Recently, independent component analysis (ICA) - a popular method for blind
signal separation - has found interest within the machine learning theory
community due to nice algebraic properties of its cumulant-based solutions and
due to recent observations that the mathematics underlying ICA also underly
other problems of interest. This talk will explore a unifying algorithmic
framework for a number of unsupervised machine learning problems including ICA,
learning mixtures of spherical Gaussians, spectral clustering, and orthogonal
tensor decompositions. The framework is based on maximizing certain functions
on the unit sphere in order to recover a hidden basis of the space. The
resulting algorithms for hidden basis recovery includes fast-converging fixed
point methods such as the classic power iteration for matrix eigenvector
recovery and its tensorial extension as special cases.
This talk will also highlight applications of hidden basis recovery within
spectral clustering and blind signal separation.
James Voss is a PhD student at the Ohio State University. He went to Michigan
State University for his undergrad, receiving B.S. degrees in Mathematics and
in Computer Science. His research interests are within theoretical aspects of
machine learning. He has done work within independent component analysis,
spectral clustering, and learning the parameters of mixture of Gaussian
distributions with theoretical guarantees.
Dr. Jiayu Zhou and Dr. Anil K. Jain