PASCAL - Pattern Analysis, Statistical Modelling and Computational Learning

Nonlinear dimensionality reduction as information retrieval
Jarkko Venna and Samuel Kaski
In: Proceedings of AISTATS 2007, the 11th International Conference on International Conference on Artificial Intelligence and Statistics (2007) Omnipress .

Abstract

Nonlinear dimensionality reduction has so far been treated either as a data representation problem or as a search for a lower-dimensional manifold embedded in the data space. A main application for both is in information visualization, to make visible the neighborhood or proximity relationships in the data, but neither approach has been designed to optimize this task. We give such visualization a new conceptualization as an information retrieval problem; a projection is good if neighbors of data points can be retrieved well based on the visualized projected points. This makes it possible to rigorously quantify goodness in terms of precision and recall. A method is introduced to optimize retrieval quality; it turns out to be an extension of Stochastic Neighbor Embedding, one of the earlier nonlinear projection methods, for which we give a new interpretation: it optimizes recall. The new method is shown empirically to outperform existing dimensionality reduction methods.

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EPrint Type:Book Section
Project Keyword:Project Keyword UNSPECIFIED
Subjects:Theory & Algorithms
ID Code:3560
Deposited By:Samuel Kaski
Deposited On:11 February 2008