Extreme learning machine (ELM) has attracted widespread attention due to its simple, quick and good performance. In this work, in order to deal with cross data quickly and efficiently, we first propose generalized eigenvalue proximal extreme learning machine (GEPELM). It takes the form of ratio into consideration to seek for two non-parallel separating hyperplanes in ELM feature space, each of which is close to the samples of its own class and far away from the others simultaneously. Then generalized eigenvalue algorithm is adopted to solve, which incurs GEPELM to enjoy faster calculation speed than TELM. Further, improved generalized eigenvalue proximal extreme learning machine (IGEPELM) is proposed, which uses minus instead of ratio to avoid singular value phenomenon and further mitigate the computational burden by solving two standard eigenvalue problems. To further improve classification performance, generalized eigenvalue proximal extreme learning machine based on inter-class graph (GGEPELM) is proposed, which incorporates the geometric structure information of dissimilar samples into the guideline of GEPELM. In addition, the proposed classifiers are all extended to kernel ELM framework to handle non-linear data more precisely. Moreover, Sherman-Morrison-Woodbury formula is utilized to reduce time complexity of matrix inversion. Simultaneously, a quick solution strategy is incorporated into GEPELMs and GGEPELMs to mitigate the burden of solving large-scale problems. The numerical simulations are carried out on three databases including a benchmark database, an artificial database and a practical application database, which demonstrates the proposed classifiers enjoy high computational speed, good generalization performance and insensitivity to parameters.

This work proposes a robust distance metric that is induced by correntropy based on Laplacian kernel. The proposed metric satisfies the properties that distance metric must have. Moreover, we demonstrate important properties of the proposed metric such as robustness, boundedness, non-convexity and approximation behaviors. The proposed metric includes and extends the traditional metrics such as L-0-norm and L-1-norm metrics. Following that we apply the proposed metric to twin support vector machine classification (TSVM), and then a new robust TSVM algorithm (called RCTSVM) is built to reduce the influence of noise and outliers. The proposed RCTSVM inherits the advantages of TSVM and improves the robustness. However, the non-convexity of the proposed model makes it difficult to optimize. A continuous optimization method is developed to solve the RCTSVM. The problem is converted into difference of convex (DC) programming, and the corresponding DC algorithm (DCA) converges linearly. Compared with the traditional algorithms, numerical experiments under different noise setting and evaluation criteria show that the proposed RCTSVM has robustness to noise and outliers in most cases, which demonstrates the feasibility and effectiveness of the proposed method. (C) 2020 Elsevier Inc. All rights reserved.

The Fractional Fourier transform (FRFT) is a relatively novel linear transforms that is a generalization of conventional Fourier transform (FT). FRFT can transform a particular signal to a unified time-frequency domain. In this survey, we try to present a comprehensive investigation of FRFT. Firstly, we provided definition of FRFT and its three discrete versions (weighted-type, sampling-type, and eigendecomposition-type). Secondly, we offered a comprehensive theoretical research and technological studies that consisted of hardware implementation, software implementation, and optimal order selection. Thirdly, we presented a survey on applications of FRFT to following fields: communication, encryption, optimal engineering, radiology, remote sensing, fractional calculus, fractional wavelet transform, pseudo-differential operator, pattern recognition, and image processing. It is hoped that this survey would be beneficial for the researchers studying on FRFT.

AIM:To develop an automatic magnetic resonance (MR) brain classification that can assist physicians to make a diagnosis and reduce wrong decisions. METHOD:This article investigated the binary particle swarm optimization (BPSO) approach and proposed its three new variants: BPSO with mutation and time-varying acceleration coefficients (BPSO-MT), BPSO with mutation (BPSO-M), and BPSO with time-varying acceleration coefficients (BPSO-T). We first extracted wavelet entropy (WE) features from both approximation and detail sub-bands of eight-level decomposition. Afterwards, we used the proposed BPSO-M, BPSO-T, and BPSO-MT to select features. Finally, the selected features were fed into a probabilistic neural network (PNN). RESULTS:The proposed BPSO-MT performed better than BPSO-T and BPSO-M. It finally selected two features of entropies of the following two sub-bands (V1, D1). The proposed system "WE + BPSO-MT + PNN" yielded perfect classification on Data160 and Data66. In addition, it yielded 99.53% average accuracy for the Data255, over 10 repetitions of k-fold stratified cross validation (SCV), higher than state-of-the-art approaches. CONCLUSIONS:The proposed method is effective for MR brain classification.

Finding an appropriate and accurate technology for early detection of disease is significantly important to research early treatments. We proposed some novel automatic classification systems based on the stationary wavelet transform (SWT) and the improved support vector machine (SVM). Magnetic Resonance Imaging (MRI) is commonly used for brain imaging as a non-invasive diagnostic tool to assist the pre-clinical diagnosis. However, MRI generates a large information set, which poses a challenge for classification. To deal with this problem we proposed a new approach, which combines SWT and Principal Component Analysis for feature extraction. In our experiments, three different datasets and four kinds of classifiers of the SVM were employed. The results over 5×6-fold stratified cross-validation (SCV) for Dataset-66, and 5×5-fold SCV for the other two datasets show that the average accuracy is almost 100.00%.

It is important to detect abnormal brains accurately and early. The wavelet-energy (WE) was a successful feature descriptor that achieved excellent performance in various applications; hence, we proposed a WE based new approach for automated abnormal detection, and reported its preliminary results in this study. The kernel support vector machine (KSVM) was used as the classifier, and quantum-behaved particle swarm optimization (QPSO) was introduced to optimize the weights of the SVM. The results based on a 5 × 5-fold cross validation showed the performance of the proposed WE + QPSO-KSVM was superior to ``DWT + PCA + BP-NN'', ``DWT + PCA + RBF-NN'', ``DWT + PCA + PSO-KSVM'', ``WE + BPNN'', ``WE +$ KSVM'', and ``DWT $+$ PCA $+$ GA-KSVM'' w.r.t. sensitivity, specificity, and accuracy. The work provides a novel means to detect abnormal brains with excellent performance.

Aim. It can help improve the hospital throughput to accelerate magnetic resonance imaging (MRI) scanning. Patients will benefit from less waiting time. Task. In the last decade, various rapid MRI techniques on the basis of compressed sensing (CS) were proposed. However, both computation time and reconstruction quality of traditional CS-MRI did not meet the requirement of clinical use. Method. In this study, a novel method was proposed with the name of exponential wavelet iterative shrinkage-thresholding algorithm with random shift (abbreviated as EWISTARS). It is composed of three successful components: (i) exponential wavelet transform, (ii) iterative shrinkage-thresholding algorithm, and (iii) random shift. Results. Experimental results validated that, compared to state-of-the-art approaches, EWISTARS obtained the least mean absolute error, the least mean-squared error, and the highest peak signal-to-noise ratio. Conclusion. EWISTARS is superior to state-of-the-art approaches.

An accurate diagnosis is important for the medical treatment of patients suffered from brain disease. Nuclear magnetic resonance images are commonly used by technicians to assist the pre-clinical diagnosis, rating them by visual evaluations. The classification of NMR images of normal and pathological brains poses a challenge from technological point of view, since NMR imaging generates a large information set that reflects the conditions of the brain. In this work, we present a computer assisted diagnosis method based on a wavelet-entropy (In this paper 2D-discrete wavelet transform has been used, in that it can extract more information) of the feature space approach and a Naive Bayes classifier classification method for improving the brain diagnosis accuracy by means of NMR images. The most relevant image feature is selected as the wavelet entropy, which is used to train a Naive Bayes classifier. The results over 64 images show that the sensitivity of the classifier is as high as 94.50

(Aim) It is of great importance to find abnormal or pathological brains in the early stage, to save hospital and social resources. However, potential of wavelet-energy is not widely used in this field. (Method) The popular "wavelet-energy" is regarded as a prevalent feature descriptor, which achieves good performance in many applications. In this work, we propose a wavelet-energy based new method for classification of magnetic resonance brain images. The approach is a three-stage system, including wavelet decomposition, energy extraction, and k-Nearest Neighbors algorithm. (Results) The proposed approach achieved excellent performance with a sensitivity of 93.75%, a specificity of 100%, and an accuracy of 95.45%. (Conclusion) Its performance is comparable to the state-of-the-art methods. It provides a new approach to detect features indicative of abnormal and pathological brains.

Aim: To detect pathological brain conditions early is a core procedure for patients so as to have enough time for treatment. Traditional manual detection is either cumbersome, or expensive, or time-consuming. We aim to offer a system that can automatically identify pathological brain images in this paper. Method: We propose a novel image feature, viz., Fractional Fourier Entropy (FRFE), which is based on the combination of Fractional Fourier Transform (FRFT) and Shannon entropy. Afterwards, the Welch’s t-test (WTT) and Mahalanobis distance (MD) were harnessed to select distinguishing features. Finally, we introduced an advanced classifier: twin support vector machine (TSVM). Results: A 10 × K-fold stratified cross validation test showed that this proposed “FRFE + WTT + TSVM” yielded an accuracy of 100.00%, 100.00%, and 99.57% on datasets that contained 66, 160, and 255 brain images, respectively. Conclusions: The proposed “FRFE + WTT + TSVM” method is superior to 20 state-of-the-art methods.

It is important to early detect pathological brains. Traditional methods used plain support vector machine (SVM) that is vulnerable to noises and outliers. In this study, we presented a hybrid method that combined wavelet-energy (WE) and fuzzy support vector machine (FSVM). The results over a 5x5-fold cross validation showed that the proposed "WE + FSVM" produced accuracy of 93.78%, higher than "WE + KSVM" of 91.78%, "DWT + PCA + RBF-NN" of 91.33%, "WE + BP-NN" of 86.67%, and "DWT + PCA + BP-NN" of 86.22%. Therefore, this study offered a new means to solve the problem with excellent performance.

With the aim of developing an accurate pathological brain detection system, we proposed a novel automatic computer-aided diagnosis (CAD) to detect pathological brains from normal brains obtained by magnetic resonance imaging (MRI) scanning. The problem still remained a challenge for technicians and clinicians, since MR imaging generated an exceptionally large information dataset. A new two-step approach was proposed in this study. We used wavelet entropy (WE) and Hu moment invariants (HMI) for feature extraction, and the generalized eigenvalue proximal support vector machine (GEPSVM) for classification. To further enhance classification accuracy, the popular radial basis function (RBF) kernel was employed. The 10 runs of k-fold stratified cross validation result showed that the proposed "WE + HMI + GEPSVM + RBF" method was superior to existing methods w.r.t. classification accuracy. It obtained the average classification accuracies of 100%, 100%, and 99.45% over Dataset-66, Dataset-160, and Dataset-255, respectively. The proposed method is effective and can be applied to realistic use.