2011 | OriginalPaper | Chapter
Multi-Subspace Representation and Discovery
Authors : Dijun Luo, Feiping Nie, Chris Ding, Heng Huang
Published in: Machine Learning and Knowledge Discovery in Databases
Publisher: Springer Berlin Heidelberg
Activate our intelligent search to find suitable subject content or patents.
Select sections of text to find matching patents with Artificial Intelligence. powered by
Select sections of text to find additional relevant content using AI-assisted search. powered by
This paper presents the multi-subspace discovery problem and provides a theoretical solution which is guaranteed to recover the number of subspaces, the dimensions of each subspace, and the members of data points of each subspace simultaneously. We further propose a data representation model to handle noisy real world data. We develop a novel optimization approach to learn the presented model which is guaranteed to converge to global optimizers. As applications of our models, we first apply our solutions as preprocessing in a series of machine learning problems, including clustering, classification, and semi-supervised learning. We found that our method automatically obtains robust data presentation which preserves the affine subspace structures of high dimensional data and generate more accurate results in the learning tasks. We also establish a robust standalone classifier which directly utilizes our sparse and low rank representation model. Experimental results indicate our methods improve the quality of data by preprocessing and the standalone classifier outperforms some state-of-the-art learning approaches.