Ming-Hu Ha

Applications of wavelet transform in medical image processing

The wavelet transform and inverse transform algorithm are introduced. The medical image plays an important role in clinical diagnosis and therapy of doctor and teaching and researching. This paper gives reviews of some applications in medical image with wavelet, such as ECG signal processing, EEG signal processing, medical image compression, medical image reinforcing and edge detection, medical image register. With the further development of wavelet theory, wavelet transform be widely applied to the domain of medical image.

Fuzzy knowledge representation and reasoning using a generalized fuzzy petri net and a similarity measure

In the study of weighted fuzzy production rules (WFPRs) reasoning, we often need to consider those rules whose consequences are represented by two or more propositions connected by “AND” or “OR”. To enhance the representation capability of those rules, this paper proposes two types of knowledge representation parameters, namely, the input weight and the output weight, for a rule. A Generalized Fuzzy Petri Net (GFPN) is also presented for WFPR reasoning. Furthermore, this paper gives a similarity measure to improve the evaluation method of WFPRs and the multilevel fuzzy reasoning in which the consequences and their certainty factors are deduced synchronously by using a GFPN.

Linear feature-weighted support vector machine

The existing support vector machines (SVMs) are all assumed that all the features of training samples have equal contributions to construct the optimal separating hyperplane. However, for a certain real-world data set, some features of it may possess more relevances to the classification information, while others may have less relevances. In this paper, the linear feature-weighted support vector machine (LFWSVM) is proposed to deal with the problem. Two phases are employed to construct the proposed model. First, the mutual information (MI) based approach is used to assign appropriate weights for each feature of the whole given data set. Second, the proposed model is trained by the samples with their features weighted by the obtained feature weight vector. Meanwhile, the feature weights are embedded in the quadratic programming through detailed theoretical deduction to obtain the dual solution to the original optimization problem. Although the calculation of feature weights may add an extra computational cost, the proposed model generally exhibits better generalization performance over the traditional support vector machine (SVM) with linear kernel function. Experimental results upon one synthetic data set and several benchmark data sets confirm the benefits in using the proposed method. Moreover, it is also shown in experiments that the proposed MI based approach to determining feature weights is superior to the other two mostly used methods.

The sub-key theorem on credibility measure space

In 1970s, Vladimir N. Vapnik proposed statistical learning theory. The theory is considered as optimum theory on small samples statistical estimation and prediction learning. It has more systematically investigated the rational conditions of the empirical risk minimization discipline and the relations between the empirical risk and the expected risk on finite samples. In fact, the key theorem of learning theory plays an important role in statistical learning theory. Its importance results in paving the way for the subsequent theories and applications. However, some theories and definitions only suit to fixed probability measure. These restricted conditions reduce the applied range of theorem. In this paper, we will generalize the applied range by means of changing the probability measure space into credibility measure space. In new measure space, we give new concepts and new theorem on classical theoretical foundation.

Optical font recognition based on Gabor filter

The font recognition of Chinese characters is an important part in OCR (optical character recognition) system. It is also a main technical challenge due to the similarity of different fonts. The reconstruction quality of layout depends on the accuracy of font recognition. However, the prevalent method of font recognition is predominant font recognition based on the fact that the most layouts are printed in a single font, which makes it impossible to reconstruct the original layout. In this paper, an improved font recognition method of individual character is proposed. The approach consists of three steps. In the first step, the guidance fonts are acquired based on Gabor filter optimized with genetic algorithm (GA). Then a single font recognizer is applied to get the matching results with the help of the guidance fonts and the layout knowledge of font typesetting. Finally, the post-processing of font recognition is fulfilled according to the layout knowledge. Experiments were carried out with samples from newspaper and magazines and the results show that the method is of immense practical and theoretical value.

A new support vector machine based on type-2 fuzzy samples

Classical support vector machine is based on the real valued random samples and established on the probability space. It is hard to deal with classification problems based on type-2 fuzzy samples established on non-probability space. The existing algorithm, type-2 fuzzy support vector machine established on generalized credibility space, transforms the classification problems based on type-2 fuzzy samples to general fuzzy optimization problems and expands the application range of traditional support vector machine. However, nonnegativeness of the decision variables of general fuzzy optimization problems is too strict to be satisfied in some practical applications. Motivated by this, the concept of expected fuzzy possibility measure is proposed. Then type-2 fuzzy support vector machine on expected fuzzy possibility space is established, and the second-order cone programming of type-2 fuzzy support vector machine on expected fuzzy possibility space is given. The results of numerical experiments show the effectiveness of the type-2 fuzzy support vector machine established on expected fuzzy possibility space.

Some theoretical results of learning theory based on random sets in set‐valued probability space

Purpose – The purpose of this paper is to introduce some basic knowledge of statistical learning theory (SLT) based on random set samples in set‐valued probability space for the first time and generalize the key theorem and bounds on the rate of uniform convergence of learning theory in Vapnik, to the key theorem and bounds on the rate of uniform convergence for random sets in set‐valued probability space. SLT based on random samples formed in probability space is considered, at present, as one of the fundamental theories about small samples statistical learning. It has become a novel and important field of machine learning, along with other concepts and architectures such as neural networks. However, the theory hardly handles statistical learning problems for samples that involve random set samples.Design/methodology/approach – Being motivated by some applications, in this paper a SLT is developed based on random set samples. First, a certain law of large numbers for random sets is proved. Second, the de...

The theoretical fundamentals of learning theory based on fuzzy complex random samples

Statistical learning theory based on real-valued random samples has been regarded as one of the influential developments for small samples statistical estimation and learning. The key theorem of learning theory and the bounds on the rate of convergence of learning process are the most important theoretical fundamentals of the statistical learning theory. In this paper, we discuss a statistical learning theory based on fuzzy complex random samples. Firstly, the definition of fuzzy complex numbers is introduced and the fuzzy complex random variables along with their numeric characteristic are investigated. Secondly, we carry out further research focused on a special type of fuzzy complex number, namely rectangular fuzzy complex number and establish some properties and develop important theorems. We also prove the strong law of large numbers based on fuzzy complex random variables. Thirdly, the definitions of the fuzzy complex expected risk functional, the fuzzy complex empirical risk functional, the fuzzy complex empirical risk minimization principle and the consistency are provided and discussed. Finally, the key theorem of learning theory and the bounds on the rate of convergence of learning process based on fuzzy complex random samples are discussed.

The Fuzzy- Number Based Key Theorem of Statistical Learning Theory

Recently, many scholars are becoming interested in the study of statistical learning theory based on fuzzy field. In this paper, we redefine the definitions of fuzzy expected risk functional, fuzzy empirical risk functional and fuzzy empirical risk minimization principal based on fuzzy samples, where the two type of fuzzy risk functional are still fuzzy number. Based on the above, we give the proof of the key theorem, which plays an important role in the statistical learning theory

Sequences of (S) fuzzy integrable functions

A new concept of the fuzzy mean fundamental convergence is introduced, and the relations among several convergences of sequences of (S) fuzzy integrable functions are discussed. Further, the equivalent relation between fuzzy mean fundamental convergence and fundamental convergence in fuzzy measure of sequences of (S) fuzzy integrable functions is proved. Three new definitions of uniform sequence, uniform weak and absolute continuous sequence, and uniform bounded sequence of (S) fuzzy integrable functions are also given, and the properties of sequences of (S) fuzzy integrable functions are discussed. Moreover, the equivalent relation between the uniform sequence and the uniform bounded sequence of (S) fuzzy integrable functions is shown.