Linear Algebra and Optimization for Machine Learning
A Textbook
Authors: Aggarwal, Charu
 First textbook to provide an integrated treatment of linear algebra and optimization with a special focus on machine learning issues
 Includes many examples to simplify exposition and facilitate in learning semantically
 Complemented by a solution manual for the numerous exercises in the book
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 About this Textbook

This textbook introduces linear algebra and optimization in the context of machine learning. Examples and exercises are provided throughout this text book together with access to a solution’s manual. This textbook targets graduate level students and professors in computer science, mathematics and data science. Advanced undergraduate students can also use this textbook. The chapters for this textbook are organized as follows:
1. Linear algebra and its applications: The chapters focus on the basics of linear algebra together with their common applications to singular value decomposition, matrix factorization, similarity matrices (kernel methods), and graph analysis. Numerous machine learning applications have been used as examples, such as spectral clustering, kernelbased classification, and outlier detection. The tight integration of linear algebra methods with examples from machine learning differentiates this book from generic volumes on linear algebra. The focus is clearly on the most relevant aspects of linear algebra for machine learning and to teach readers how to apply these concepts.
2. Optimization and its applications: Much of machine learning is posed as an optimization problem in which we try to maximize the accuracy of regression and classification models. The “parent problem” of optimizationcentric machine learning is leastsquares regression. Interestingly, this problem arises in both linear algebra and optimization, and is one of the key connecting problems of the two fields. Leastsquares regression is also the starting point for support vector machines, logistic regression, and recommender systems. Furthermore, the methods for dimensionality reduction and matrix factorization also require the development of optimization methods. A general view of optimization in computational graphs is discussed together with its applications to back propagation in neural networks.
A frequent challenge faced by beginners in machine learning is the extensive background required in linear algebra and optimization. One problem is that the existing linear algebra and optimization courses are not specific to machine learning; therefore, one would typically have to complete more course material than is necessary to pick up machine learning. Furthermore, certain types of ideas and tricks from optimization and linear algebra recur more frequently in machine learning than other applicationcentric settings. Therefore, there is significant value in developing a view of linear algebra and optimization that is better suited to the specific perspective of machine learning.
 About the authors

Charu C. Aggarwal is a Distinguished Research Staff Member (DRSM) at the IBM T. J. Watson Research Center in Yorktown Heights, New York. He completed his undergraduate degree in Computer Science from the Indian Institute of Technology at Kanpur in 1993 and his Ph.D. in Operations Research from the Massachusetts Institute of Technology in 1996. He has published more than 400 papers in refereed conferences and journals and has applied for or been granted more than 80 patents. He is author or editor of 19 books, including textbooks on data mining, neural networks, machine learning (for text), recommender systems, and outlier analysis. Because of the commercial value of his patents, he has thrice been designated a Master Inventor at IBM. He has received several internal and external awards, including the EDBT TestofTime Award (2014), the IEEE ICDM Research Contributions Award (2015), and the ACM SIGKDD Innovation Award (2019). He has served as editorinchief of the ACM SIGKDD Explorations, and is currently serving as an editorinchief of the ACM Transactions on Knowledge Discovery from Data. He is a fellow of the SIAM, ACM, and the IEEE, for “contributions to knowledge discovery and data mining algorithms.”
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Bibliographic Information
 Bibliographic Information

 Book Title
 Linear Algebra and Optimization for Machine Learning
 Book Subtitle
 A Textbook
 Authors

 Charu Aggarwal
 Copyright
 2020
 Publisher
 Springer International Publishing
 Copyright Holder
 Springer Nature Switzerland AG
 eBook ISBN
 9783030403447
 DOI
 10.1007/9783030403447
 Hardcover ISBN
 9783030403430
 Edition Number
 1
 Number of Pages
 X, 490
 Number of Illustrations
 20 b/w illustrations
 Topics