Sparse coding-that is, modelling data vectors as sparse linear combinations of basis elements-is widely used in machine learning, neuroscience, signal processing, and statistics. This paper focuses on learning the basis set, also called dictionary, to adapt it to specific data, an approach that has recently proven to be very effective for signal reconstruction and classification in the audio and image processing domains. This paper proposes a new online optimization algorithm for dictionary learning, based on stochastic approximations, which scales up gracefully to large datasets with millions of training samples. A proof of convergence is presented, along with experiments with natural images demonstrating that it leads to faster performance and better dictionaries than classical batch algorithms for both small and large datasets.

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We present a class of algorithms for Independent Component Analysis (ICA) which use contrast functions based on canonical correlations in a reproducing kernel Hilbert space. On the one hand, we show that our contrast functions are related to mutual information and have desirable mathematical properties as measures of statistical dependence. On the other hand, building on recent developments in kernel methods, we show that these criteria and their derivatives can be computed efficiently. Minimizing these criteria leads to flexible and robust algorithms for ICA. We illustrate with simulations involving a wide variety of source distributions, showing that our algorithms outperform many of the presently known algorithms.