Title
Simultaneous Fractional Discriminant Analysis: Applications to Face Recognition
Speaker
John Draper, The Ohio State University
Abstract
Linear Discriminant Analysis (LDA) has served as a standard technique in classification for many years. Many improvements have been proposed to boost the performance of LDA yet maintain its simplicity, intuitive appeal, and robust nature. Lotlikar and Kothari proposed fractional LDA (F-LDA) as an improved version of LDA. However, for a large number of classes, F-LDA is not feasible to implement in real time due to huge computational effort in the sequential search process for each dimension to be reduced. In addition, F-LDA is a directed projection pursuit technique, which takes several iterations to reduce just one dimension. Our research is focused on modifying these methods to be applicable to the face recognition problem (high-dimensional image data, large number of classes). Simultaneous Adaptive Fractional Discriminant Analysis (SAFDA) is a procedure developed specifically to learn a specified or fixed low-dimensional subspace in which classes are well separated by sequentially downweighting all dimensions to be removed simultaneously. Via analysis of a weighted between class scatter matrix of whitened data, S~B, the best projected space is learned through a directed projection pursuit method that focuses on class separation in the reduced space (rather than the full space like LDA). An adaptive kernel (Gaussian) was found to be the most suitable to avoid extra time considerations inherent in cross-validation by allowing the data to determine optimal bandwidth choice. While the SAFDA algorithm showed a marked improvement over standard LDA techniques in terms of classification, the additional computational time, compared to LDA, was minimal in situations involving a small number of classes (MNIST) as well as a large number of classes (AR face database). SAFDA also provides a procedure that matches (or in some cases, outperforms) the F-LDA benchmark in terms of classification, yet is much more feasible in computational time and effort.
Dr. John Draper is a recent PhD graduate of the Department of Statistics at The Ohio State University with an Interdisciplinary Specialization in Biomedical Imaging under Dr. Prem Goel and is currently a Visiting Assistant Professor at Ohio State. His research interests include improving classification/regression techniques (specifically in the realm of face recognition) for both accuracy and speed. John has taught a variety of courses in statistical techniques in across a wide variety of disciplines (mathematics, statistics, business, public health, etc.). John is an alumnus of TBDBITL (Ohio State Marching Band) and remains an active member of The Ohio State University Basketball Pep Band.
