  Representing images by compact codes has proven beneficial for many visual
recognition tasks. Most existing techniques, however, perform this coding step
directly in image feature space, where the distributions of the different
classes are typically entangled. In contrast, here, we study the problem of
performing coding in a high-dimensional Hilbert space, where the classes are
expected to be more easily separable. To this end, we introduce a general
coding formulation that englobes the most popular techniques, such as bag of
words, sparse coding and locality-based coding, and show how this formulation
and its special cases can be kernelized. Importantly, we address several
aspects of learning in our general formulation, such as kernel learning,
dictionary learning and supervised kernel coding. Our experimental evaluation
on several visual recognition tasks demonstrates the benefits of performing
coding in Hilbert space, and in particular of jointly learning the kernel, the
dictionary and the classifier.
