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- S. Seo and K. Obermayer.
Self-Organizing Maps and Clustering Methods for Matrix Data.
.
Neural Networks Special Issue, 17:1211-1229, 2004.
Unfortunately, there are some typos in the equation (11)-(13) of this paper.
Please see the file ERRATUM for the correction.
(FTP PDF, 432 kb)
In this contribution we present extensions of the Self Organizing
Map and clustering methods for the categorization and visualization of data
which are described by matrices rather than feature vectors. Rows and columns
of these matrices correspond to objects which may or may not belong to the
same set, and the entries in the matrix describe the relationships between
them. The clustering task is formulated as an optimization problem: Model
complexity is minimized under the constraint, that the error one makes when
reconstructing objects from class information is fixed, usually to a small
value. The data is then visualized with help of modified Self Organizing Maps
methods, i.e. by constructing a neighborhood preserving non-linear projection
into a low-dimensional ``map-space''. Grouping of data objects is done using
an improved optimization technique, which combines deterministic annealing
with ``growing'' techniques. Performance of the new methods is evaluated by
applying them to two kinds of matrix data: (i) pairwise data, where row and
column objects are from the same set and where matrix elements denote
dissimilarity values and (ii) co-occurrence data, where row and column
objects are from different sets and where the matrix elements describe how
often object pairs occur.
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