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In recent years, considerable progress has been made in the
understanding of problems of learning and generalization. In this
context, intelligence basically means the ability to perform well
on new data after learning a model on the basis of given data. Such
problems arise in many different areas and are becoming
increasingly important and crucial towards many applications such
as in bioinformatics, multimedia, computer vision and signal
processing, internet search and information retrieval, datamining
and textmining, finance, fraud detection, measurement systems,
process control and several others. Currently, the development of
new technologies enables to generate massive amounts of data
containing a wealth of information that remains to become explored.
Often the dimensionality of the input spaces in these novel
applications is huge. This can be seen in the analysis of
micro-array data, for example, where expression levels of thousands
of genes need to be analyzed given only a limited number of
experiments. Without performing dimensionality reduction, the
classical statistical paradigms show fundamental shortcomings at
this point. Facing these new challenges, there is a need for new
mathematical foundations and models in a way that the data can
become processed in a reliable way. The subjects in this
publication are very interdisciplinary and relate to problems
studied in neural networks, machine learning, mathematics and
statistics.
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