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Context-Dependent Kernels for Object Classification
April 2011 (vol. 33 no. 4)
pp. 699-708
Hichem Sahbi, CNRS, LTCI Lab, Telecom ParisTech, Paris
Jean-Yves Audibert, Certis, Université Paris-Est, Ecole des Ponts ParisTech, Paris, LIGM, Imagine, Marne-la-Vallée, and Willow, CNRS/ENS/INRIA, Paris
Renaud Keriven, Certis, Université Paris-Est, Ecole des Ponts ParisTech, Paris, LIGM, Imagine, Marne-la-Vallée
Kernels are functions designed in order to capture resemblance between data and they are used in a wide range of machine learning techniques, including support vector machines (SVMs). In their standard version, commonly used kernels such as the Gaussian one show reasonably good performance in many classification and recognition tasks in computer vision, bioinformatics, and text processing. In the particular task of object recognition, the main deficiency of standard kernels such as the convolution one resides in the lack in capturing the right geometric structure of objects while also being invariant. We focus in this paper on object recognition using a new type of kernel referred to as "context dependent.” Objects, seen as constellations of interest points, are matched by minimizing an energy function mixing 1) a fidelity term which measures the quality of feature matching, 2) a neighborhood criterion which captures the object geometry, and 3) a regularization term. We will show that the fixed point of this energy is a context-dependent kernel which is also positive definite. Experiments conducted on object recognition show that when plugging our kernel into SVMs, we clearly outperform SVMs with context-free kernels.

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Index Terms:
Kernel design, statistical machine learning, support vector machines, context-free kernels, context-dependent kernels, object recognition.
Hichem Sahbi, Jean-Yves Audibert, Renaud Keriven, "Context-Dependent Kernels for Object Classification," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 33, no. 4, pp. 699-708, April 2011, doi:10.1109/TPAMI.2010.198
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