Linear Algebra and Optimization for Machine Learning: A Textbook

This textbook provides an introduction to linear algebra and optimization in the context of machine learning,with examples and exercises throughout. It is targeted at graduate level students and professors in computer science, mathematics and data science, and advanced undergraduate students can also use it. The chapters are organized into two parts: linear algebra and its applications, and optimization and its applications. The book emphasizes the most relevant aspects of linear algebra for machine learning and teaches readers how to apply these concepts.

Format: Paperback / softback
Length: 495 pages
Publication date: 13 May 2021
Publisher: Springer Nature Switzerland AG

This comprehensive textbook provides an in-depth introduction to linear algebra and optimization,with a focus on their applications in machine learning. It offers a wealth of examples and exercises to aid in understanding the concepts,and a solution manual is available for teaching instructors. The textbook is designed for graduate-level students and professors in computer science, mathematics, and data science,as well as advanced undergraduate students.

The chapters in the textbook are organized as follows:

1. Linear Algebra and Its Applications:

This chapter explores the fundamentals of linear algebra,including matrix operations,vector spaces,and linear equations. It also discusses the common applications of linear algebra in fields such as singular value decomposition,matrix factorization,kernel methods,and graph analysis. Numerous machine learning applications are used as examples,including spectral clustering,kernel-based classification,and outlier detection. The tight integration of linear algebra methods with examples from machine learning sets this book apart from generic volumes on linear algebra. The focus is on the most relevant aspects of linear algebra for machine learning and teaching readers how to apply these concepts.

2. Optimization and Its Applications:

Much of machine learning is posed as an optimization problem,where we aim to maximize the accuracy of regression and classification models. The "parent problem" of optimization-centric machine learning is least-squares regression,which arises in both linear algebra and optimization. Least-squares regression is the starting point for support vector machines,logistic regression,and recommender systems. Furthermore,methods for dimensionality reduction and matrix factorization also require the use of linear algebra techniques.

In conclusion,this textbook is an essential resource for anyone interested in learning linear algebra and optimization for machine learning. It provides a comprehensive and up-to-date coverage of the topics,with a wealth of examples and exercises to aid in understanding and applying the concepts. Whether you are a graduate-level student,professor,or advanced undergraduate student,this textbook will be valuable in your pursuit of knowledge in this field.

Weight: 979g
Dimension: 254 x 178 (mm)
ISBN-13: 9783030403461
Edition number: 1st ed. 2020