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Activity Number: 247 - Sufficient Dimension Reduction and High-Dimensional Data
Type: Contributed
Date/Time: Monday, July 29, 2019 : 2:00 PM to 3:50 PM
Sponsor: Section on Nonparametric Statistics
Abstract #304337
Title: A Sparse Sufficient Dimension Reduction Approach for Multiclass Linear Discriminant Analysis
Author(s): Jing Zeng* and Qing Mai and Xin Zhang
Companies: Florida State University and Florida State University and Florida State University
Keywords: Multiclass linear discriminant analysis; Sufficient dimension reduction; Variable selection; High-dimension data

Sufficient dimension reduction has been a popular tool for multivariate analysis in the past few decades. In this paper, we study the problem of multiclass classification in ultra-high dimensions where the optimal classification can be achieved by projecting the data onto a linear dimension reduction subspace. The sparse dimension reduction subspace is used to drastically reduce the dimensionality while preserving all the useful information about classification. Specifically, we propose a fast and widely applicable algorithm for simultaneously estimating the dimension reduction subspace and selecting important variables. We establish both estimation consistency and dimension selection consistency of the proposed approach under mild regularity conditions in the ultra-high dimensional setting. We illustrate our approach in both simulated data and real data examples.

Authors who are presenting talks have a * after their name.

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