Nonlinear Dimensionality Reduction with Side Information
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Date
2006
Authors
Ghodsi Boushehri, Ali
Journal Title
Journal ISSN
Volume Title
Publisher
University of Waterloo
Abstract
In this thesis, I look at three problems with important applications in data processing. Incorporating side information, provided by the user or derived from data, is a main theme of each of these problems. <br /><br /> This thesis makes a number of contributions. The first is a technique for combining different embedding objectives, which is then exploited to incorporate side information expressed in terms of transformation invariants known to hold in the data. It also introduces two different ways of incorporating transformation invariants in order to make new similarity measures. Two algorithms are proposed which learn metrics based on different types of side information. These learned metrics can then be used in subsequent embedding methods. Finally, it introduces a manifold learning algorithm that is useful when applied to sequential decision problems. In this case we are given action labels in addition to data points. Actions in the manifold learned by this algorithm have meaningful representations in that they are represented as simple transformations.
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Keywords
Mathematics, Statistics, Computer Science, Artificial intelligence, Machine learning, Dimensionality reduction, Manifold learning, Unsupervised learning, High dimensional data