Joao DeAndrade

Joao DeAndrade

University of Massachusetts, Dartmouth

Oriented Mathematics


2002

Mentor: Dr. L. Gordon Kraft, Professor of Electrical & Computer Engineering & Dr. Kondagunta Sivaprasad, Professor of Electrical & Computer Engineering

An application of The Generalized Rayleigh Quotient to Artificial Neural Networks

The generalized Rayleigh quotient problem (GRQ) is defined by: R (x)=x’Ax/x’Bx where A and B are n x n matrices for all vectors x in R^n.

My research project is to use mathematical techniques to solve the generalized Rayleigh quotient to find the minimum and maximum values subject to a linear constraints of the form Cx=0 and Cx=d where C is third matrix. The problem of minimizing and maximizing the GRQ has application to Artificial Neural Networks (ANNs). ANNs is a computer system that learns by training and able to provide accurate output similar to human brain. ANNs are well suited for problem such as, handwritten word recognition, undersea mine detection, three-dimensional object recognition, and facial recognition.

Solving this particular problem will help understand how fast the ANNs are able to accomplish the learning task.

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