10.1 Support Vector Machines

Support vector machines (SVMs) are supervised machine learning (ML) models used to solve regression and classification problems. However, it is widely used for solving classification problems. The main goal of SVM is to segregate the n-dimensional space into labels or classes by defining a decision boundary or hyperplanes. In this chapter, we shall explore SVM for solving classification problems.

10.1.1 SVM Working Principle

SVM Working Principle | Parteek Bhatia, https://youtu.be/UhzBKrIKPyE

To understand the working principle of the SVM classifier, we will take a standard ML problem where we want a machine to distinguish between a peach and an apple based on their size and color.

Let us suppose the size of the fruit is represented on the X-axis and the color of the fruit is on the Y-axis. The distribution of the dataset of apple and peach is shown in Figure 10.1.

To classify it, we must provide the machine with some sample stock of fruits and label each of the fruits in the stock as an “apple” or “peach”. For example, we have a labeled dataset of some 100 fruits with corresponding labels, i.e., “apple” or “peach”. When this data is fed into a machine, it will analyze these fruits and train itself. Once the training is completed, if some new fruit comes into the stock, the machine will classify whether it is an “apple” or a “peach”.

Most of the traditional ML algorithms would learn by observing the perfect apples and perfect peaches in the stock, i.e., they will train themselves by observing the ideal apples of stock (apples which are very much like apples in terms of their size and color) and the perfect peaches of stock (peaches which are very much like peaches in terms of their size and color). These standard samples are likely to be found in the heart of stock. The heart of the stock is shown in Figure 10.2.

9.1 INTRODUCTION [LO1]

Stresses given by relatively simple equations in the strength of materials for structures or machine members are based on the assumed continuity of the elastic medium. However, the presence of discontinuity destroys the assumed regularity of stress distribution in a member and a sudden increase in stresses occurs in the neighborhood of the discontinuity. In developing machines, it is impossible to avoid abrupt changes in cross-sections, holes, notches, shoulders, etc. Abrupt changes in cross-section also occur at the roots of gear teeth and threads of bolts. Some examples are shown in Figure 9.1.

Any such discontinuity acts as a stress raiser. Ideally, discontinuity in materials such as non-metallic inclusions in metals, casting defects, residual stresses from welding may also act as stress raisers. In this chapter, however, we shall consider only the geometric discontinuity that arises from design considerations of structures or machine parts.

Many theoretical methods and experimental techniques have been developed to determine stress concentrations in different structural and mechanical systems. In order to understand the concept, we shall begin with a plate with a centrally located hole. The plate is subjected to uniformly distributed tensile loading at the ends, as shown in Figure 9.2.