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Interactive Knowledge-Based Kernel PCA

  • Conference paper

Part of the Lecture Notes in Computer Science book series (LNAI,volume 8725)

Abstract

Data understanding is an iterative process in which domain experts combine their knowledge with the data at hand to explore and confirm hypotheses. One important set of tools for exploring hypotheses about data are visualizations. Often, however, traditional, unsupervised dimensionality reduction algorithms are used for visualization. These tools allow for interaction, i.e., exploring different visualizations, only by means of manipulating some technical parameters of the algorithm. Therefore, instead of being able to intuitively interact with the visualization, domain experts have to learn and argue about these technical parameters. In this paper we propose a knowledge-based kernel PCA approach that allows for intuitive interaction with data visualizations. Each embedding direction is given by a non-convex quadratic optimization problem over an ellipsoid and has a globally optimal solution in the kernel feature space. A solution can be found in polynomial time using the algorithm presented in this paper. To facilitate direct feedback, i.e., updating the whole embedding with a sufficiently high frame-rate during interaction, we reduce the computational complexity further by incremental up- and down-dating. Our empirical evaluation demonstrates the flexibility and utility of this approach.

Keywords

  • Interactive visualization
  • kernel methods
  • dimensionality reduction

Parts of this work have been presented in workshops[18, 19].

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Oglic, D., Paurat, D., Gärtner, T. (2014). Interactive Knowledge-Based Kernel PCA. In: Calders, T., Esposito, F., Hüllermeier, E., Meo, R. (eds) Machine Learning and Knowledge Discovery in Databases. ECML PKDD 2014. Lecture Notes in Computer Science(), vol 8725. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-44851-9_32

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  • DOI: https://doi.org/10.1007/978-3-662-44851-9_32

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-44850-2

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