Artificial neural networks (ANNs) constitute a class of flexible nonlinear models designed to mimic biological neural systems. In this entry, we introduce ANN using familiar econometric terminology and provide an overview of ANN modeling approach and its implementation methods. † Correspondence: Chung-Ming Kuan, Institute of Economics, Academia Sinica, 128 Academia Road, Sec. 2, Taipei 115, Taiwan; ckuan@econ.sinica.edu.tw. †† I would like to express my sincere gratitude to the editor, Professor Steven Durlauf, for his patience and constructive comments on early drafts of this entry. I also thank Shih-Hsun Hsu and Yu-Lieh Huang for very helpful suggestions. The remaining errors are all mine.

Artificial neural networks

Handwritten digit recognition plays a significant role in many user authentication applications in the modern world. As the handwritten digits are not of the same size, thickness, style, and orientation, therefore, these challenges are to be faced to resolve this problem. A lot of work has been done for various non-Indic scripts particularly, in case of Roman, but, in case of Indic scripts, the research is limited. This paper presents a script invariant handwritten digit recognition system for identifying digits written in five popular scripts of Indian subcontinent, namely, Indo-Arabic, Bangla, Devanagari, Roman, and Telugu. A 130-element feature set which is basically a combination of six different types of moments, namely, geometric moment, moment invariant, affine moment invariant, Legendre moment, Zernike moment, and complex moment, has been estimated for each digit sample. Finally, the technique is evaluated on CMATER and MNIST databases using multiple classifiers and, after performing statistical significance tests, it is observed that Multilayer Perceptron MLP classifier outperforms the others. Satisfactory recognition accuracies are attained for all the five mentioned scripts.

/pdf/a-study-of-moment-based-features-on-handwritten-digit-2e8lgvkrl1.pdf

A Study of Moment Based Features on Handwritten Digit Recognition

Evolution Strategies, a class of Evolutionary Algorithms based on Gaussian mutation and deterministic selection, are today considered the best choice as far as parameter optimization is concerned. However, there are multiple ways to tune the covariance matrix of the Gaussian mutation. After reviewing the state of the art in covariance matrix adaptation, a new approach is proposed, in which the update of the covariance matrix is based on a quadratic approximation of the target function, obtained by some Least-Square minimization. A dynamic criterion is designed to detect situations where the approximation is not accurate enough, and original Covariance Matrix Adaptation (CMA) should rather be directly used. The resulting algorithm is experimentally validated on benchmark functions, outperforming CMA-ES on a large class of problems.

LS-CMA-ES: A second-order algorithm for Covariance Matrix Adaptation

A convolutional recursive modified Self Organizing Map for handwritten digits recognition

Semi-supervised clustering generally assumes that prior knowledge is helpful to improve clustering performance. However, the prior knowledge may degenerate the clustering performance if one collects wrong information, such as wrong labels. Hence, it is meaningful to design a safe semi-supervised clustering method which never performs worse than the corresponding unsupervised and semi-supervised clustering methods. In this paper, we develop local homogeneous consistent safe semi-supervised clustering where class labels are given as the prior knowledge. To the best of our knowledge, it is the first time safe semi-supervised clustering has been studied. The basic idea is that the predictions of a labeled sample and its nearest homogeneous unlabeled ones should be similar when the labeled one is risky. In our algorithm, we firstly build a local graph to model the relationship between the labeled sample and its nearest homogeneous unlabeled ones through the results obtained by unsupervised clustering. A graph-based regularization term is then constructed to allow the predictions of the labeled samples to approach that of the local homogeneous neighbors. It is expected to reduce the risk of the labeled samples. Meanwhile, our algorithm positively exploits the labeled samples by restricting the corresponding outputs to be the given class labels when the labeled ones may be helpful. In this sense, the predictions of the labeled samples in our algorithm are a tradeoff between the given class labels and the predictions of local homogeneous neighbors. To verify the effectiveness of our algorithm, we conduct a series of experiments on several UCI datasets. The results show that our algorithm outperforms the corresponding unsupervised and semi-supervised clustering methods even if the wrongly labeled ratio reaches 30%. In this sense, the proposed algorithm will not only enrich the theoretical knowledge in the machine learning field, but significantly improve the practicability of semi-supervised clustering in the expert and intelligent systems.

Local homogeneous consistent safe semi-supervised clustering

Discriminative structure selection method of Gaussian Mixture Models with its application to handwritten digit recognition

The optimization method is one of key issues in discriminative learning of pattern classifiers. This paper proposes a hybrid approach of the Covariance Matrix Adaptation Evolution Strategy (CMA-ES) and the gradient decent method for optimizing Bayesian classifiers under the SOFT target based Max-Min posterior Pseudo-probabilities (Soft-MMP) learning framework. In our hybrid optimization approach, the weighted mean of the parent population in the CMA-ES is adjusted by exploiting the gradient information of objective function, based on which the offspring is generated. As a result, the efficiency and the effectiveness of the CMA-ES are improved. We apply the Soft-MMP with the proposed hybrid optimization approach to handwritten digit recognition. The experiments on the CENPARMI database show that our handwritten digit classifier outperforms other state-of-the-art techniques. Furthermore, our hybrid optimization approach behaved better than not only the single gradient decent method but also the single CMA-ES in the experiments.

/pdf/combining-evolution-strategy-and-gradient-descent-method-for-4m95iigguv.pdf

Combining evolution strategy and gradient descent method for discriminative learning of bayesian classifiers

Learning is important for classifiers. This paper proposes a new approach to handwritten digit recognition based on the max-min posterior pseudo-probabilities framework for learning pattern classification. Each digit class is modeled as a posterior pseudo-probability function, the parameters in which are trained from positive and negative samples of this digit class using the max-min posterior pseudo-probabilities criterion. In the process of digit classification, an input pattern is classified as one of ten digit classes or refused as being unrecognized according to the posterior pseudo-probabilities. Experiments on NIST database show the effectiveness of the proposed approach in reducing the error rate and making rejection decisions to those input pattern which can not be reliably by even human.

Learning Handwritten Digit Recognition by the Max-Min Posterior Pseudo-Probabilities Method

The problem of determining the appropriate number of components is important in finite mixture modeling for pattern classification. This paper considers the application of an unsupervised clustering method called AutoClass to training of Orthogonal Gaussian Mixture Models (OGMM). Actually, the number of components in OGMM of each class is selected based on AutoClass. In this way, the structures of OGMM for difference classes are not necessarily be the same as those in usual modeling scheme, so that the dissimilarity between the data distributions of different classes can be described more exactly. After the model selection is completed, a discriminative learning framework of Bayesian classifiers called Max-Min posterior pseudo-probabilities (MMP) is employed to estimate component parameters in OGMM of each class. We apply the proposed learning approach of OGMM to handwritten digit recognition. The experimental results on the MNIST database show the effectiveness of our approach.

http://www.cvc.uab.es/icdar2009/papers/3725b151.pdf

Unsupervised Selection and Discriminative Estimation of Orthogonal Gaussian Mixture Models for Handwritten Digit Recognition

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Papers

Discriminative structure selection method of Gaussian Mixture Models with its application to handwritten digit recognition

Combining evolution strategy and gradient descent method for discriminative learning of bayesian classifiers

Learning Handwritten Digit Recognition by the Max-Min Posterior Pseudo-Probabilities Method

Unsupervised Selection and Discriminative Estimation of Orthogonal Gaussian Mixture Models for Handwritten Digit Recognition