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Machine Learning Classifiers
Published in Rashmi Agrawal, Marcin Paprzycki, Neha Gupta, Big Data, IoT, and Machine Learning, 2020
Initially an arbitrary hyperplane is drawn and its distance is measured from the closest data points known as support vectors. The distance between hyperplanes and support vectors is known as the margin. Many separating hyperplanes can be drawn but the one that maximises the margin between two subsets is the optimal one. As the dataset is linearly separable, the hyperplane defined is a linear line and is represented as H:wt(X) + B, where w is a normal vector to the hyperplane. A data point with wt(x) + B>0 will belong to one class and the point where wt(x) + B<0 will belong to another class in two-class problems. If wt(x) + B = 0, the point will lie on the hyperplane. In the figure, two hyperplanes are shown describing the above concepts
A Reassuring Introduction to Support Vector Machines
Published in Mark Stamp, Introduction to Machine Learning with Applications in Information Security, 2017
The goal when training an SVM is to find a separating hyperplane, where a hyperplane is defined as a subspace of one dimension less than the space in which we are working. For example, if our data lives in two-dimensional space, a hyperplane is just a line. And “separating” means exactly what it says, namely, that the hyperplane separates the two classes. If a separating hyperplane exists, we say the data is linearly separable. If our training data happens to be linearly separable, then any separating hyperplane could be used as the basis for subsequent classification.
Fundamentals of Neural Networks
Published in Ali Zilouchian, Mo Jamshidi, Intelligent Control Systems Using Soft Computing Methodologies, 2001
In this chapter, the fundamentals of neural networks were introduced. The perceptron is the simplest form of neural network used for the classification of linearly separable patterns. Multi-layer perceptron overcome many limitations of single-layer perceptron. They can form arbitrarily complex decision regions in order to separate various nonlinear patterns. The next chapter is devoted to several neural network architectures. Applications of NN will be presented in Chapters 4–7 and Chapter 15 of the book.
Landslide Classification and Prediction of Debris Flow Using Machine Learning Models
Published in IETE Journal of Research, 2023
A. Shameem Ansar, S. Sudha, Savita Vinayagamoorthi, Michelle Marianne Menachery, Suresh Francis
Training data make hyperplanes in the coordinate space of different target categories. Non-linearly separable data on higher dimensional feature space allow training error. Let Xi (i = 1, 2, … , n).is a set of linear separable training vectors. Yi = ±1 specifies classes for training vectors. The SVM aims at an n-dimensional hyperplane differentiating the two classes by their maximum deviation [27]. It can be expressed in Equations (3) and (4) as follows: where indicates xi is not on the correct side of the separating plane, C is the regularization parameter, is a normal vector, is the transformed input training vector, is the bias parameter.
Improved Precision Crop Yield Prediction Using Weighted-Feature Hybrid SVM: Analysis of ML Algorithms
Published in IETE Journal of Research, 2023
Pavani S., Augusta Sophy Beulet P.
SVMs are better than conventional ML models regarding classification and regression because they increase the margin and decrease the classification error. It categorizes the linearly separable data. It divides the information into two groups and determines which group the new data point belongs in. The data points are known as support vectors and are divided into two classes by a hyperplane, as shown in Figure 11. The fundamental idea of SVM [26] is to choose a hyperplane that makes it easier to divide clusters, hence magnifying or widening any differences on either side of the hyperplane to achieve efficacy and accuracy. According to [27], it employs SVM to maintain soil quality and the right fertilizers. Due to its ability to express complicated functions, this technique is non-parametric [28]. SVM uses a linear kernel because it can split the data along a single line, which speeds up SVM training.
Predicting and explaining severity of road accident using artificial intelligence techniques, SHAP and feature analysis
Published in International Journal of Crashworthiness, 2023
Chakradhara Panda, Alok Kumar Mishra, Aruna Kumar Dash, Hedaytullah Nawab
The support vector machine attempts to find the best possible boundaries between different groups by optimally choosing a hyperplane [41,42]. The algorithm can be used to solve both linear and nonlinear problems in a variety of applications. For linearly separable data, the classifier tries to maximise the margin around the separating hyperplane. However, for nonlinearly separable data, the slack variables are added to relax the margin constraints [43,44]. In practice, however, real data is often not linearly separable, for which, a kernel can be used to map the data to higher dimensional feature space. Therefore, the choice of an appropriate kernel is critical for SVM's classification ability [45]. Various types of kernels such as linear, polynomial, gaussian, radial basis function and sigmoid are used in SVM classification.