Time Series Forecasting Using Support Vector Machines

The problem of optimization in machine learning is well established but it entails several approximations. The theory of Hilbert spaces, which is principled and well established, helps solve the representation problem in machine learning by providing a rich (universal) class of functions where the optimization can be conducted. Working with functions is cumbersome, but for the class of reproducing kernel Hilbert spaces (RKHSs) it is still manageable provided the algorithm is restricted to inner products. The best example is the support vector machine (SVM), which is a batch mode algorithm that uses a very efficient (supralinear) optimization procedure. However, the problem of SVMs is that they display large memory and computational complexity. For the large-scale data limit, SVMs are restrictive because for fast operation the Gram matrix, which increases with the square of the number of samples, must fit in computer memory. The computation in this best-case scenario is also proportional to number of samples square. This is not specific to the SVM algorithm and is shared by kernel regression. There are also other relevant data processing scenarios such as streaming data (also called a time series) where the size of the data is unbounded and potentially nonstationary, therefore batch mode is not directly applicable and brings added difficulties.

A principled approach to machine learning (ML) problems because of its mathematical foundations in statistical learning theory, support vector machines (SVM), a non-parametric method, require all the data to be available during the training phase. However, once the model parameters are identified, SVM relies only, for future prediction, on a subset of these training instances, called support vectors (SV). The SVM model is mathematically written as a weighted sum of these SV whose number, rather than the dimensionality of the input space, defines SVM's complexity. Since the final number of these SV can be up to half the size of the training dataset, SVM becomes challenged to run on energy aware computing platforms. We propose in this work Knee-Cut SVM (KCSVM) and Knee-Cut Ordinal Optimization inspired SVM (KCOOSVM) that use a soft trick of ordered kernel values and uniform subsampling to reduce SVM's prediction computational complexity while maintaining an acceptable impact on its generalization capability. When tested on several databases from UCL KCSVM and KCOOSVM produced promising results, comparable to similar published algorithms.

Using information technology such as search engine for collecting and monitoring of network public opinion is a practical and effective method. This paper puts forward an improved algorithm of SVM classifier based on incremental learning online, and then implements a topic crawler system for network public opinion and to grab the public opinion.

Time series analysis is an important and complex problem in machine learning. In this paper, least squares support vector machine (LS-SVM) combined with particle swarm optimization (PSO) is used to time series prediction. The LS-SVM can overcome some shortcoming in the multilayer perceptron (MLP) and the PSO is used to tune the LS-SVM parameters automatically. A benchmark problem, Hénon map time series, has been used as an example for demonstration. It is showed this approach can escape from the blindness of man-made choice of the LS-SVM parameters. It enhances the efficiency and the capability of prediction.

Machine learning and pattern recognition recently become a hot topic in computing world. This is due to the fast-growing of resources as well as techniques that make it easier to solve machine learning and pattern recognition problems. Problems that require machine learning solutions may be very simple for humans but actually can be very complex for machines to solve them. Face recognition is amongst those problems. Almost all human can easily recognize others without require specific knowledge to do it, different from machines which require its. This paper discussed face recognition task using machine learning strategies which involved Kernel Principal Component Analysis (KPCA) and Support Vector Machine (SVM) to identify person. KPCA extracted features from 2D image input and produced the important features of an image input. The extracted face features are recognized by SVM by classifying human face according to their stored identity in a database. SVM, which was basically a binary classifier worked by using one-against-one strategy to compare the face feature vector of a single test image to the stored face image in a face image database. Experiment results on grayscale images with size 92x112 pixels gave 96.25% of accuracy rate. Hence, KPCA and SVM for face recognition is a robust machine learning method.

The main purpose of modeling time series data is for forecasting. Time series modeling can be categorized into the univariate and multivariate approach. In univariate time series modeling, there are several methods of forecasting; one of them is ARIMA. Time series modeling can also consider the exogenous variables to improve the accuracy of forecasting or to obtain a more meaningful model. Recently, machine learning methods are widely employed in various field, including time series forecasting, particularly for solving nonlinear relationship among the variables. One of the most popular machine learning methods is Support Vector Machine (SVM). SVM can solve classification and regression problem. The SVM method used in time series is called Support Vector Regression (SVR). In SVR method, one of the most important things to improve the accuracy of forecasting is input selection. One of the approaches to select input in SVR is by choosing the significant lag obtained from the classical time series analysis and expand the ARIMA model to get multiplicative lag. In addition, the data on daily sales contains seasonal and calendar variation. The models are evaluated using Root Mean Square Error (RMSE) and Mean Absolute Percentage Error (MAPE). The best method is the SVR method using multiplicative lag from the best ARIMA model without dummy variable.

The support vector machine (SVM) has been widely applied for classification problems in both machine learning and statistics. Despite its popularity, however, SVM has some drawbacks in certain situations. In particular, the SVM classifier can be very sensitive to outliers in the training sample. Moreover, the number of support vectors (SVs) can be very large in many applications. To circumvent these drawbacks, we propose the robust truncated hinge loss SVM (RSVM), which uses a truncated hinge loss. The RSVM is shown to be more robust to outliers and to deliver more accurate classifiers using a smaller set of SVs than the standard SVM. Our theoretical results show that the RSVM is Fisher-consistent, even when there is no dominating class, a scenario that is particularly challenging for multicategory classification. Similar results are obtained for a class of margin-based classifiers.

Support Vector Machines (SVMs) are a type of supervised machine learning algorithm widely used for classification tasks. In contrast to traditional methods that split the data into separate training and testing sets, here we propose an innovative approach where subsets of the original data are randomly selected to train the model multiple times. This iterative training process aims to identify a representative data subset, leading to improved inferences about the population. Additionally, we introduce a novel distance-based kernel specifically designed for binary-type features based on a similarity matrix that efficiently handles both binary and multi-class classification problems. Computational experiments on publicly available datasets of varying sizes demonstrate that our proposed method significantly outperforms existing approaches in terms of classification accuracy. Furthermore, the distance-based kernel achieves superior performance compared to other well-known kernels from the literature and those used in previous studies on the same datasets. These findings validate the effectiveness of our proposed classification method and distance-based kernel for SVMs. By leveraging random subset selection and a unique kernel design, we achieve notable improvements in classification accuracy. These results have significant implications for diverse classification problems in Machine Learning and data analysis.

EMU(Electric Multiple Units) maintenance platform is one of the key equipments of the motor Train base and EMU application, provides convenient for EMU daily maintenance and inspection, maintenance and repair. In the process design of the equipment, hydraulic crossover and other methods are adopted to meet the needs of the maintenance personnel on different types of EMUs. Therefore, the tipping boards are set up on the actual platform and protection network to ensure the safety of the workers' reaching the top. The EMUs usually use a four line storehouse, and the number of tipping plates is hundreds of them. Most of them are reversing / receiving by cylinder driving, and a large number of flip plates are distributed in the workshop. Besides, the state of the retractable boards and the faults have important influence on the operation. Therefore, it is very important to monitor the state of the flip plate. At present, it is more dependent on the monitoring and controlling system of the mechanical stroke switch in China. Due to the state of the hardware and the stability of the system, the method has the risk of omission and false alarm in some cases. Meanwhile, the switch signal can not directly display the real-time state of the tipping board. Therefore, the present invention provides a high-definition network camera image processing board state detection system based on double plate state real-time monitoring and detection, enhance the safety of EMU maintenance platform. The real-time image acquisition, calculating the specified texture information area gray co-occurrence matrix, generating feature vector descriptor, using support vector machine (SVM) classification method for feature vector classification, training classifier, and use the classifier to recognize the flap, and locate the flap position. And SVM is a novel method of machine learning evolving from statistics. SVM presents many own advantages in solving machine learning problems such as small samples, nonlinearity and high dimension. In this paper, the image texture SVM classification method construct feature vectors through the extraction of image gray level co-occurrence matrix texture information.The metioned texture imformation include gray-level co-occurrence matrix energy, contrast and entropy. And the gray level co-occurrence matrix reflects the image direction, adjacent interval and the change in value of integrated information.The results show that the image texture SVM classification method can effectively combine the method of template matching for the identification of condition detection of overhaul platform.

We survey some nonlinear models for classification problems arising in machine learning. In the last years this field has become more and more relevant due to a lot of practical applications, such as text and web classification, object recognition in machine vision, gene expression profile analysis, DNA and protein analysis, medical diagnosis, customer profiling etc. Classification deals with separation of sets by means of appropriate separation surfaces, which is generally obtained by solving a numerical optimization model.While linear separability is the basis of the most popular approach to classification, the Support Vector Machine (SVM), in the recent years using nonlinear separating surfaces has received some attention. The objective of this work is to recall some of such proposals, mainly in terms of the numerical optimization models. In particular we tackle the polyhedral, ellipsoidal, spherical and conical separation approaches and, for some of them, we also consider the semisupervised versions.

Convex optimization methods are used for many machine learning models such as support vector machine. However, the requirement of a convex formulation can place limitations on machine learning models. In recent years, a number of machine learning methods not requiring convexity have emerged. In this paper, we study non-convex optimization problems on the Stiefel manifold in which the feasible set consists of a set of rectangular matrices with orthonormal column vectors. We present examples of non-convex optimization problems in machine learning and apply three nonlinear optimization methods for finding a local optimal solution; geometric gradient descent method, augmented Lagrangian method of multipliers, and alternating direction method of multipliers. Although the geometric gradient method is often used to solve non-convex optimization problems on the Stiefel manifold, we show that the alternating direction method of multipliers generally produces higher quality numerical solutions within a reasonable computation time.

Bond rating is regarded as an important event for measuring financial risk of companies and for determining the investment returns of investors. As a result, it has been a popular research topic for researchers to predict companies' credit ratings by applying statistical and machine learning techniques. The statistical techniques, including multiple regression, multiple discriminant analysis (MDA), logistic models (LOGIT), and probit analysis, have been traditionally used in bond rating. However, one major drawback is that it should be based on strict assumptions. Such strict assumptions include linearity, normality, independence among predictor variables and pre-existing functional forms relating the criterion variablesand the predictor variables. Those strict assumptions of traditional statistics have limited their application to the real world. Machine learning techniques also used in bond rating prediction models include decision trees (DT), neural networks (NN), and Support Vector Machine (SVM). Especially, SVM is recognized as a new and promising classification and regression analysis method. SVM learns a separating hyperplane that can maximize the margin between two categories. SVM is simple enough to be analyzed mathematical, and leads to high performance in practical applications. SVM implements the structuralrisk minimization principle and searches to minimize an upper bound of the generalization error. In addition, the solution of SVM may be a global optimum and thus, overfitting is unlikely to occur with SVM. In addition, SVM does not require too many data sample for training since it builds prediction models by only using some representative sample near the boundaries called support vectors. A number of experimental researches have indicated that SVM has been successfully applied in a variety of pattern recognition fields. However, there are three major drawbacks that can be potential causes for degrading SVM's performance. First, SVM is originally proposed for solving binary-class classification problems. Methods for combining SVMs for multi-class classification such as One-Against-One, One-Against-All have been proposed, but they do not improve the performance in multi-class classification problem as much as SVM for binary-class classification. Second, approximation algorithms (e.g. decomposition methods, sequential minimal optimization algorithm) could be used for effective multi-class computation to reduce computation time, but it could deteriorate classification performance. Third, the difficulty in multi-class prediction problems is in data imbalance problem that can occur when the number of instances in one class greatly outnumbers the number of instances in the other class. Such data sets often cause a default classifier to be built due to skewed boundary and thus the reduction in the classification accuracy of such a classifier. SVM ensemble learning is one of machine learning methods to cope with the above drawbacks. Ensemble learning is a method for improving the performance of classification and prediction algorithms. AdaBoost is one of the widely used ensemble learning techniques. It constructs a composite classifier by sequentially training classifiers while increasing weight on the misclassified observations through iterations. The observations that are incorrectly predicted by previous classifiers are chosen more often than examples that are correctly predicted. Thus Boosting attempts to produce new classifiers that are better able to predict examples for which the current ensemble's performance is poor. In this way, it can reinforce the training of the misclassified observations of the minority class. This paper proposes a multiclass Geometric Mean-based Boosting (MGM-Boost) to resolve multiclass prediction problem. Since MGM-Boost introduces the notion of geometric mean into AdaBoost, it can perform learning process considering the geometric mean-based accuracy and errors of multiclass. This study applies MGM-Boost to the real-world bond rating case for Korean companies to examine the feasibility of MGM-Boost. 10-fold cross validations for threetimes with different random seeds are performed in order to ensure that the comparison among three different classifiers does not happen by chance. For each of 10-fold cross validation, the entire data set is first partitioned into tenequal-sized sets, and then each set is in turn used as the test set while the classifier trains on the other nine sets. That is, cross-validated folds have been tested independently of each algorithm. Through these steps, we have obtained the results for classifiers on each of the 30 experiments. In the comparison of arithmetic mean-based prediction accuracy between individual classifiers, MGM-Boost (52.95%) shows higher prediction accuracy than both AdaBoost (51.69%) and SVM (49.47%). MGM-Boost (28.12%) also shows the higher prediction accuracy than AdaBoost (24.65%) and SVM (15.42%)in terms of geometric mean-based prediction accuracy. T-test is used to examine whether the performance of each classifiers for 30 folds is significantly different. The results indicate that performance of MGM-Boost is significantly different from AdaBoost and SVM classifiers at 1% level. These results mean that MGM-Boost can provide robust and stable solutions to multi-classproblems such as bond rating.

Multivariate discrimination or classification is one of the best-studied problem in machine learning, with a plethora of well-tested and well-performing algorithms. There are also several good general textbooks [1–9] on the subject written to an average engineering, computer science, or statistics graduate student; most of them are also accessible for an average physics student with some background on computer science and statistics. Hence, instead of writing a generic introduction, we concentrate here on relating the subject to a practitioner experimental physicist. After a short introduction on the basic setup (Section 1) we delve into the practical issues of complexity regularization, model selection, and hyperparameter optimization (Section 2), since it is this step that makes high-complexity non-parametric fitting so different from low-dimensional parametric fitting. To emphasize that this issue is not restricted to classification, we illustrate the concept on a low-dimensional but non-parametric regression example (Section 2.1). Section 3 describes the common algorithmic-statistical formal framework that unifies the main families of multivariate classification algorithms. We explain here the large-margin principle that partly explains why these algorithms work. Section 4 is devoted to the description of the three main (families of) classification algorithms, neural networks, the support vector machine, and AdaBoost. We do not go into the algorithmic details; the goal is to give an overview on the form of the functions these methods learn and on the objective functions they optimize. Besides their technical description, we also make an attempt to put these algorithm into a socio-historical context. We then briefly describe some rather heterogeneous applications to illustrate the pattern recognition pipeline and to show how widespread the use of these methods is (Section 5). We conclude the chapter with three essentially open research problems that are either relevant to or even motivated by certain unorthodox applications of multivariate discrimination in experimental physics.

Classification and high dimensional data are the challenging problems in machine learning. In this paper, we carry out an empirical study of model selection for high dimensional data. We select three single classifiers, i.e., decision tree, support vector machine, and naive bayes, and two ensemble methods, i.e., bagging and random forest, to compare the performance of these five methods through real high dimensional data. Six real gene datasets with high correlation are used in this empirical study. Experimental results have illustrated that ensemble methods are better than single classifiers in terms of accuracy metric. In which, decision tree model is the weakest one, and bagging is the best model. The performance of random forest is much more efficient in terms of computing time metrics compared with bagging. From this empirical study, we can conclude that ensemble methods are an effective solution for high dimensional data.KeywordsHigh dimensional dataSupervised learningClassification

Spike sorting of neural data from single electrode recordings is a hard problem in machine learning that relies on significant input by human experts. We approach the task of learning to detect and classify spike waveforms in additive noise using two stages of large margin kernel classification and probability regression. Controlled numerical experiments using spike and noise data extracted from neural recordings indicate significant improvements in detection and classification accuracy over linear amplitude- and template-based spike sorting techniques.