On Class Visualisation for High Dimensional Data: Exploring Scientific Data Sets

Parametric Embedding (PE) has recently been proposed as a general-purpose algorithm for class visualisation. It takes class posteriors produced by a mixture-based clustering algorithm and projects them in 2D for visualisation. However, although this fully modularised combination of objectives (clustering and projection) is attractive for its conceptual simplicity, in the case of high dimensional data, we show that a more optimal combination of these objectives can be achieved by integrating them both into a consistent probabilistic model. In this way, the projection step will fulfil a role of regularisation, guarding against the curse of dimensionality. As a result, the tradeoff between clustering and visualisation turns out to enhance the predictive abilities of the overall model. We present results on both synthetic data and two real-world high-dimensional data sets: observed spectra of early-type galaxies and gene expression arrays.

[1]  Thomas Hofmann,et al.  Latent semantic models for collaborative filtering , 2004, TOIS.

[2]  Hagai Attias.  Learning in high dimensions: modular mixture models , 2001, AISTATS.

[3]  A. Rukhin.  Bayes and Empirical Bayes Methods for Data Analysis , 1997 .

[4]  T. Louis,et al.  Bayes and Empirical Bayes Methods for Data Analysis. , 1997 .

[5]  Heekuck Oh,et al.  Neural Networks for Pattern Recognition , 1993, Adv. Comput..

[6]  Colin Campbell,et al.  The Latent Process Decomposition of cDNA Microarray Data Sets , 2005, TCBB.

[7]  Astronomy,et al.  A data-driven Bayesian approach for finding young stellar populations in early-type galaxies from their ultraviolet-optical spectra , 2005, astro-ph/0511503.

[8]  Edinburgh,et al.  The star formation histories of elliptical galaxies across the fundamental plane , 2006, astro-ph/0605417.

[9]  John Rice,et al.  Reflections on SCMA III , 2003 .

[10]  Ata Kabán,et al.  Finding Young Stellar Populations in Elliptical Galaxies from Independent Components of Optical Spectra , 2005, SDM.

[11]  Christopher M. Bishop,et al.  GTM: The Generative Topographic Mapping , 1998, Neural Computation.

[12]  Ian Davidson,et al.  Visual Data Mining: Techniques and Tools for Data Visualization and Mining , 2002 .

[13]  U. Alon,et al.  Broad patterns of gene expression revealed by clustering analysis of tumor and normal colon tissues probed by oligonucleotide arrays. , 1999, Proceedings of the National Academy of Sciences of the United States of America.