Estimation of Subspace Arrangements : Its Algebra and Statistics

ISBN-13: 9783639153774 / Angielski / Miękka / 2009 / 80 str.

Allen Y. Yang

Opis

In the literature of computer vision and image processing, a fundamental problem in modeling visual data is that multivariate image or video data tend to be heterogeneous or multimodal. That is, subsets of the data may have significantly different geometric or statistical properties. Recently, subspace arrangements have become an increasingly popular class of mathematical objects to use for modeling multivariate mixed data that are (approximately) piecewise linear. A subspace arrangement is a union of multiple subspaces. Each subspace can be used to model a homogeneous subset of the data. In this work, we study the problem of segmenting subspace arrangements. Built on past extensive study of subspace arrangements in algebraic geometry, we propose a principled framework that summarizes important algebraic properties and statistical facts that are crucial for making the inference of subspace arrangement models both efficient and robust, even when the given data are corrupted with noise and/or contaminated by outliers. The new solutions in many ways improve and generalize extant methods for modeling or clustering mixed data.

O autorze

Allen Y. Yang received his PhD in ECE from the University of
Illinois, Urbana. His primary research is in pattern
analysis of geometric and statistical models in high-dimensional
data spaces, and applications in motion segmentation, image
segmentation, and object recognition. Currently he is a research
scientist at the UC Berkeley.