Connectionists: Data Visualization and Dimensionality Reduction

[Johan Suykens]

Dear Connectionists,

Please find enclosed a new technical report on data visualization and 
dimensionality reduction,
together with a demo file.

Best regards,
Johan Suykens


J.A.K. Suykens, "Data Visualization and Dimensionality Reduction using 
Kernel Maps with a Reference Point",
Internal Report 07-22, ESAT-SISTA, K.U. Leuven (Leuven, Belgium), Feb. 2007.
PDF: http://www.esat.kuleuven.ac.be/sista/lssvmlab/KMref/KMref0722.pdf
Matlab demo: 
http://www.esat.kuleuven.ac.be/sista/lssvmlab/KMref/demoswissKMref.m

Abstract-
In this paper a new kernel based method for data visualization and 
dimensionality reduction is proposed.
A reference point is considered corresponding to additional constraints 
taken in the problem formulation.
In contrast with the class of kernel eigenmap methods, the solution 
(coordinates in the low dimensional space)
is characterized by a linear system instead of an eigenvalue problem. 
The kernel maps with a reference point
are generated from a least squares support vector machine core part that 
is extended with an additional
regularization term for preserving local mutual distances together with 
reference point constraints.
The kernel maps possess primal and dual model representations and 
provide out-of-sample extensions
e.g. for validation based tuning. The method is illustrated on toy 
problems and real life data sets.







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