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Title: Performance analysis and robustness for dimension reduction Authors:  Shojaeddin Chenouri - University of Waterloo (Canada) [presenting]
Abstract: Information in the data often has far fewer degrees of freedom than the number of variables encoding the data. Dimensionality reduction attempts to reduce the number of variables used to describe the data. There are several dimensionality reduction methods available in the literature for linear and nonlinear manifolds. Each method works only under certain underlying assumptions. There is no universal agreement on how to assess and compare the performance of these different methods, and their robustness properties have not been studied. We attempt to discuss these issues and provide some answers. We introduce a goodness measure called local Spearman correlation for assessing performance and then employ it to define types of influence function and breakdown point to study the robustness of dimensionality reduction methods.