Context-dependent kernel design for object matching and recognition

The success of kernel methods including support vector networks (SVMs) strongly depends on the design of appropriate kernels. While initially kernels were designed in order to handle fixed-length data, their extension to unordered, variable-length data became more than necessary for real pattern recognition problems such as object recognition and bioinformatics. We focus in this paper on object recognition using a new type of kernel referred to as ldquocontext-dependentrdquo. Objects, seen as constellations of local features (interest points, regions, etc.), are matched by minimizing an energy function mixing (1) a fidelity term which measures the quality of feature matching, (2) a neighborhood criteria which captures the object geometry and (3) a regularization term. We will show that the fixed-point of this energy is a ldquocontext-dependentrdquo kernel (ldquoCDKrdquo) which also satisfies the Mercer condition. Experiments conducted on object recognition show that when plugging our kernel in SVMs, we clearly outperform SVMs with ldquocontext-freerdquo kernels.