  In complex visual recognition tasks it is typical to adopt multiple
descriptors, that describe different aspects of the images, for obtaining an
improved recognition performance. Descriptors that have diverse forms can be
fused into a unified feature space in a principled manner using kernel methods.
Sparse models that generalize well to the test data can be learned in the
unified kernel space, and appropriate constraints can be incorporated for
application in supervised and unsupervised learning. In this paper, we propose
to perform sparse coding and dictionary learning in the multiple kernel space,
where the weights of the ensemble kernel are tuned based on graph-embedding
principles such that class discrimination is maximized. In our proposed
algorithm, dictionaries are inferred using multiple levels of 1-D subspace
clustering in the kernel space, and the sparse codes are obtained using a
simple levelwise pursuit scheme. Empirical results for object recognition and
image clustering show that our algorithm outperforms existing sparse coding
based approaches, and compares favorably to other state-of-the-art methods.
