SENNS: Sparse Extraction Neural NetworkS for Feature Extraction
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By drawing on ideas from optimisation theory, artificial neural networks (ANN), graph embeddings and sparse representations, I develop a novel technique, termed SENNS (Sparse Extraction Neural NetworkS), aimed at addressing the feature extraction problem. The proposed method uses (preferably deep) ANNs for projecting input attribute vectors to an output space wherein pairwise distances are maximized for vectors belonging to different classes, but minimized for those belonging to the same class, while simultaneously enforcing sparsity on the ANN outputs. The vectors that result from the projection can then be used as features in any classifier of choice. Mathematically, I formulate the proposed method as the minimisation of an objective function which can be interpreted, in the ANN output space, as a negative factor of the sum of the squares of the pair-wise distances between output vectors belonging to different classes, added to a positive factor of the sum of squares of the pair-wise distances between output vectors belonging to the same classes, plus sparsity and weight decay terms. To derive an algorithm for minimizing the objective function via gradient descent, I use the multi-variate version of the chain rule to obtain the partial derivatives of the function with respect to ANN weights and biases, and find that each of the required partial derivatives can be expressed as a sum of six terms. As it turns out, four of those six terms can be computed using the standard back propagation algorithm; the fifth can be computed via a slight modification of the standard backpropagation algorithm; while the sixth one can be computed via simple arithmetic. Finally, I propose experiments on the ARABASE Arabic corpora of digits and letters, the CMU PIE database of faces, the MNIST digits database, and other standard machine learning databases.
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