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2012 NIPS NeurIPS 2012

Semi-supervised Eigenvectors for Locally-biased Learning

Abstract

In many applications, one has 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.

🧭 Keyword Pioneer — locally-biased learning
🐣 Hot Topic Early Bird — semi-supervised learning
🐝 Cross-Pollinator — Artificial Intelligence, Computer Science, Computer Vision, Data Science & Analytics, Deep Learning, Healthcare & Medicine, Interdisciplinary, Knowledge & Reasoning, Machine Learning, Mathematics & Optimization, Natural Language Processing, Reinforcement Learning, Robotics, Speech & Audio

Authors

Toke Hansen , Michael W. Mahoney

Topics

Machine Learning > Core Methods > Representation Learning Machine Learning > Core Methods > Embedding Learning Machine Learning > Learning Types > Semi-Supervised Learning Machine Learning > Core Methods > Dimensionality Reduction Machine Learning > Learning Paradigms > Semi-Supervised Learning

Keywords

dimensionality reduction semi-supervised learning graph laplacian spectral analysis locally-biased learning eigenvector decomposition eigenvectors spectral method seed node semi-supervised eigenvector
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