Shallow and deep learning for image classification

The paper is focused on the idea to demonstrate the advantages of deep learning approaches over ordinary shallow neural network on their comparative applications to image classifying from such popular benchmark databases as FERET and MNIST. An autoassociative neural network is used as a standalone program realized the nonlinear principal component analysis for prior extracting the most informative features of input data for neural networks to be compared further as classifiers. A special study of the optimal choice of activation function and the normalization transformation of input data allows to improve efficiency of the autoassociative program. One more study devoted to denoising properties of this program demonstrates its high efficiency even on noisy data. Three types of neural networks are compared: feed-forward neural net with one hidden layer, deep network with several hidden layers and deep belief network with several pretraining layers realized restricted Boltzmann machine. The number of hidden layer and the number of hidden neurons in them were chosen by cross-validation procedure to keep balance between number of layers and hidden neurons and classification efficiency. Results of our comparative study demonstrate the undoubted advantage of deep networks, as well as denoising power of autoencoders. In our work we use both multiprocessor graphic card and cloud services to speed up our calculations. The paper is oriented to specialists in concrete fields of scientific or experimental applications, who have already some knowledge about artificial neural networks, probability theory and numerical methods.     

一种估计前馈神经网络中隐层神经元数目的新方法

前馈神经网络中隐层神经元的数目一般凭经验的给出，这种方法往往造成隐单元数目的不足或过甚，从而导致网络存储容量不够或出现学习过拟现象，本研究提出了一种基于信息熵的估计三层前馈神经网络隐结点数目的方法，该方法首先利用训练集来训练具有足够隐单元数目的初始神经网络，然后计算训练集中能被训练过的神经网络正确识别的样本在隐层神经元的激活值，并对其进行排序，计算这些激活值的各种划分的信息增益，从而构造能将整个样本空间正确划分的决策树，最后遍历整棵树寻找重要的相关隐层神经元，并删除冗余无关的其它隐单元，从而估计神经网络中隐层神经元的较佳数目，文章最后以构造用于茶叶品质评定的具有较佳隐单元数目的神经网络为例，介绍本方法的使用，结果表明，本方法能有效估计前馈神经网络的隐单元数目。     

二阶神经网络映射能力的研究

本文讨论了二阶神经网络的映射能力。主要内容包括：（１）从理论上严格地证明了二阶神经网络能以任意精度逼近任意连续函数。（２）给出二阶神经网络的ＢＰ算法。（３）模拟实验结果。模拟实验表明：在中间隐层单元数目相同的条件下，二阶神经网络的误差函数比一阶神经网络下降得快；在误差精度相同的条件下，二阶神经网络的隐层单元数目远比一阶神经网络少。     

基于多级神经元的神经网络及其在分类中的应用

为了提高前向神经网络的分类能力,该文将多级神经元扩展使用到多层感知器的输出层和隐含层中,并提出了量子神经网络的学习算法。通过一个实际的分类问题实验验证了该方法的有效性。实验表明,无论输出层或隐含采用多级神经元,都可以带来分类能力的提高。而当输出层采用多级神经元时,还可以导致连接的减少和训练速度的加快。     

Comparative analysis on hidden neurons estimation in multi layer perceptron neural networks for wind speed forecasting

In this paper methodologies are proposed to estimate the number of hidden neurons that are to be placed numbers in the hidden layer of artificial neural networks (ANN) and certain new criteria are evolved for fixing this hidden neuron in multilayer perceptron neural networks. On the computation of the number of hidden neurons, the developed neural network model is applied for wind speed forecasting application. There is a possibility of over fitting or under fitting occurrence due to the random selection of hidden neurons in ANN model and this is addressed in this paper. Contribution is done in developing various 151 different criteria and the evolved criteria are tested for their validity employing various statistical error means. Simulation results prove that the proposed methodology minimized the computational error and enhanced the prediction accuracy. Convergence theorem is employed over the developed criterion to validate its applicability for fixing the number of hidden neurons. To evaluate the effectiveness of the proposed approach simulations were carried out on collected real-time wind data. Simulated results confirm that with minimum errors the presented approach can be utilized for wind speed forecasting. Comparative analysis has been performed for the estimation of the number of hidden neurons in multilayer perceptron neural networks. The presented approach is compact, enhances the accuracy rate with reduced error and faster convergence.     

Model selection of extreme learning machine based on multi-objective optimization

As a novel learning algorithm for single-hidden-layer feedforward neural networks, extreme learning machines (ELMs) have been a promising tool for regression and classification applications. However, it is not trivial for ELMs to find the proper number of hidden neurons due to the nonoptimal input weights and hidden biases. In this paper, a new model selection method of ELM based on multi-objective optimization is proposed to obtain compact networks with good generalization ability. First, a new leave-one-out (LOO) error bound of ELM is derived, and it can be calculated with negligible computational cost once the ELM training is finished. Furthermore, the hidden nodes are added to the network one-by-one, and at each step, a multi-objective optimization algorithm is used to select optimal input weights by minimizing this LOO bound and the norm of output weight simultaneously in order to avoid over-fitting. Experiments on five UCI regression data sets are conducted, demonstrating that the proposed algorithm can generally obtain better generalization performance with more compact network than the conventional gradient-based back-propagation method, original ELM and evolutionary ELM.     

前馈神经网络中隐层神经元数目的一种直接估计方法

目前还没有一个行之有效的方法直接估计前馈网络隐层神经元的数目。该文首先提出一种利用单调指数直接估算三层前馈网络隐层经元数目的方法,以保证网络近似逼近任意给定的训练数据。理论分析和计算实验表明,此方法能够在训练之前预先确定最优（最少）或接近最优的隐层神经元数目,使得网络在训练之后不仅可以较好地反映训练数据的变化趋势,而且有较为满意的逼近精度。     

Application of Sequential Learning Neural Networks to Civil Engineering Modeling Problems

A sequential orthogonal approach to the building and training of a single hidden layer neural network is presented in this paper. The Sequential Learning Neural Network (SLNN) model proposed by Zhang and Morris [1]is used in this paper to tackle the common problem encountered by the conventional Feed Forward Neural Network (FFNN) in determining the network structure in the number of hidden layers and the number of hidden neurons in each layer. The procedure starts with a single hidden neuron and sequentially increases in the number of hidden neurons until the model error is sufficiently small. The classical Gram–Schmidt orthogonalization method is used at each step to form a set of orthogonal bases for the space spanned by output vectors of the hidden neurons. In this approach it is possible to determine the necessary number of hidden neurons required. However, for the problems investigated in this paper, one hidden neuron itself is sufficient to achieve the desired accuracy. The neural network architecture has been trained and tested on two practical civil engineering problems – soil classification, and the prediction o strength and workability of high performance concrete.     

Estimating the Number of Hidden Neurons in a Feedforward Network Using the Singular Value Decomposition

In this letter, we attempt to quantify the significance of increasing the number of neurons in the hidden layer of a feedforward neural network architecture using the singular value decomposition (SVD). Through this, we extend some well-known properties of the SVD in evaluating the generalizability of single hidden layer feedforward networks (SLFNs) with respect to the number of hidden layer neurons. The generalization capability of the SLFN is measured by the degree of linear independency of the patterns in hidden layer space, which can be indirectly quantified from the singular values obtained from the SVD, in a postlearning step. A pruning/growing technique based on these singular values is then used to estimate the necessary number of neurons in the hidden layer. More importantly, we describe in detail properties of the SVD in determining the structure of a neural network particularly with respect to the robustness of the selected model     

基于特征可视化分析深度神经网络的内部表征

基于可视化的方式理解深度神经网络能直观地揭示其工作机理,即提供了黑盒模型做出决策的解释,在医疗诊断、自动驾驶等领域尤其重要。大部分现有工作均基于激活值最大化框架,即选定待观测神经元,通过优化输入值(如隐藏层特征图谱、原始图片),定性地将待观测神经元产生最大激活值时输入值的改变作为一种解释。然而,这种方法缺乏对深度神经网络深入的定量分析。文中提出了结构可视化和基于规则可视化两种可视化的元方法。结构可视化从浅至深依层可视化,发现浅层神经元具有一般性的全局特征,而深层神经元更针对细节特征。基于规则可视化包括交集与差集规则,可以帮助发现共享神经元与抑制神经元的存在,它们分别学习了不同类别的共有特征与抑制不相关的特征。实验针对代表性卷积网络VGG和残差网络ResNet在ImageNet和微软COCO数据集上进行了分析。通过量化分析发现,ResNet和VGG均有很高的稀疏性,通过屏蔽一些低激活值的“噪音”神经元,发现其对深度神经网络分类准确率均没有影响,甚至有一定程度的提高作用。文中通过可视化和量化分析深度神经网络的隐藏层特征,揭示其内部特征表达,从而为高性能深度神经网络的设计提供指导和借鉴。     

Heuristic configuration of single hidden-layer feed-forward neural networks

For optimum statistical classification and generalization with single hidden-layer neural network models, two tasks must be performed: (a) learning the best set of weights for a network of k hidden units and (b) determining k, the best complexity fit. We contrast two approaches to construction of neural network classifiers: (a) standard back-propagation as applied to a series of single hidden-layer feed-forward nerual networks with differing number of hidden units and (b) a heuristic cascade-correlation approach that quickly and dynamically configures the hidden units in a network and learns the best set of weights for it. Four real-world applications are considered. On these examples, the back-propagation approach yielded somewhat better results, but with far greater computation times. The best complexity fit, k, for both approaches were quite similar. This suggests a hybrid approach to constructing single hidden-layer feed-forward neural network classifiers in which the number of hidden units is determined by cascade-correlation and the weights are learned by back-propagation.     

Research on using genetic algorithms to optimize Elman neural networks

There is a function of dynamic mapping when processing non-linear complex data with Elman neural networks. Because Elman neural network inherits the feature of back-propagation neural network to some extent, it has many defects; for example, it is easy to fall into local minimum, the fixed learning rate, the uncertain number of hidden layer neuron and so on. It affects the processing accuracy. So we optimize the weights, thresholds and numbers of hidden layer neurons of Elman networks by genetic algorithm. It improves training speed and generalization ability of Elman neural networks to get the optimal algorithm model. It has been proved by instance analysis that new algorithm was superior to the traditional model in terms of convergence rate, predicted value error, number of trainings conducted successfully, etc. It indicates the effect of the new algorithm and deserves further popularization.     

Pruning recurrent neural networks for improved generalizationperformance

Determining the architecture of a neural network is an important issue for any learning task. For recurrent neural networks no general methods exist that permit the estimation of the number of layers of hidden neurons, the size of layers or the number of weights. We present a simple pruning heuristic that significantly improves the generalization performance of trained recurrent networks. We illustrate this heuristic by training a fully recurrent neural network on positive and negative strings of a regular grammar. We also show that rules extracted from networks trained with this pruning heuristic are more consistent with the rules to be learned. This performance improvement is obtained by pruning and retraining the networks. Simulations are shown for training and pruning a recurrent neural net on strings generated by two regular grammars, a randomly-generated 10-state grammar and an 8-state, triple-parity grammar. Further simulations indicate that this pruning method can have generalization performance superior to that obtained by training with weight decay.     

A unified mathematical form for removing neurons based on orthogonal projection and crosswise propagation

It is a common practice to adjust the number of hidden neurons in training, and the removal of neurons in neural networks plays an indispensable role in this architecture manipulation. In this paper, a succinct and unified mathematical form is upgraded to the generic case for removing neurons based on orthogonal projection and crosswise propagation in a feedforward layer with different architectures of neural networks, and further developed for several neural networks with different architectures. For a trained neural network, the method is divided into three stages. In the first stage, the output vectors of the feedforward observation layer are classified to clusters. In the second stage, the orthogonal projection is performed to locate a neuron whose output vector can be approximated by the other output vectors in the same cluster with the least information loss. In the third stage, the previous located neuron is removed and the crosswise propagation is implemented in each cluster. On accomplishment of the three stages, the neural network with the pruned architecture is retrained. If the number of clusters is one, the method is degenerated into its special case with only one neuron being removed. The applications to different architectures of neural networks with an extension to the support vector machine are exemplified. The methodology supports in theory large-scale applications of neural networks in the real world. In addition, with minor modifications, the unified method is instructive in pruning other networks as far as they have similar network structure to the ones in this paper. It is concluded that the unified pruning method in this paper equips us an effective and powerful tool to simplify the architecture in neural networks.     

Feedforward neural network construction using cross validation.

This article presents an algorithm that constructs feedforward neural networks with a single hidden layer for pattern classification. The algorithm starts with a small number of hidden units in the network and adds more hidden units as needed to improve the network's predictive accuracy. To determine when to stop adding new hidden units, the algorithm makes use of a subset of the available training samples for cross validation. New hidden units are added to the network only if they improve the classification accuracy of the network on the training samples and on the cross-validation samples. Extensive experimental results show that the algorithm is effective in obtaining networks with predictive accuracy rates that are better than those obtained by state-of-the-art decision tree methods.     

A Novel Pruning Algorithm for Optimizing Feedforward Neural Network of Classification Problems

Optimizing the structure of neural networks is an essential step for the discovery of knowledge from data. This paper deals with a new approach which determines the insignificant input and hidden neurons to detect the optimum structure of a feedforward neural network. The proposed pruning algorithm, called as neural network pruning by significance (N2PS), is based on a new significant measure which is calculated by the Sigmoidal activation value of the node and all the weights of its outgoing connections. It considers all the nodes with significance value below the threshold as insignificant and eliminates them. The advantages of this approach are illustrated by implementing it on six different real datasets namely iris, breast-cancer, hepatitis, diabetes, ionosphere and wave. The results show that the proposed algorithm is quite efficient in pruning the significant number of neurons on the neural network models without sacrificing the networks performance.     

MLP bilinear separation

In this paper, we present a thorough mathematical analysis of the use of neural networks to solve a specific classification problem consisting of a bilinear boundary. The network under consideration is a three-layered perceptron with two hidden neurons having the sigmoid serving as the activation function. The analysis of the hidden space created by the outputs of the hidden neurons will provide results on the network’s capacity to isolate two classes of data in a bilinear fashion, and the importance of the value of the sigmoid parameter is highlighted. We will obtain an explicit analytical function describing the boundary generated by the network, thus providing information on the effect each parameter has on the network’s behavior. Generalizations of the results are obtained with additional neurons, and a theorem concerned with analytical reproducibility of the boundary function is established.     

Time-series prediction with single integrate-and-fire neuron

In this paper, a learning algorithm for a single integrate-and-fire neuron (IFN) is proposed and tested for various applications in which a multilayer perceptron neural network is conventionally used. It is found that a single IFN is sufficient for the applications that require a number of neurons in different hidden layers of a conventional neural network. Several benchmark and real-life problems of classification and time-series prediction have been illustrated. It is observed that the inclusion of some more biological phenomenon in an artificial neural network can make it more powerful.     

Thalassaemia classification by neural networks and genetic programming

This paper presents the use of a neural network and a decision tree, which is evolved by genetic programming (GP), in thalassaemia classification. The aim is to differentiate between thalassaemic patients, persons with thalassaemia trait and normal subjects by inspecting characteristics of red blood cells, reticulocytes and platelets. A structured representation on genetic algorithms for non-linear function fitting or STROGANOFF is the chosen architecture for genetic programming implementation. For comparison, multilayer perceptrons are explored in classification via a neural network. The classification results indicate that the performance of the GP-based decision tree is approximately equal to that of the multilayer perceptron with one hidden layer. But the multilayer perceptron with two hidden layers, which is proven to have the most suitable architecture among networks with different number of hidden layers, outperforms the GP-based decision tree. Nonetheless, the structure of the decision tree reveals that some input features have no effects on the classification performance. The results confirm that the classification accuracy of the multilayer perceptron with two hidden layers can still be maintained after the removal of the redundant input features. Detailed analysis of the classification errors of the multilayer perceptron with two hidden layers, in which a reduced feature set is used as the network input, is also included. The analysis reveals that the classification ambiguity and misclassification among persons with minor thalassaemia trait and normal subjects is the main cause of classification errors. These results suggest that a combination of a multilayer perceptron with a blood cell analysis may give rise to a guideline/hint for further investigation of thalassaemia classification.     

An investigation of neural networks for linear time-series forecasting

This study examines the capability of neural networks for linear time-series forecasting. Using both simulated and real data, the effects of neural network factors such as the number of input nodes and the number of hidden nodes as well as the training sample size are investigated. Results show that neural networks are quite competent in modeling and forecasting linear time series in a variety of situations and simple neural network structures are often effective in modeling and forecasting linear time series.Scope and purposeNeural network capability for nonlinear modeling and forecasting has been established in the literature both theoretically and empirically. The purpose of this paper is to investigate the effectiveness of neural networks for linear time-series analysis and forecasting. Several research studies on neural network capability for linear problems in regression and classification have yielded mixed findings. This study aims to provide further evidence on the effectiveness of neural network with regard to linear time-series forecasting. The significance of the study is that it is often difficult in reality to determine whether the underlying data generating process is linear or nonlinear. If neural networks can compete with traditional forecasting models for linear data with noise, they can be used in even broader situations for forecasting researchers and practitioners.