Many approaches to transform classification problems from non-linear to linear by feature transformation have been recently presented in the literature. These notably include sparse coding methods and deep neural networks. However, many of these approaches require the repeated application of a learning process upon the presentation of unseen data input vectors, or else involve the use of large numbers of parameters and hyper-parameters, which must be chosen through cross-validation, thus increasing running time dramatically. In this paper, we propose and experimentally investigate a new approach for the purpose of overcoming limitations of both kinds. The proposed approach makes use of a linear auto-associative network (called SCNN) with just one hidden layer. The combination of this architecture with a specific error function to be minimized enables one to learn a linear encoder computing a sparse code which turns out to be as similar as possible to the sparse coding that one obtains by re-training the neural network. Importantly, the linearity of SCNN and the choice of the error function allow one to achieve reduced running time in the learning phase. The proposed architecture is evaluated on the basis of two standard machine learning tasks. Its performances are compared with those of recently proposed non-linear auto-associative neural networks. The overall results suggest that linear encoders can be profitably used to obtain sparse data representations in the context of machine learning problems, provided that an appropriate error function is used during the learning phase.
Both networks, ASCNN and SAANN, are trained by means of the mini batch stochastic gradient descent learning algorithm because the error function is differentiable as the penalization term is differentiable. The possibility of identifying valid alternatives to non-linear approaches to sparse coding, in the context of non-linear autoassociative networks with a single hidden layer, is suggested by some classification which were successfully addressed on the basis of linear network approaches. Notably, linear approaches were successfully used to model the early stage responses of the visual system. In the early stage visual information is a small number of simultaneously active neurons among the much larger number of available neurons. The first attempt to model this behaviour of the visual system is due to Olshausen and Field ( @cite_17 ). The authors built a simple single weight layer feed forward neural network (Sparsenet) where the observed data @math are a linear combination of top-bottom basis vectors @math and top-layer sparse responses @math . The sparsity of the solution is obtained by minimizing an error function composed of the standard sum-of-squares error and a regularization term, which can be expressed as follows:
@cite_17
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Optimizing deep neural networks (DNNs) often suffers from the ill-conditioned problem. We observe that the scaling-based weight space symmetry property in rectified nonlinear network will cause this negative effect. Therefore, we propose to constrain the incoming weights of each neuron to be unit-norm, which is formulated as an optimization problem over Oblique manifold. A simple yet efficient method referred to as projection based weight normalization (PBWN) is also developed to solve this problem. PBWN executes standard gradient updates, followed by projecting the updated weight back to Oblique manifold. This proposed method has the property of regularization and collaborates well with the commonly used batch normalization technique. We conduct comprehensive experiments on several widely-used image datasets including CIFAR-10, CIFAR-100, SVHN and ImageNet for supervised learning over the state-of-the-art convolutional neural networks, such as Inception, VGG and residual networks. The results show that our method is able to improve the performance of DNNs with different architectures consistently. We also apply our method to Ladder network for semi-supervised learning on permutation invariant MNIST dataset, and our method outperforms the state-of-the-art methods: we obtain test errors as 2.52 , 1.06 , and 0.91 with only 20, 50, and 100 labeled samples, respectively. Despite their great success, there is still no comprehensive theoretical understanding of learning with Deep Neural Networks (DNNs) or their inner organization. Previous work proposed to analyze DNNs in the ; i.e., the plane of the Mutual Information values that each layer preserves on the input and output variables. They suggested that the goal of the network is to optimize the Information Bottleneck (IB) tradeoff between compression and prediction, successively, for each layer. In this work we follow up on this idea and demonstrate the effectiveness of the Information-Plane visualization of DNNs. Our main results are: (i) most of the training epochs in standard DL are spent on ph compression of the input to efficient representation and not on fitting the training labels. (ii) The representation compression phase begins when the training errors becomes small and the Stochastic Gradient Decent (SGD) epochs change from a fast drift to smaller training error into a stochastic relaxation, or random diffusion, constrained by the training error value. (iii) The converged layers lie on or very close to the Information Bottleneck (IB) theoretical bound, and the maps from the input to any hidden layer and from this hidden layer to the output satisfy the IB self-consistent equations. This generalization through noise mechanism is unique to Deep Neural Networks and absent in one layer networks. (iv) The training time is dramatically reduced when adding more hidden layers. Thus the main advantage of the hidden layers is computational. This can be explained by the reduced relaxation time, as this it scales super-linearly (exponentially for simple diffusion) with the information compression from the previous layer. The spiking neural networks (SNNs) are the third generation of neural networks and perform remarkably well in cognitive tasks such as pattern recognition. The spike emitting and information processing mechanisms found in biological cognitive systems motivate the application of the hierarchical structure and temporal encoding mechanism in spiking neural networks, which have exhibited strong computational capability. However, the hierarchical structure and temporal encoding approach require neurons to process information serially in space and time respectively, which reduce the training efficiency significantly. For training the hierarchical SNNs, most existing methods are based on the traditional back-propagation algorithm, inheriting its drawbacks of the gradient diffusion and the sensitivity on parameters. To keep the powerful computation capability of the hierarchical structure and temporal encoding mechanism, but to overcome the low efficiency of the existing algorithms, a new training algorithm, the Normalized Spiking Error Back Propagation (NSEBP) is proposed in this paper. In the feedforward calculation, the output spike times are calculated by solving the quadratic function in the spike response model instead of detecting postsynaptic voltage states at all time points in traditional algorithms. Besides, in the feedback weight modification, the computational error is propagated to previous layers by the presynaptic spike jitter instead of the gradient decent rule, which realizes the layer-wised training. Furthermore, our algorithm investigates the mathematical relation between the weight variation and voltage error change, which makes the normalization in the weight modification applicable. Adopting these strategies, our algorithm outperforms the traditional SNN multi-layer algorithms in terms of learning efficiency and parameter sensitivity, that are also demonstrated by the comprehensive experimental results in this paper. Feature matters. In this paper, a novel deep neural network framework integrated with low-level features for salient object detection is proposed for complex images. We utilise the advantage of convolutional neural networks to automatically learn the high-level features that capture the structured information and semantic context in the image. In order to better adapt a CNN model into the saliency task, we redesign the network architecture based on typical saliency datasets, which is relatively small-scale compared to ImageNet. Several low-level features are extracted, which can effectively capture contrast and spatial information in the salient regions, and incorporated to compensate with the learned high-level features at the output of the very last fully connected layer. The concatenated feature vector is further fed into a hinge-loss SVM detector in a joint discriminative learning manner and the final saliency score of each region within the bounding box is obtained by the linear combination of the detector's weights. Experiments on three challenging benchmarks demonstrate our algorithm to be effective and superior than most low-level oriented state-of-the-arts in terms of precision-recall curves, F-measure and mean absolute errors. Moreover, a series of ablation studies are conducted to verify our algorithm's simplicity and efficiency from different aspects. Propose a novel deep neural network framework embedded with low-level features (LCNN) for salient object detection in complex images.Utilise the advantage of convolutional neural networks to automatically learn the high-level features that capture the structured information and semantic context in the image.Experiments on three challenging benchmarks demonstrate our algorithm to be effective and superior than most low-level oriented state-of-the-arts in terms of precision-recall curves, F-measure and mean absolute errors.