On Dimension Folding of Matrix or Array Valued Statistical Objects

Open Access
Author:
Kim, Min Kyung
Graduate Program:
Statistics
Degree:
Doctor of Philosophy
Document Type:
Dissertation
Date of Defense:
January 12, 2010
Committee Members:
  • Bing Li, Dissertation Advisor
  • Bing Li, Committee Chair
  • Naomi S Altman, Committee Member
  • Runze Li, Committee Member
  • C Lee Giles, Committee Member
Keywords:
  • Kronecker Envelop
  • Directional Regression
  • Sliced Inverse Regression
  • Sliced Average Variance Estimate
Abstract:
We consider a dimension reduction problem for regression or classification in which the predictors are matrix- or array-valued. This type of predictor arises when measurements are obtained for each combination of two or more underlying variables - for example, the voltage measured at different channels and times in electroencephalography data. For these applications it is desirable to preserve the array structure of the reduced predictor (e.g. time versus channel), but this cannot be achieved within the conventional dimension reduction formulation. In this dissertation we introduce a dimension reduction method, to be called dimension folding, for matrix- or array-valued predictors that preserves the array structure. In an application of dimension folding to an electroencephalography data set, we correctly classified 97 out of 122 subjects as alcoholic or nonalcoholic based on their electroencephalography in validation samples.