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.

1.1 Introduction

In today’s data-driven world, information flows through the digital landscape like an untapped river of potential. Within this vast data stream lies the key to unlocking a new era of discovery and innovation. Machine learning (ML), a revolutionary field, acts as the gateway to this wealth of opportunities. With its ability to uncover patterns, make predictive insights, and adapt to evolving information, ML has transformed industries, redefined technology, and opened the door to limitless possibilities. This book is your gateway to the fascinating realm of ML—a journey that empowers you to harness the power of data, enabling you to build intelligent systems, make informed decisions, and explore the boundless possibilities of the digital age.

ML has emerged as the dominant approach for solving problems in the modern world, and its wide-ranging applications have made it an integral part of our lives. Right from search engines to social networking sites, everything is powered by ML algorithms. Your favorite search engine uses ML algorithms to get you the appropriate search results. Smart home assistants like Alexa and Siri use ML to serve us better. The influence of ML in our day-to-day activities is so much that we cannot even realize it. Online shopping sites like Amazon, Flipkart, and Myntra use ML to recommend products. Facebook is using ML to display our feed. Netflix and YouTube are using ML to recommend videos based on our interests.

Data is growing exponentially with the Internet and smartphones, and ML has just made this data more usable and meaningful. Social media, entertainment, travel, mining, medicine, bioinformatics, or any field you could name uses ML in some form.

To understand the role of ML in the modern world, let us first discuss the applications of ML.

1.1 INTRODUCTION [LO1]

Mechanics is one of the oldest physical sciences, dating back to the times of Aristotle and Archimedes. The subject deals with force, displacement, and motion. The concepts of mechanics have been used to solve many mechanical and structural engineering problems through the ages. Because of its intriguing nature, many great scientists including Sir Isaac Newton and Albert Einstein delved into it for solving intricate problems in their own fields.

Engineering mechanics and mechanics of materials developed over centuries with a few experiment-based postulates and assumptions, particularly to solve engineering problems in designing machines and structural parts. Problems are many and varied. However, in most cases, the requirement is to ensure sufficient strength, stiffness, and stability of the components, and eventually those of the whole machine or structure. In order to do this, we first analyze the forces and stresses at different points in a member, and then select materials of known strength and deformation behavior, to withstand the stress distribution with tolerable deformation and stability limits. The methodology has now developed to the extent of coding that takes into account the whole field stress, strain, deformation behaviors, and material characteristics to predict the probability of failure of a component at the weakest point. Inputs from the theory of elasticity and plasticity, mathematical and computational techniques, material science, and many other branches of science are needed to develop such sophisticated coding.

The theory of elasticity too developed but as an applied mathematics topic, and engineers took very little notice of it until recently, when critical analyses of components in high-speed machinery, vehicles, aerospace technology, and many other applications became necessary. The types of problems considered in both the elementary strength of material and the theory of elasticity are similar, but the approaches are different. The strength of the materials approach is generally simple. Here the emphasis is on finding practical solutions to a problem with simplifying assumptions.

This chapter explores one of the key facets of animals’ lack of legal inclusion in the context of civil law: their lack of legal standing. That animals are unable to take legal actions to seek redress for the wrongs done to them is particularly salient given – as the previous chapter demonstrated through the discussion of animal welfare laws – animals’ only other avenue for seeking legal justice is severely limited. This chapter explores the issue of animal standing by comparing various court cases that have involved animal plaintiffs, including the Animal Legal Defense Fund’s case on behalf of Justice the horse, and PETA’s cases on behalf of Naruto the macaque and orcas held captive in a Sea World. These cases have hinged on whether these animals – and indeed, non-human animals in general – can be regarded as having the legal and cognitive capacities that tend to be associated with legal subjecthood. With the courts in these cases finding that animals lack these capacities, the issue of standing exemplifies the broader problem that animals face in the legal system: they are rendered more-or-less invisible to the legal system because they lack the right legal status.