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Structure Spaces
Citation key Jain2009c
Author Jain, B. and Obermayer, K.
Pages 2667 – 2714
Year 2009
ISSN 1532-4435
Journal Journal of Machine Learning Research
Volume 10
Abstract Finite structures such as point patterns, strings, trees, and graphs occur as "natural" representations of structured data in different application areas of machine learning. We develop the theory of structure spaces and derive geometrical and analytical concepts such as the angle between structures and the derivative of functions on structures. In particular, we show that the gradient of a differentiable structural function is a well-defined structure pointing in the direction of steepest ascent. Exploiting the properties of structure spaces, it will turn out that a number of problems in structural pattern recognition such as central clustering or learning in structured output spaces can be formulated as optimization problems with cost functions that are locally Lipschitz. Hence, methods from nonsmooth analysis are applicable to optimize those cost functions.
Bibtex Type of Publication Selected:main selected:structured selected:publications
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