Quadratic Transform for Fractional Programs in Signal Processing and Machine Learning

Explore a comprehensive lecture on fractional programming (FP) techniques in signal processing and machine learning. Delve into the quadratic transform method, a cutting-edge approach for solving complex optimization problems. Begin with a brief overview of classic FP theory before focusing on the quadratic transform's applications, including its ability to tackle sum-of-ratios max problems where traditional methods fall short. Examine extensions of the quadratic transform to more intricate FP problems, such as matrix-ratio cases. Gain insights into the method's connections with other optimization techniques, including majorization-minimization, fixed-point iteration, weighted minimum mean squared error algorithm, Schur complement, and gradient projection. Analyze the convergence speed of the quadratic transform and discuss potential acceleration strategies. Learn how these advanced FP techniques apply to key metrics in signal processing and machine learning, such as signal-to-interference-plus-noise ratio, Cramer-Rao bound, support vector machine margin, and normalized cut for data clustering.