A Multiobjective Sparse Feature Learning Model for Deep Neural Networks

Convolutional Sparse Autoencoders for Image Classification

Convolutional sparse coding (CSC) can model local connections between image content and reduce the code redundancy when compared with patch-based sparse coding. However, CSC needs a complicated optimization procedure to infer the codes (i.e., feature maps). In this brief, we proposed a convolutional sparse auto-encoder (CSAE), which leverages the structure of the convolutional AE and incorporates the max-pooling to heuristically sparsify the feature maps for feature learning. Together with competition over feature channels, this simple sparsifying strategy makes the stochastic gradient descent algorithm work efficiently for the CSAE training; thus, no complicated optimization procedure is involved. We employed the features learned in the CSAE to initialize convolutional neural networks for classification and achieved competitive results on benchmark data sets. In addition, by building connections between the CSAE and CSC, we proposed a strategy to construct local descriptors from the CSAE for classification. Experiments on Caltech-101 and Caltech-256 clearly demonstrated the effectiveness of the proposed method and verified the CSAE as a CSC model has the ability to explore connections between neighboring image content for classification tasks.

Cascaded Subpatch Networks for Effective CNNs

Conventional convolutional neural networks use either a linear or a nonlinear filter to extract features from an image patch (region) of spatial size (typically, is small and is equal to , e.g., is 5 or 7). Generally, the size of the filter is equal to the size of the input patch. We argue that the representational ability of equal-size strategy is not strong enough. To overcome the drawback, we propose to use subpatch filter whose spatial size is smaller than . The proposed subpatch filter consists of two subsequent filters. The first one is a linear filter of spatial size and is aimed at extracting features from spatial domain. The second one is of spatial size and is used for strengthening the connection between different input feature channels and for reducing the number of parameters. The subpatch filter convolves with the input patch and the resulting network is called a subpatch network. Taking the output of one subpatch network as input, we further repeat constructing subpatch networks until the output contains only one neuron in spatial domain. These subpatch networks form a new network called the cascaded subpatch network (CSNet). The feature layer generated by CSNet is called the csconv layer. For the whole input image, we construct a deep neural network by stacking a sequence of csconv layers. Experimental results on five benchmark data sets demonstrate the effectiveness and compactness of the proposed CSNet. For example, our CSNet reaches a test error of 5.68% on the CIFAR10 data set without model averaging. To the best of our knowledge, this is the best result ever obtained on the CIFAR10 data set.

Structure Learning for Deep Neural Networks Based on Multiobjective Optimization

This paper focuses on the connecting structure of deep neural networks and proposes a layerwise structure learning method based on multiobjective optimization. A model with better generalization can be obtained by reducing the connecting parameters in deep networks. The aim is to find the optimal structure with high representation ability and better generalization for each layer. Then, the visible data are modeled with respect to structure based on the products of experts. In order to mitigate the difficulty of estimating the denominator in PoE, the denominator is simplified and taken as another objective, i.e., the connecting sparsity. Moreover, for the consideration of the contradictory nature between the representation ability and the network connecting sparsity, the multiobjective model is established. An improved multiobjective evolutionary algorithm is used to solve this model. Two tricks are designed to decrease the computational cost according to the properties of input data. The experiments on single-layer level, hierarchical level, and application level demonstrate the effectiveness of the proposed algorithm, and the learned structures can improve the performance of deep neural networks.

Convolution in Convolution for Network in Network

Network in network (NiN) is an effective instance and an important extension of deep convolutional neural network consisting of alternating convolutional layers and pooling layers. Instead of using a linear filter for convolution, NiN utilizes shallow multilayer perceptron (MLP), a nonlinear function, to replace the linear filter. Because of the powerfulness of MLP and convolutions in spatial domain, NiN has stronger ability of feature representation and hence results in better recognition performance. However, MLP itself consists of fully connected layers that give rise to a large number of parameters. In this paper, we propose to replace dense shallow MLP with sparse shallow MLP. One or more layers of the sparse shallow MLP are sparely connected in the channel dimension or channel-spatial domain. The proposed method is implemented by applying unshared convolution across the channel dimension and applying shared convolution across the spatial dimension in some computational layers. The proposed method is called convolution in convolution (CiC). The experimental results on the CIFAR10 data set, augmented CIFAR10 data set, and CIFAR100 data set demonstrate the effectiveness of the proposed CiC method.

Homotopy Methods Based on $l_{0}$ -Norm for Compressed Sensing

This paper proposes two homotopy methods for solving the compressed sensing (CS) problem, which combine the homotopy technique with the iterative hard thresholding (IHT) method. The homotopy methods overcome the difficulty of the IHT method on the choice of the regularization parameter value, by tracing solutions of the regularized problem along a homotopy path. We prove that any accumulation point of the sequences generated by the proposed homotopy methods is a feasible solution of the problem. We also show an upper bound on the sparsity level for each solution of the proposed methods. Moreover, to improve the solution quality, we modify the two methods into the corresponding heuristic algorithms. Computational experiments demonstrate effectiveness of the two heuristic algorithms, in accurately and efficiently generating sparse solutions of the CS problem, whether the observation is noisy or not.

A Deep Convolutional Coupling Network for Change Detection Based on Heterogeneous Optical and Radar Images

We propose an unsupervised deep convolutional coupling network for change detection based on two heterogeneous images acquired by optical sensors and radars on different dates. Most existing change detection methods are based on homogeneous images. Due to the complementary properties of optical and radar sensors, there is an increasing interest in change detection based on heterogeneous images. The proposed network is symmetric with each side consisting of one convolutional layer and several coupling layers. The two input images connected with the two sides of the network, respectively, are transformed into a feature space where their feature representations become more consistent. In this feature space, the different map is calculated, which then leads to the ultimate detection map by applying a thresholding algorithm. The network parameters are learned by optimizing a coupling function. The learning process is unsupervised, which is different from most existing change detection methods based on heterogeneous images. Experimental results on both homogenous and heterogeneous images demonstrate the promising performance of the proposed network compared with several existing approaches.

Broad Learning System: An Effective and Efficient Incremental Learning System Without the Need for Deep Architecture

Broad Learning System (BLS) that aims to offer an alternative way of learning in deep structure is proposed in this paper. Deep structure and learning suffer from a time-consuming training process because of a large number of connecting parameters in filters and layers. Moreover, it encounters a complete retraining process if the structure is not sufficient to model the system. The BLS is established in the form of a flat network, where the original inputs are transferred and placed as "mapped features" in feature nodes and the structure is expanded in wide sense in the "enhancement nodes." The incremental learning algorithms are developed for fast remodeling in broad expansion without a retraining process if the network deems to be expanded. Two incremental learning algorithms are given for both the increment of the feature nodes (or filters in deep structure) and the increment of the enhancement nodes. The designed model and algorithms are very versatile for selecting a model rapidly. In addition, another incremental learning is developed for a system that has been modeled encounters a new incoming input. Specifically, the system can be remodeled in an incremental way without the entire retraining from the beginning. Satisfactory result for model reduction using singular value decomposition is conducted to simplify the final structure. Compared with existing deep neural networks, experimental results on the Modified National Institute of Standards and Technology database and NYU NORB object recognition dataset benchmark data demonstrate the effectiveness of the proposed BLS.

A Novel Method Based on Line-Segment Visualizations for Hyper-Parameter Optimization in Deep Networks

Recently, deep learning has been widely applied in various areas and achieved remarkable research findings. The major reason that makes the deep learning paradigm successful is that it can effectively learn a hierarchical feature structure for the training data. However, most deep learning algorithms rely on massive well-labeled training datasets and hyper-parameter configurations. This paper proposed a novel methodology that uses the geometric characteristics of line-segment representations to optimize the hyper-parameters for the deep networks. The methodology is applied to a line-segment-based stacked auto-encoder to verify its effectiveness. It is found that the line-segment-based visualizations can increase the interpretability of the deep models and facilitate the configurations for the hyper-parameters.

A Hierarchical Predictive Coding Model of Object Recognition in Natural Images

Predictive coding has been proposed as a model of the hierarchical perceptual inference process performed in the cortex. However, results demonstrating that predictive coding is capable of performing the complex inference required to recognise objects in natural images have not previously been presented. This article proposes a hierarchical neural network based on predictive coding for performing visual object recognition. This network is applied to the tasks of categorising hand-written digits, identifying faces, and locating cars in images of street scenes. It is shown that image recognition can be performed with tolerance to position, illumination, size, partial occlusion, and within-category variation. The current results, therefore, provide the first practical demonstration that predictive coding (at least the particular implementation of predictive coding used here; the PC/BC-DIM algorithm) is capable of performing accurate visual object recognition.

Probe Machine

In this paper, we present a novel computing model, called probe machine (PM). Unlike the turing machine (TM), PM is a fully parallel computing model in the sense that it can simultaneously process multiple pairs of data, rather than sequentially process every pair of linearly adjacent data. We establish the mathematical model of PM as a nine-tuple consisting of data library, probe library, data controller, probe controller, probe operation, computing platform, detector, true solution storage, and residue collector. We analyze the computation capability of the PM model, and in particular, we show that TM is a special case of PM. We revisit two NP-complete problems, i.e., the graph coloring and Hamilton cycle problems, and devise two algorithms on basis of the established PM model, which can enumerate all solutions to each of these problems by only one probe operation. Furthermore, we show that PM can be implemented by leveraging the nano-DNA probe technologies. The computational power of an electronic computer based on TM is known far more than that of the human brain. A question naturally arises: will a future computer based on PM outperform the human brain in more ways beyond the computational power?