Deterministic graph spectral sparsification

An important technique in data analysis is principal component analysis or PCA. Given a covariance matrix S, in PCA we need to compute the eigenvector associated to a greatest eigenvalue of S in order to determine the direction of the so-called principal components.CONACYT – Consejo Nacional de Ciencia y TecnologíaPROCIENCI

Protocolos de comunicación y dispersión espectral de grafos.

Throughout the writing of this dissertation I have received a great deal of support and assistance. I would first like to acknowledge the “Consejo Nacional de Ciencia y Tecnolog´ıa (Conacyt)” for granting me a scholarship that allow me to finish this graduate course. Secondly, I like to thank my supervisor, Professor Dr. Marcos Villagra, whose expertise and methodology was invaluable in formulating the research questions. Your insightful feedback pushed me to sharpen my thinking and brought my work to a higher level. Big thanks also goes to the staff of researchers and professors at the “N´ucleo de Investigaci´on y Desarrollo Tecnol´ogico (NIDTEC)” from the Polytechnic School whose expertise and patience help to go through this academic program. I have been also benefited from conversations and discussions with several colleagues from NIDTEC which served me as insightful distractions for cleaning my mind and thinking clearer. I like to thank to Professor Dr. Inocencio Ortiz for his comments and suggestions and for the time and help he has dedicated to improve the writing of this thesis. And finally, I would like to thank my parents for their support through this entire learning process.CONACYT - Consejo Nacional de Ciencia y TecnologíaPROCIENCI