Spring Seminar Series - April 21, 2005
University of Minnesota
School of Statistics
College of Liberal Arts
Techniques for Application-Driven Dimension Reduction of Large Datasets
Anuj Srivastava
Department of Statistics
Florida State University
Thursday, April 21, 2005
3:30 PM, 115
Ford Hall
Minneapolis, East Bank Campus
Social at 3:00 PM, 300 Ford Hall
Abstract
In
many applications dealing with statistical analysis of real
data, we are confronted with large data sizes. One often needs to
project the data down to smaller dimensions before any statistical
modeling or testing can become feasible. This situation arises for
example in image analysis, meteorology, and oceanography.
Simplicity and efficiency of linear transformations make them a
popular tool for reducing dimension before or during statistical
analysis. Commonly used techniques are principal component
analysis, Fisher's discriminant analysis, independent component
analysis, etc. Linear transformations with natural orthogonality
constraints can be represented as elements of Stiefel and
Grassmann manifolds. We advocate that the choice of a
transformation for dimension reduction is not standard; it is
dictated by the application and the data set, and can be
formulated as an optimization problem on these above-mentioned
manifolds. We demonstrate this idea by deriving dimension-reducing
transformations in several applications, including image-based
recognition of objects and content-based retrieval of images.