Summary: JOURNAL OF LATEX CLASS FILES, VOL. ?, NO. ?, ?? 1
Context-Dependent Kernels for Object
Hichem Sahbi, Jean-Yves Audibert and Renaud Keriven
Abstract--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, bio-informatics 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 (CDK) which is also positive definite. Experiments conducted on object
recognition show that when plugging our kernel in SVMs, we clearly outperform SVMs with context-free kernels (CFK).
Index Terms--Kernel Design, Statistical Machine Learning, Support Vector Machines, Context-Free Kernels, Context-Dependent
Kernels, Object Recognition.
INITIALLY introduced in , kernel methods including
support vector machines (SVMs) show a particular