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Computational Intelligence - Learning with Neural Methods on Structured Data |
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Computational Intelligence - Learning with Neural Methods on Structured Data |
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Usually, Multidimensional Scaling (MDS) is performed on high-dimensional
data to be mapped it into a lower dimension. The vehicle between the data space and
the projection space is to minimize the discrepancy of data pair distances
in the data space within the domain of the target space. Since two different metrics
can be used, MDS also yields a metric conversion, especially if source and target
dimension are equal. An example for MDS is the projection data describing the
economical situation of a country (average income, rate of employment,
netto production, ...) to a 2-dimensional map, which can be easily visualized for
the further inspection of mutual relations.
The animation is a simple R2 to R2 mapping from image pixel
locations where the points in the target space have been randomly initialized.
Note, however, that there are certain degrees of freedom for
reconstructing the original data in the projection space. Here, the originally
horizontally oriented image has 'suffered' from a rotational transform, but
also bendings and translations are possible, not to think of arranging data with an
intrinsic dimension higher then the projection dimension... In my work, MDS is used for a bootstrap representation of entities which have no specific location in RK: textual information. My only ingredients are a set of words and a distance measure between them, the Levenshtein distance, which shall be used for the creation of a 'dual' space where ordinary arithmetics can be performed. |