Nonlinear dimensionality reduction methods are often used to visualize high-dimensional data, although the existing methods have been designed for other related tasks such as manifold learning. It has been difficult to assess the quality of visualizations since the task has not been well-defined. We give a rigorous definition for a specific visualization task, resulting in quantifiable goodness measures and new visualization methods. The task is information retrieval given the visualization: to find similar data based on the similarities shown on the display. The fundamental tradeoff between precision and recall of information retrieval can then be quantified in visualizations as well. The user needs to give the relative cost of missing similar points vs. retrieving dissimilar points, after which the total cost can be measured. We then introduce a new method NeRV (neighbor retrieval visualizer) which produces an optimal visualization by minimizing the cost. We further derive a variant for supervised visualization; class information is taken rigorously into account when computing the similarity relationships. We show empirically that the unsupervised version outperforms existing unsupervised dimensionality reduction methods in the visualization task, and the supervised version outperforms existing supervised methods.

© 2010 Jarkko Venna, Jaakko Peltonen, Kristian Nybo, Helena Aidos and Samuel Kaski.

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The authors belong to the Adaptive Informatics Research Centre, a national CoE of the Academy of Finland, and to Helsinki Institute for Information Technology HIIT. Jarkko Venna is currently at Numos Ltd. JP was supported by the Academy of Finland, decision number 123983, and HA by the Portuguese Foundation for Science and Technology, scholarship number SFRH/BD/39642/2007. This work was also supported in part by the PASCAL2 Network of Excellence, ICT 216886.