, M., Gambardella, L.M., Birattari, M., Martinoli, A., Poli, R., Stützle, T. (eds.) ANTS 2006. LNCS, vol. 4150, pp. 340–347. Springer, Heidelberg (2006)
Kennedy, J., Eberhart, R.: Particle swarm optimization. In: Proceedings of IEEE International Conference on Neural Networks, pp. 1942–1948 (1995)
Kohonen, T.: Self-Organizing Maps. Springer (2001)
Kramer, O.: Dimensionalty reduction by unsupervised nearest neighbor regression. In: International Conference on Machine Learning and Applications (ICMLA), pp. 275–278. IEEE (2011)
Kramer, O.: On unsupervised nearest-neighbor regression and robust loss functions. In: International Conference on Artificial Intelligence, pp. 164–170 (2012)
Lawrence, N.D.: Probabilistic non-linear principal component analysis with gaussian process latent variable models. Journal of Machine Learning Research 6, 1783–1816 (2005)
Lee, J.A., Verleysen, M.: Quality assessment of dimensionality reduction: Rank-based criteria. Neurocomputing 72(7-9), 1431–1443 (2009)
Meinicke, P.: Unsupervised Learning in a Generalized Regression Framework. PhD thesis, University of Bielefeld (2000)
Meinicke, P., Klanke, S., Memisevic, R., Ritter, H.: Principal surfaces from unsupervised kernel regression. IEEE Transactions on Pattern Analysis and Maching Intelligence 27(9), 1379–1391 (2005)
O’Neill, M., Brabazon, A.: Self-organizing swarm (SOSwarm) for financial credit-risk assessment (2008)
Roweis, S.T., Saul, L.K.: Nonlinear dimensionality reduction by locally linear embedding. Science 290, 2323–2326 (2000)
Shi, Y., Eberhart, R.: A modified particle swarm optimizer. In: Proceedings of the International Conference on Evolutionary Computation, pp. 69–73 (1998)
Smola, A.J., Mika, S., Schölkopf, B., Williamson, R.C.: Regularized principal manifolds. Journal of Machine Learning Research 1, 179–209 (2001)
Tan, S., Mavrovouniotis, M.: Reducing data dimensionality through optimizing neural network inputs. AIChE Journal 41(6), 1471–1479 (1995)
Tenenbaum, J.B., Silva, V.D., Langford, J.C.: A global geometric framework for nonlinear dimensionality reduction. Science 290, 2319–2323 (2000)
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Kramer, O. (2012). A Particle Swarm Embedding Algorithm for Nonlinear Dimensionality Reduction. In: Dorigo, M., et al. Swarm Intelligence. ANTS 2012. Lecture Notes in Computer Science, vol 7461. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-32650-9_1
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DOI: https://doi.org/10.1007/978-3-642-32650-9_1
Publisher Name: Springer, Berlin, Heidelberg
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