Unsupervised Bayesian visualization of high-dimensional data

We propose a data reduction method based on a probabilistic similarity framework where two vectors are considered similar if they lead to similar predictions. We show how this type of a probabilistic similarity metric can be de ned both in a supervised and unsupervised manner. As a concrete application of the suggested multidimensional scaling scheme, we describe how the method can be used for producing visual images of high-dimensional data, and give several examples of visualizations obtained by using the suggested scheme with probabilistic Bayesian network models.

[1]  Samuel B. Williams,et al.  ASSOCIATION FOR COMPUTING MACHINERY , 2000 .

[2]  Peter E. Hart,et al.  Pattern classification and scene analysis , 1974, A Wiley-Interscience publication.

[3]  Henry Tirri,et al.  Prababilistic Instance-Based Learning , 1996, ICML.

[4]  Henry Tirri,et al.  On Supervised Selection of Bayesian Networks , 1999, UAI.

[5]  Richard E. Neapolitan,et al.  Probabilistic reasoning in expert systems - theory and algorithms , 2012 .

[6]  Richard O. Duda,et al.  Pattern classification and scene analysis , 1974, A Wiley-Interscience publication.

[7]  Henry Tirri,et al.  On Bayesian Case Matching , 1998, EWCBR.

[8]  D. J. Newman,et al.  UCI Repository of Machine Learning Database , 1998 .

[9]  David Heckerman,et al.  A Tutorial on Learning with Bayesian Networks , 1998, Learning in Graphical Models.

[10]  Richard E. Neapolitan,et al.  Probabilistic reasoning in expert systems - theory and algorithms , 2012 .

[11]  David J. Spiegelhalter,et al.  Local computations with probabilities on graphical structures and their application to expert systems , 1990 .

[12]  Henry Tirri,et al.  On predictive distributions and Bayesian networks , 2000, Stat. Comput..

[13]  David Heckerman,et al.  Models and Selection Criteria for Regression and Classification , 1997, UAI.

[14]  Judea Pearl,et al.  Probabilistic reasoning in intelligent systems - networks of plausible inference , 1991, Morgan Kaufmann series in representation and reasoning.

[15]  A. J. Collins,et al.  Introduction To Multivariate Analysis , 1981 .

[16]  Teuvo Kohonen,et al.  Self-Organizing Maps , 2010 .

[17]  Henry Tirri,et al.  BAYDA: Software for Bayesian Classification and Feature Selection , 1998, KDD.