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Twin support vector regression (TSVR) has been widely applied in regression problems. TSVR seeks a pair of ε -insensitive proximal planes by solving two support vector machine type problems. TSVR assumes that the matrices appearing in the dual formulation are positive definite. However, in real-world scenarios, such an assumption may not be fulfilled and, hence, leads to suboptimal performance. ε -Twin support vector regression (ε -TSVR) improved the TSVR by introducing the regularisation term to avoid the singularity issues. Most of the twin support vector machine models involve the computation of matrix inverses. Also, TSVR implements the empirical risk minimization principle. In this paper, we propose an improved twin support vector regression (ITSVR) for brain age estimation by introducing different Lagrangian functions for the primal problems of the TSVR. The proposed ITSVR implements the structural risk minimization principle and avoids the computation of the matrix inverses. To solve the optimization problem more efficiently, we used successive overrelaxation (SOR) technique. We evaluated the proposed ITSVR on cognitively healthy subjects, mild cognitive impairment subjects and Alzheimer's disease subjects. The experimental results demonstrate that the proposed ITSVR has superior performance compared to the baseline models for brain age estimation. [ABSTRACT FROM AUTHOR]

Collecting and analyzing data from all devices to improve the efficiency of business processes is an important task of Industrial Internet of Things (IIoT). In the age of data explosion, extensive text data generated by the IIoT have given birth to a variety of text representation methods. The task of text representation is to convert the natural language to a form that computer can understand with retaining the original semantics. However, these methods are difficult to effectively extract the semantic features among words and distinguish polysemy in natural language. Combining the advantages of convolutional neural network (CNN) and variational autoencoder (VAE), this paper proposes an intelligent CNN-VAE text representation algorithm as an advanced learning method for social big data within next-generation IIoT, which help users identify the information collected by sensors and perform further processing. This method employs the convolution layer to capture the local features of the context and uses the variational technique to reconstruct feature space to make it conform to the normal distribution. In addition, the improved word2vec model based on topical word embedding (TWE) is utilized to add topical information to word vectors to distinguish polysemy. This paper takes the social big data as an example to illustrate the way of the proposed algorithm applied in the next-generation IIoT and utilizes Cnews dataset to verify the performance of proposed method with four evaluating metrics (i.e., recall, accuracy, precision, and F1-score). Experimental results indicate that the proposed method outperforms word2vec-avg and CNN-AE in K-nearest neighbor (KNN), random forest (RF), and support vector machine (SVM) classifiers and distinguishes polysemy effectively. [ABSTRACT FROM AUTHOR]

This study utilizes classification models to provide a robust algorithm for imbalanced data where the minority class is of the interest, that is, in the context of default payments. In developing an integrated predictive accuracy algorithm, this study proposes machine learning classifiers and applies DNN, SVM, KNN, and ANN. The proposed algorithm utilizes a 30,000 imbalanced dataset to improve the accuracy of the prediction of default payments by implementing oversampling and undersampling strategies, such as synthetic minority oversampling technique (SMOTE), SVM SMOTE, random undersampling, and ALL-KNN. The results indicate that the SVM under the ALL-KNN sampling technique is able to achieve an accuracy of 98.6%, with the lowest cross entropy loss measurement of 0.028. Through the accurate implementation of the neural networks and neurons used in the proposed algorithm, this paper presents better insights into the functioning of the neural networks when used in conjunction with the resampling techniques. Using the methodology and algorithm presented in this study, credit risk assessments can be more accurately predicted in practical applications where most of the clients are categorized as non-default payments. [ABSTRACT FROM AUTHOR]

In this paper, we present difference of convex algorithms for solving bilevel programs in which the upper level objective functions are difference of convex functions, and the lower level programs are fully convex. This nontrivial class of bilevel programs provides a powerful modelling framework for dealing with applications arising from hyperparameter selection in machine learning. Thanks to the full convexity of the lower level program, the value function of the lower level program turns out to be convex and hence the bilevel program can be reformulated as a difference of convex bilevel program. We propose two algorithms for solving the reformulated difference of convex program and show their convergence to stationary points under very mild assumptions. Finally we conduct numerical experiments to a bilevel model of support vector machine classification. [ABSTRACT FROM AUTHOR]

This paper is proposing an machine learning based expert system for preliminary prediction of the insulation fire resisting performance of shallow floor systems when subject to exposure to the ISO 834 Standard Fire Curve. The proposed system is a digital tool which incorporates a machine learning algorithm trained on the outcomes of pre-run two-dimensional finite element heat transfer analyses of shallow floor system details. The algorithm predicts the insulation performance of similar details with a measurable accuracy of 96% (i.e the insulation rating band was predicted correctly in 96% of the cases) without the requirement for an explicit deterministic analysis. The paper presents the challenges and prerequisites to build such an expert system and acts as a proof of concept for the use of machine learning for the assessment of the insulation performance of shallow floor system under the guidance of BS EN 1363-1:2012. A Support Vector Machine machine learning algorithm is adopted in this work. The required processes that were needed for the development of the expert system include the stages of data acquisition, exploratory data analysis, choice of machine learning algorithm, model training, tuning, and validation. This expert system is useful for practitioners to rapidly assess the feasibility of different construction details at early stages of the design process. [ABSTRACT FROM AUTHOR]

The psychological health of a person plays an important role in their daily life activities. The paper addresses depression issues with the machine learning model using facial expressions of the patient. Some research has already been done on visual based on depression detection methods, but those are illumination variant. The paper uses feature extraction using LBP (Local Binary Pattern) descriptor, which is illumination invariant. The Viola-Jones algorithm is used for face detection and SVM (support vector machine) is considered for classification along with the LBP descriptor to make a complete model for depression level detection. The proposed method captures frontal face from the videos of subjects and their facial features are extracted from each frame. Subsequently, the facial features are analyzed to detect depression levels with the post-processing model. The performance of the proposed system is evaluated using machine learning algorithms in MATLAB. For the real-time system design, it is necessary to test it on the hardware platform. The LBP descriptor has been implemented on FPGA using Xilinx VIVADO 16.4. The results of the proposed method show satisfactory performance and accuracy for depression detection comparison with similar previous work. [ABSTRACT FROM AUTHOR]

Breast cancer (BC) is the leading cause of death among women worldwide. It affects in general women older than 40 years old. Medical images analysis is one of the most promising research areas since it provides facilities for diagnosis and decision-making of several diseases such as BC. This paper conducts a Structured Literature Review (SLR) of the use of Machine Learning (ML) and Image Processing (IP) techniques to deal with BC imaging. A set of 530 papers published between 2000 and August 2019 were selected and analyzed according to ten criteria: year and publication channel, empirical type, research type, medical task, machine learning techniques, datasets used, validation methods, performance measures and image processing techniques which include image pre-processing, segmentation, feature extraction and feature selection. Results showed that diagnosis was the most used medical task and that Deep Learning techniques (DL) were largely used to perform classification. Furthermore, we found out that classification was the most ML objective investigated followed by prediction and clustering. Most of the selected studies used Mammograms as imaging modalities rather than Ultrasound or Magnetic Resonance Imaging with the use of public or private datasets with MIAS as the most frequently investigated public dataset. As for image processing techniques, the majority of the selected studies pre-process their input images by reducing the noise and normalizing the colors, and some of them use segmentation to extract the region of interest with the thresholding method. For feature extraction, we note that researchers extracted the relevant features using classical feature extraction techniques (e.g. Texture features, Shape features, etc.) or DL techniques (e. g. VGG16, VGG19, ResNet, etc.), and finally few papers used feature selection techniques in particular the filter methods. [ABSTRACT FROM AUTHOR]

This paper utilizes the cognitive radio (CR) spectrum to the fullest extent for extended applications requiring discretion. The CR technology provides various supports for cognitive radio networks (CRNs). The latter has CR nodes that sense free channels. Then, the CRN allocates the unused channels to secondary users (SUs) or unlicensed users. This allocation is termed the spectrum handoff. In this paper, by considering the identical channels in CR networks, a novel machine learning algorithm (the support vector machine—SVM) is employed. In addition, the queuing model of the preemptive resume priority M/M/1 is used. The proposed spectrum handoff algorithm selects the best possible CR network channel. The spectrum handoff algorithm uses the stated SVM algorithm scheme, which covers the transmitted and received power, the minimum service time, the data rate and the maximum vacancy time for the SU, to attain the maximum throughput. However, in multi-user greedy channel selection (GCS), only two parameters are considered. The proposed spectrum handoff algorithm based on the SVM scheme enhances the performance, and the SU throughput is improved to 68.7%. This approach is better than the GCS channel selection scheme. Additionally, this approach decreases the number of spectrum handoffs. As a result, the training accuracy of the SVM method is 97.6%, and it outperforms conventional methods. [ABSTRACT FROM AUTHOR]

Fuzzy support vector machine and their variants are prominent classification techniques that reduce the adverse effects of noises and outliers as compare to classical support vector machine. However, in these methods, only the distance between the training pattern and the class center is considered, and hence, the edge support vectors cannot be distinguished from noises and outliers properly. These limitations are overcome by intuitionistic fuzzy-based support vector machine which allocate two parameters (membership and non-membership degrees) to each pattern of a dataset and hence define score number based on the importance of a pattern. In this paper, an intuitionistic fuzzy proximal support vector machine for multi-category classification problems is proposed. The method significantly reduces the impacts of noises and outliers present in the dataset by assigning the intuitionistic fuzzy score function to each training point based on its location and surroundings. Moreover, the method is computationally efficient as the robust classifiers are obtained by solving the system of linear equations instead of large size quadratic programming problems. In the proposed method, using polynomial and Gaussian kernels, the hyperplanes are also developed in the feature space. The geometrical advantages of the suggested method over the existing techniques are ascertained using the simulated two-dimensional artificial dataset having three target classes. Further, extensive experimental studies on ten UCI benchmark datasets have been performed which demonstrate that the proposed algorithm predicts more precisely about future data as comparison to some well-established algorithms. Figures are also illustrated by varying different parameters involved in the model which confirms the performance of the method over the existing algorithms. Moreover, the analysis of the predictive behavior of the proposed approach is done using the Friedman test, a nonparametric alternative to the analysis of variance test at 5 % significance level. Further, the proposed method has also been applied to image classification and gesture-phase segmentation problems which confirms the efficiency and handling capabilities of the proposed algorithm in practical applications. [ABSTRACT FROM AUTHOR]

Among the extensions of twin support vector machine (TSVM), some scholars have utilized K-nearest neighbor (KNN) graph to enhance TSVM's classification accuracy. However, these KNN-based TSVM classifiers have two major issues such as high computational cost and overfitting. In order to address these issues, this paper presents an enhanced regularized K-nearest neighbor-based twin support vector machine (RKNN-TSVM). It has three additional advantages: (1) Weight is given to each sample by considering the distance from its nearest neighbors. This further reduces the effect of noise and outliers on the output model. (2) An extra stabilizer term was added to each objective function. As a result, the learning rules of the proposed method are stable. (3) To reduce the computational cost of finding KNNs for all the samples, location difference of multiple distances-based K-nearest neighbors algorithm (LDMDBA) was embedded into the learning process of the proposed method. The extensive experimental results on several synthetic and benchmark datasets show the effectiveness of our proposed RKNN-TSVM in both classification accuracy and computational time. Moreover, the largest speedup in the proposed method reaches to 14 times. [ABSTRACT FROM AUTHOR]

Support vector machine (SVM) is a widely used and reliable machine learning algorithm. It has been successfully applied to many real-world problems, with remarkable results. However, it has also been observed that SVM computational complexity increases with the increase in data size. Although many SVM speed optimization techniques have been proposed in the literature, there is still need for further improvement on the performance speed and accuracy of this algorithm. In this paper, a boundary detection algorithm for SVM speed optimization called ant colony optimization instance selection algorithm (ACOISA) is proposed. ACOISA is inspired by edge selection in ant colony optimization (ACO) algorithm, and it performs two primary functions: boundary detection and boundary instance selection. In the algorithm, ACO is used for boundary detection and k-nearest neighbor algorithm is used for boundary instance selection. Different sets of experiments are carried out to validate the efficiency of the proposed technique. All the experiments were performed on 35 datasets containing three well-known e-fraud types (credit card fraud, email spam and phishing email) and 31 other datasets available at UCI data repository. The experimental results showed that the proposed technique efficiently improved SVM training speed in 100% of the datasets used for evaluation, without significantly affecting SVM classification quality. Furthermore, the Freidman's and Holm's post hoc tests were conducted to statistically validate the credibility of the results. The statistical test results revealed that the proposed technique is significantly faster, compared to the standard SVM and some existing instance selection techniques, in all cases. [ABSTRACT FROM AUTHOR]

Learning from categorical data is a critical yet challenging task. Current research focuses on either leveraging the complex interaction between and within categorical values to generate a numerical representation, or designing a model that can tackle this types of data directly. However, both of these paradigms overlook the relation between the data characteristics and learning model hypothesis. In this paper, we propose a model-aware categorical data embedding framework that jointly reveals the intrinsic categorical data characteristics and optimizes the fitness of the representation for the follow-up learning model. An ELM-aware and a SVM-aware representation methods have been instantiated under this framework. Extensive experiments of classification with the embedded representation on 17 data sets demonstrate that the proposed framework can significantly improve the categorical data representation performance compared with state-of-the-art competitors. [ABSTRACT FROM AUTHOR]

Twin support vector machine (TWSVM) has gained increasing interest from various research fields recently. In this paper, we aim to report the current state of the theoretical research and practical advances on TWSVM. We first give the basic thought and theory of TWSVM, including the theory of proximal support vector machine, generalized eigenvalue proximal support vector machine, and TWSVM. Then, we focus on the various improvements made to TWSVM, mainly including least squares twin support vector machine, smooth twin support vector machine, regularized twin support vector machine, projection twin support vector machine, and modified TWSVM on the model selection problem. These newly emerging algorithms greatly expand the applications of TWSVM. In recent years, there is a lot of research on application of TWSVM. Next, we list some research on application of TWSVM in detail. Finally, we try to provide a comprehensive view of these advances in TWSVM and discuss the direction of future research. [ABSTRACT FROM AUTHOR]

In many real-world applications in the areas of data mining, the distributions of testing data are different from that of training data. And on the other hand, many data are often represented by multiple views which are of importance to learning. However, little work has been done for it. In this paper, we explored to leverage the multi-view information across different domains for knowledge transfer. We proposed a novel transfer learning model which integrates the domain distance and view consistency into a 2-view support vector machine framework, namely DV2S. The objective of DV2S is to find the optimal feature mapping such that under the projections the classification margin is maximized, while both the domain distance and the disagreement between multiple views are minimized simultaneously. Experiments showed that DV2S outperforms a variety of state-of-the-art algorithms. [ABSTRACT FROM AUTHOR]

Motivated by the support vector data description, a classical one-class support vector machine, and the twin support vector machine classifier, this paper formulates a twin support vector hypersphere (TSVH) classifier, a novel binary support vector machine (SVM) classifier that determines a pair of hyperspheres by solving two related SVM-type quadratic programming problems, each of which is smaller than that of a conventional SVM, which means that this TSVH is more efficient than the classical SVM. In addition, the TSVH successfully avoids matrix inversion compared with the twin support vector machine, which indicates learning algorithms of the SVM can be easily extended to this TSVH. Computational results on several synthetic as well as benchmark data sets indicate that the proposed TSVH is not only faster, but also obtains better generalization. [ABSTRACT FROM AUTHOR]

Most state-of-the-art speaker recognition systems are based on discriminative learning approaches. On the other hand, generative Gaussian mixture models (GMM) have been widely used in speaker recognition during the last decades. In an earlier work, we proposed an algorithm for discriminative training of GMM with diagonal covariances under a large margin criterion. In this paper, we propose an improvement of this algorithm, which has the major advantage of being computationally highly efficient, thus well suited to handle large-scale databases. We also develop a new strategy to detect and handle the outliers that occur in the training data. To evaluate the performances of our new algorithm, we carry out full NIST speaker identification and verification tasks using NIST-SRE'2006 data, in a Symmetrical Factor Analysis compensation scheme. The results show that our system significantly outperforms the traditional discriminative support vector machines (SVM)-based system of SVM-GMM supervectors, in the two speaker recognition tasks. [ABSTRACT FROM AUTHOR]

In this paper, a simple and linearly convergent Lagrangian support vector machine algorithm for the dual of the twin support vector regression (TSVR) is proposed. Though at the outset the algorithm requires inverse of matrices, it has been shown that they would be obtained by performing matrix subtraction of the identity matrix by a scalar multiple of inverse of a positive semi-definite matrix that arises in the original formulation of TSVR. The algorithm can be easily implemented and does not need any optimization packages. To demonstrate its effectiveness, experiments were performed on well-known synthetic and real-world datasets. Similar or better generalization performance of the proposed method in less training time in comparison with the standard and twin support vector regression methods clearly exhibits its suitability and applicability. [ABSTRACT FROM AUTHOR]

In this paper, extreme learning machine (ELM) for ε-insensitive error loss function-based regression problem formulated in 2-norm as an unconstrained optimization problem in primal variables is proposed. Since the objective function of this unconstrained optimization problem is not twice differentiable, the popular generalized Hessian matrix and smoothing approaches are considered which lead to optimization problems whose solutions are determined using fast Newton-Armijo algorithm. The main advantage of the algorithm is that at each iteration, a system of linear equations is solved. By performing numerical experiments on a number of interesting synthetic and real-world datasets, the results of the proposed method are compared with that of ELM using additive and radial basis function hidden nodes and of support vector regression (SVR) using Gaussian kernel. Similar or better generalization performance of the proposed method on the test data in comparable computational time over ELM and SVR clearly illustrates its efficiency and applicability. [ABSTRACT FROM AUTHOR]

This paper presents a new classification method utilizing distance-based decision surface with nearest neighbor projection approach, called DDC. Kernel type of DDC has been extended to take into account the effective nonlinear structure of the data. DDC has some properties: (1) does not need conventional learning procedure (as k-NN algorithm), (2) does not need searching time to locate the k-nearest neighbors, and (3) does not need optimization process unlike some classification methods such as Support Vector Machine (SVM). In DDC, we compute the weighted average of distances to all the training samples. Unclassified sample will be classified as belonging to a class that has the minimum obtained distance. As a result, by such a rule we can derive a formula that can be used as the decision surface. DDC is tested on both synthetic and real-world data sets from the UCI repository, and the results were compared with k-NN, RBF Network, and SVM. The experimental results indicate DDC outperforms k-NN in the most experiments and the results are comparable to or better than SVM with some data sets. [ABSTRACT FROM AUTHOR]

Twin support vector machine (TSVM) is a new machine learning algorithm, which aims at finding two nonparallel planes for each class. In order to do so, one needs to resolve a pair of smaller-sized quadratic programming problems (QPPs) rather than a single large one. However, when constructing the classification plane for one class, a large number of samples of this class are considered in the objective function, but only fewer samples in the other class are considered, which easily results in over-fitting problem. In addition, the same penalties are given to each misclassified samples in the TSVM. In fact, the misclassified samples have different effects on the decision of the hyper-plane. In order to overcome these two disadvantages, by introducing the rough set theory into ν-TSVM, we propose a rough margin-based ν-TSVM in this paper. In the proposed algorithm, the different points in the different positions are proposed to have different effects on the separating hyper-plane. We firstly construct rough lower margin, rough upper margin, and rough boundary in the ν-TSVM and then give the different penalties to the different misclassified samples according to their positions. The new classifier can avoid the over-fitting problem to a certain extent. Numerical experiments on one artificial dataset and six benchmark datasets demonstrate the feasibility and validity of the proposed algorithm. [ABSTRACT FROM AUTHOR]

The 'Brainstorming' approach presented in this paper is a weighted voting method that can improve the quality of predictions generated by several machine learning (ML) methods. First, an ensemble of heterogeneous ML algorithms is trained on available experimental data, then all solutions are gathered and a consensus is built between them. The final prediction is performed using a voting procedure, whereby the vote of each method is weighted according to a quality coefficient calculated using multivariable linear regression (MLR). The MLR optimization procedure is very fast, therefore no additional computational cost is introduced by using this jury approach. Here, brainstorming is applied to selecting actives from large collections of compounds relating to five diverse biological targets of medicinal interest, namely HIV-reverse transcriptase, cyclooxygenase-2, dihydrofolate reductase, estrogen receptor, and thrombin. The MDL Drug Data Report (MDDR) database was used for selecting known inhibitors for these protein targets, and experimental data was then used to train a set of machine learning methods. The benchmark dataset (available at ) can be used for further testing of various clustering and machine learning methods when predicting the biological activity of compounds. Depending on the protein target, the overall recall value is raised by at least 20% in comparison to any single machine learning method (including ensemble methods like random forest) and unweighted simple majority voting procedures. [ABSTRACT FROM AUTHOR]

The Support Vector Machine (SVM) is an interesting classifier with excellent power of generalization. In this paper, we consider applying the SVM to semi-supervised learning. We propose using an additional criterion with the standard formulation of the semi-supervised SVM ( S VM) to reinforce classifier regularization. Since, we deal with nonconvex and combinatorial problem, we use a genetic algorithm to optimize the objective function. Furthermore, we design the specific genetic operators and certain heuristics in order to improve the optimization task. We tested our algorithm on both artificial and real data and found that it gives promising results in comparison with classical optimization techniques proposed in literature. [ABSTRACT FROM AUTHOR]

Recently, learning to rank technology is attracting increasing attention from both academia and industry in the areas of machine learning and information retrieval. A number of algorithms have been proposed to rank documents according to the user-given query using a human-labeled training dataset. A basic assumption behind general learning to rank algorithms is that the training and test data are drawn from the same data distribution. However, this assumption does not always hold true in real world applications. For example, it can be violated when the labeled training data become outdated or originally come from another domain different from its counterpart of test data. Such situations bring a new problem, which we define as cross domain learning to rank. In this paper, we aim at improving the learning of a ranking model in target domain by leveraging knowledge from the outdated or out-of-domain data (both are referred to as source domain data). We first give a formal definition of the cross domain learning to rank problem. Following this, two novel methods are proposed to conduct knowledge transfer at feature level and instance level, respectively. These two methods both utilize Ranking SVM as the basic learner. In the experiments, we evaluate these two methods using data from benchmark datasets for document retrieval. The results show that the feature-level transfer method performs better with steady improvements over baseline approaches across different datasets, while the instance-level transfer method comes out with varying performance depending on the dataset used. [ABSTRACT FROM AUTHOR]

This paper presents a new method for fault classification in series-compensated transmission line using multiclass support vector machine (MCSVM) and multi class extreme learning machine (MCELM). These methods use the information obtained from the wavelet decomposition of fault current signals for fault classification. Using MATLAB simulink, data set has been generated with different types of fault and system variables, which include the fault resistance, fault distance, load angle and fault inception angle. The proposed method has been tested on a 400-kV, 300-km transmission line under variety of fault conditions. The performance of MCSVM and MCELM is compared in terms of training time and classification accuracy. The comparisons have been made for both One-Versus-One and One-Versus-Rest methods of SVMs and ELMs. Results show that MCELMs need less training time compared to MCSVMs, and the classification accuracy of MCELMs is more or less similar to MCSVMs. The feasibility of the proposed methods is also tested on a practical 220-kV series-compensated transmission line, and the results obtained are quite promising. [ABSTRACT FROM AUTHOR]

Abstract  Aiming at the common support vector machine’s biased disadvantage and computational complexity, an unbiased least squares support vector machine (LSSVM) model is proposed in this paper. The model eliminates the bias item of LSSVM by improving the form of structure risk, then the unbiased least squares support vector classifier and the unbiased least squares support vector regression are deduced. Based on this model, we design a new learning algorithm using Cholesky factorization according to the characteristic of kernel function matrix, in this way the calculation of Lagrangian multipliers is greatly simplified. Several experiments on diffenert datasets are carried out, including the common datasets classification, synthetic aperture radar image automatic target recognition and chaotic time series prediction. The experimental results of correct recognition rate and the fitting precision testify that the unbiased LSSVM model has good universal ability and fitting accuracy, better generalization capability and stability, and have a great improvement in learning speed. [ABSTRACT FROM AUTHOR]

We propose a computationally efficient method for cross-validation of the Support Vector Regression (SVR) by generalizing the decremental algorithm of SVR. Incremental and decremental algorithm of Support Vector Machines (SVM)) efficiently update the trained SVM model when a single data point is added to or removed from the training set. The computational cost of leave-one-out cross-validation can be reduced using the decremental algorithm. However, when we perform leave-m-out cross-validation (m>1), we have to repeatedly apply the decremental algorithm for each data point. In this paper, we extend the decremental algorithm of SVR ) in such a way that several data points can be removed more efficiently. Experimental results indicate that the proposed approach can reduce the computational cost. In particular, we observed that the number of breakpoints, which is the main computational cost of the involved path-following, were reduced from (O(m) to O(√m). [ABSTRACT FROM AUTHOR]

Semi-supervised support vector machine ( S 3 V M ) is a popular strategy for many machine learning tasks due to the expensiveness of getting enough labeled data. In this paper, we propose a quantum Help-Training S 3 V M and design a quantum Parzen window model to select n 1 + n 2 unlabeled data from l labeled and n unlabeled data set in each iteration, the time complexity is O (τ n n 1 + τ n n 2 + τ n) for τ iterations, which exhibits a quadratic speed-up over classical algorithm, we adopt quantum linear system to build Lagrangian multipliers with accuracy ε , the time complexity is O (τ κ 3 ε - 3 polylog (N (n + l))) , where condition number is κ and feature dimension is N, it is exponentially faster than classical S 3 V M algorithm. Our scheme has two significant merits, (i) we provide the first quantum method for semi-supervised learning, which uses multiple unlabeled data with quantum superposition to predict Lagrangian multipliers at the same time, (ii) quantum matrix decomposition method avoids building matrices of different dimensions in one iteration; specially, this work provides inspiration to explore the potential quantum machine learning applications. [ABSTRACT FROM AUTHOR]