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SHOJA’EDDIN CHENOURI - University of Waterloo

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Measures of robustness for dimensionality reduction
09 April 2015 from 4:00 PM to 5:00 PM
201 Thomas Bldg.
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Nonlinear dimensionality reduction has been of much interest in the recent years and many methods have been introduced in the literature such as local linear embedding, Isomap, Spanifold, etc. Each method works only under certain underlying assumptions and their robustness is generally unknown. In the example of PCA, for linear dimensionality reduction, a few robust alternatives have been introduced. In the nonlinear framework, the robustness of dimensionality reduction methods has not been explored thoroughly. Unlike estimation problems, there is no general framework for robustness in dimensionality reduction. In this talk we attempt to tackle this problem. We introduce a goodness measure called local Spearman correlation for assessing the performance of dimensionality reduction methods. Based on this goodness measure, a type of influence function and breakdown point are defined to study the robustness of dimensionality reduction methods.


This is an ongoing joint work with PhD student Jiaxi Liang and Professor Christopher G. Small from University of Waterloo. 

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