Kernel-based framework for spectral dimensionality reduction and clustering formulation: a theoretical study

• BLANCO VALENCIA, Xiomara Patricia ^[1] ; BECERRA, M. A. ^[2] ; CASTRO OSPINA, A. E. ^[3] ; ORTEGA ADARME, M. ^[4] ; VIVEROS MELO, D. ^[6] ; PELUFFO ORDÓÑEZ, D. H. ^[5] ; Juan Carlos Alvarado Pérez
  1. [1] Universidad de Salamanca

     Universidad de Salamanca

     Salamanca, España

     
  2. [2] Institución Universitaria Salazar y Herrera

     Institución Universitaria Salazar y Herrera

     Colombia

     
  3. [3] Instituto Tecnológico Metropolitano

     Instituto Tecnológico Metropolitano

     Colombia

     
  4. [4] Universidad de Nariño

     Universidad de Nariño

     Colombia

     
  5. [5] Universidad Técnica del Norte

     Universidad Técnica del Norte

     San Miguel De Ibarra, Ecuador

     
  6. [6] Coorporación Universitaria Autónoma de Nariño

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• Localización: ADCAIJ: Advances in Distributed Computing and Artificial Intelligence Journal, ISSN-e 2255-2863, Vol. 6, Nº. 1, 2017, págs. 31-40
• Idioma: inglés
• DOI: 10.14201/ADCAIJ2017613140
• Enlaces
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• Resumen

  • This work outlines a unified formulation to represent spectral approaches for both dimensionality reduction and clustering. Proposed formulation starts with a generic latent variable model in terms of the projected input data matrix.Particularly, such a projection maps data onto a unknown high-dimensional space. Regarding this model, a generalized optimization problem is stated using quadratic formulations and a least-squares support vector machine.The solution of the optimization is addressed through a primal-dual scheme.Once latent variables and parameters are determined, the resultant model outputs a versatile projected matrix able to represent data in a low-dimensional space, as well as to provide information about clusters. Particularly, proposedformulation yields solutions for kernel spectral clustering and weighted-kernel principal component analysis.

• Referencias bibliográficas
  • Aldrich, C. and Auret, L., 2013. Statistical Learning Theory and Kernel-Based Methods. In Unsupervised Process Monitoring and Fault Diagnosis...
  • Alvarado-Pérez, J. C. and Peluffo-Ordó’nez, D. H., 2015. Artificial and Natural Intelligence Integration. In 12th International Conference...
  • Alvarado-Pérez, J. C., Peluffo-Ordó-ez, D. H., and Therón, R., 2015. Bridging the gap between human knowledge and machine learning. ADCAIJ:...
  • Alzate, C. and Suykens, J. A. K., 2010. Multiway spectral clustering with out-of-sample extensions through weighted kernel PCA. Pattern Analysis...
  • Belanche Mu-oz, L. A., 2013. Developments in kernel design. In European Symposium on Artificial Neural Networks, Computational Intelligence...
  • Domeniconi, C., Peng, J., and Yan, B., 2011. Composite kernels for semi-supervised clustering. Knowledge and information systems, 28(1):99–116....
  • Filippone, M., Camastra, F., Masulli, F., and Rovetta, S., 2008. A survey of kernel and spectral methods for clustering. Pattern recognition,...
  • González, F., Bermeo, D., Ramos, L., and Nasraoui, O., 2012. On the Robustness of Kernel-Based Clustering. Progress in Pattern Recognition,...
  • Ham, J., Lee, D. D., Mika, S., and Schölkopf, B., 2004. A kernel view of the dimensionality reduction of manifolds. In Proceedings of the...
  • Harchaoui, Z., Bach, F., Cappé, O., and Moulines, E., 2013. Kernel-based methods for hypothesis testing: a unified view. IEEE Signal Processing...
  • Huang, H., Chuang, Y., and Chen, C., 2012. Multiple Kernel Fuzzy Clustering. Fuzzy Systems, IEEE Transactions on, 20(1):120–134.
  • Langone, R., Alzate, C., and Suykens, J. A., 2013. Kernel spectral clustering with memory effect. Physica A: Statistical Mechanics and its...
  • Molina-Giraldo, S., Álvarez-Meza, A., Peluffo-Ordo-ez, D., and Castellanos-Domínguez, G., 2012. Image Segmentation Based on Multi-Kernel Learning...
  • Peluffo-Ordó-ez, D. H., Lee, J. A., Verleysen, M., Rodr?guez, J. L., and Castellanos-Dom?nguez, G., 2014. Unsupervised relevance analysis...
  • Peluffo-Ordónez,D., Garcia-Vega, S., Langone, R., Suykens, J., Castellanos-Dominguez,G. et al., 2013. Kernel spectral clustering for dynamic...
  • Peluffo-Ordonez,D. H., Aldo Lee, J., and Verleysen,M., 2014. Generalized kernel framework for unsupervised spectral methods of dimensionality...
  • Peluffo-Ordónez, D. H., Alvarado-Pérez, J. C., Lee, J. A., and Verleysen, M., 2015. Geometrical homotopy for data visualization. In European...
  • Peluffo-Ordó-ez, D. H., Alzate, C., Suykens, J. A., and Castellanos-Domínguez, G., 2014a. Optimal Data Projection for Kernel Spectral Clustering....
  • Peluffo-Ordó-ez, D. H., Lee, J. A., and Verleysen,M., 2014b. Recent methods for dimensionality reduction: A brief comparative analysis. In...
  • Peluffo Ordo-ez, D. H., Lee, J. A., Verleysen, M., Rodriguez, J. L., Castellanos-Dominguez, G. et al., 2015. Unsupervised relevance analysis...
  • Schölkopf, B. and Smola, A. J., 2002. Learning with Kernels.
  • Seeland, M., Karwath, A., and Kramer, S., 2012. A structural cluster kernel for learning on graphs. In Proceedings of the 18th ACM SIGKDD...
  • Wolf, L. and Bileschi, S., 2005. Combining variable selection with dimensionality reduction. In 2005 IEEE Computer Society Conference on Computer...
  • Wolf, L. and Shashua, A., 2005. Feature selection for unsupervised and supervised inference: The emergence of sparsity in a weight-based approach....
  • Wu, Y., Ma, W., Gong, M., Li, H., and Jiao, L., 2015. Novel Fuzzy Active Contour Model With Kernel Metric for Image Segmentation. Applied...
  • Zelnik-manor, L. and Perona, P., 2004. Self-tuning spectral clustering. In Advances in Neural Information Processing Systems 17, pages 1601–1608.MIT...