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Deep Probabilistic Machine Learning for Intelligent Control
Published in Alex Martynenko, Andreas Bück, Intelligent Control in Drying, 2018
We start our discussion of methods by first assuming we have a low-dimensional representation of the letters. Assume we already have a way to derive some measures such as the amount of curvature and maybe the length of strokes combined; these features are called X1 and X2. A hypothetical distribution is shown in Figure 11.2 for two classes shown as dots and crosses. With such a distribution it is easy to find a separating line (in general a separating hyperplane if we have more dimensions). While the decision boundary shown in Figure 11.2a will do the trick, it is possible that new data points might be misclassified as the line is so close to existing data. Robust generalization to new data points is really what we want. Therefore, to make the classification of future data more robust we chose a separating line so that the margins between this line and the nearest data points are maximized. This is shown in Figure 11.2b. The closest data points are called the support vectors, and this large margin classifier is called a support vector machine (SVM) (Cortes and Vapnik 1995).
Supervised Learning
Published in Peter Wlodarczak, Machine Learning and its Applications, 2019
A support vector machine (SVM) is a widely-used machine learning algorithm that can be applied for classification and regression problems. It is a discriminative, non-probabilistic binary linear classifier. It is often preferred over other machine learning algorithms, such as neural networks, since support vector machines are simpler, less computation is required and yet a high accuracy can often be achieved. There are also variants for non-linear classification. The basic idea behind support vector machines is to find a hyperplane in an n-dimensional space that distinctly separates the data points in two classes, where n is the number of features. In machine learning, a hyperplane is a decision boundary that is used to classify data points. If the data is linearly separable, we can find two parallel hyperplanes that separate the two classes of data. In Figure 4.9, the two hyperplanes, R1 and R2, are represented by the two dotted lines. The hyperplane that lies in the middle of the two dotted hyperplanes is the maximum margin hyperplane. The support vector machine algorithm finds the hyperplane with the maximum distance from the nearest training samples. The data points on the two dotted hyperplanes are the support vectors. They influence the position and orientation of the hyperplane. In Figure 4.9, the support vectors are shown as solid dots. They are at the nearest distance b from the hyperplane. The hyperplane is learned using a procedure that maximizes the margin, i.e., that finds a plane with the maximum distance between the data points of both classes. We use the support vectors to maximize the margin of b. The support vector machine algorithm is, thus, called a maximum margin classifier. The larger the margin the better the generalization.
Supervised Machine Learning and Its Deployment in SAS and R
Published in Tanya Kolosova, Samuel Berestizhevsky, Supervised Machine Learning, 2020
Tanya Kolosova, Samuel Berestizhevsky
SVM uses a kernel function to find a hyperplane that maximizes the distance (margin) between two classes while minimizing training error. The maximum margin classifier is the discriminant function that maximizes the geometric margin 1‖w‖ which is equivalent to minimizing ‖w‖2. The soft-margin optimization problem (Cortes and Vapnik, 1995) is formulated as follows: minimizeonw,b:12‖w‖2+C∑i=1neisubjectto:yi(wTxi+b)≥1−ei,ei≥0,i=1,…,n
Modeling lateral movement decisions of powered two wheelers in disordered heterogeneous traffic conditions
Published in Transportation Letters, 2022
SVM is a large margin classifier that fits an optimal separating hyperplane (OSH) by which the considered database can be classified into two different classes (Cortes and Vapnik 1995). This technique was primarily developed for binary classification and later extended to a multi-class paradigm (Hsu and Lin 2002). Thus, the multiclass problem is usually decomposed into a series of binary problems on which the standard SVM can be directly applied (Wang and Xue 2014). There are two ensemble schemes to achieve this objective (i) one-versus-rest approach and (ii) one-versus-one approach. The present study employs the second approach was used as it is more suitable for the imbalanced classification problems (Wang and Xue 2014). The SVM model formulation for a multiclass classification problem comprises an objective function (Equation 8), which has to be minimized, and two constraints associated with the objective function as shown in Equation 9 and Equation 10.
Visa trial of international trade: evidence from support vector machines and neural networks
Published in Journal of Management Analytics, 2020
Engin Akman, Abdullah S. Karaman, Cemil Kuzey
The SVM, among the most accurate and robust algorithms in data mining, was originally developed by Vapnik (1995). It is also known as a maximal margin classifier. The theoretical foundation of SVM comes from the statistical learning theory, and it encompasses the machine learning as well as statistics. SVM learns from examinations by creating input and output-matching functions resulted from training data sets. It is one of the supervised learning approaches in which the structure includes input space, training set, output space, and a learning form (Cortes & Vapnik, 1995). The learning form is decided by the output space. The mapping functions match the data to a many-dimensional feature space (named classification or regression). It belongs to the type of maximal margin classifier. Besides performing linear classification, SVMs perform a nonlinear classification by mapping the inputs into high-dimensional feature spaces which are called kernel trick in order to induce the input data effortlessly distinguishable as opposed to the original data, thus the kernel functions transform the input data to high-dimensional feature space. They incorporate four kernel functions known as Linear, Polynomial, Radial Based, and Sigmoid functions. The kernel functions are used in the case of not simply distinguishable input data for classification problems. The objective of the SVM is to locate the optimum hyperplane that splits the clusters of the vector (most suitable demonstration) so as those facts with one group of the objective variable are on one lateral of the plane and facts with the other group are on the alternative lateral of the plane. The support vectors are those vectors that are near the hyperplane. A separator found between the split classes is drawn as the hyperplane.
A review of chewing detection for automated dietary monitoring
Published in Journal of the Chinese Institute of Engineers, 2022
Yanxin Wei, Khairun Nisa’ Minhad, Nur Asmiza Selamat, Sawal Hamid Md Ali, Mohammad Arif Sobhan Bhuiyan, Kelvin Jian Aun Ooi, Siti Balqis Samdin
The SVM is a supervised learning algorithm that helps address classification and regression problems. SVM has two kinds, namely, linear SVM and nonlinear SVM. A linear SVM is a maximum margin classifier, which can formalize the notion of the best linear separator, whereas a nonlinear SVM extends the linear one with kernels. It presents data into a higher-dimensional space to make them linearly separable. In this project, a linear SVM is used to classify signals. The separating hyperplane created by the linear SVM is shown in Equation 4.