Semi-supervised Eigenvectors for Locally-biased Learning

Toke Jansen Hansen, Michael W. Mahoney

Research output: Chapter in Book/Report/Conference proceedingArticle in proceedingsResearchpeer-review

Abstract

In many applications, one has side information, e.g., labels that are provided in a semi-supervised manner, about a specific target region of a large data set, and one wants to perform machine learning and data analysis tasks "nearby" that pre-specified target region. Locally-biased problems of this sort are particularly challenging for popular eigenvector-based machine learning and data analysis tools. At root, the reason is that eigenvectors are inherently global quantities. In this paper, we address this issue by providing a methodology to construct semi-supervised eigenvectors of a graph Laplacian, and we illustrate how these locally-biased eigenvectors can be used to perform locally-biased machine learning. These semi-supervised eigenvectors capture successively-orthogonalized directions of maximum variance, conditioned on being well-correlated with an input seed set of nodes that is assumed to be provided in a semi-supervised manner. We also provide several empirical examples demonstrating how these semi-supervised eigenvectors can be used to perform locally-biased learning.
Original languageEnglish
Title of host publicationAdvances in Neural Information Processing Systems 25
EditorsP. Bartlett, F. C. N. Pereira, C. J. C. Burges, L. Bottou, K. Q. Weinberger
Volume4
PublisherNeural Information Processing Systems Foundation
Publication date2012
Pages2537-2545
ISBN (Print)9781627480031
Publication statusPublished - 2012
Event26th Annual Conference on Neural Information Processing Systems (NIPS 2012) - Lake Tahoe, Nevada, United States
Duration: 3 Dec 20126 Dec 2012
http://nips.cc/Conferences/2012/

Conference

Conference26th Annual Conference on Neural Information Processing Systems (NIPS 2012)
CountryUnited States
CityLake Tahoe, Nevada
Period03/12/201206/12/2012
Internet address
SeriesAdvances in Neural Information Processing Systems
Volume25
ISSN1049-5258

Cite this

Hansen, T. J., & Mahoney, M. W. (2012). Semi-supervised Eigenvectors for Locally-biased Learning. In P. Bartlett, F. C. N. Pereira, C. J. C. Burges, L. Bottou, & K. Q. Weinberger (Eds.), Advances in Neural Information Processing Systems 25 (Vol. 4, pp. 2537-2545). Neural Information Processing Systems Foundation. Advances in Neural Information Processing Systems, Vol.. 25 http://books.nips.cc/papers/files/nips25/NIPS2012_1209.pdf