Linear Algebra And Optimization For Machine Learning - A Textbook - Aggarwal Charu C.

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Résumé :
A frequent challenge faced by beginners in machine learning is the extensive background requireeent in linear algebra and optimization. This makes the learning curve very steep. Thisbpok. therefore, reverses the focus by teaching linear algebra and optimization asthe priery topics of interest, and solutions to machine learning problems as applications of the a methods. Therefore, the book also provides significant exposure to machine learning. The chapters of this book belong to two categories : 1. Linear algebra and its applications : These chapters focus on the basics of linear algebra together with their common applications to singular value decomposition, similarity matrices (kernel methods), and graph analysis. Numerous machine learning applications have been used as examples, such as spectral clustering, kernel-based classification, and outlier detection. 2. Optimization and its applications : Basic methods in optimization such as gradient descent, Newton's method, and coordinate descent are discussed. Constrained optimization methods are introduced as well. Machine learning applications such as linear regression, SVMs, logistic regression, matrix factorization, recommender systems, and K-means clustering are discussed in detail. A general view of optimization in computational graphs is discussed together with its applications to backpropagation in neural networks. Exercises are included both within the text of the chapters and at the end of the chapters. The book is written fora diverse audience, including graduate students, researchers, and practitioners.

Biographie:
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 A Jet Research from the Massachusetts Institute of Technology in 1996. He has published more than goo papers in refereed conferences and journals, and has applied for or been granted more than 8o 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 Test-of-Time Award lung), the IEEE ICDM Research Contributions Award (2015), and the ACM SIGKDD Innovation Award (2019). He has served as editor-in-chief of the ACM SIGKDD Explorations, and is currently serving as an editor-in-chief of the ACM Transactions on Knowledge Discovery from Data. He is also an editor-in-chief of ACM Books. He is a fellow of the SIAM, ACM, and the IEEE, for "contributions to knowledge discovery and data mining algorithms ? ".

Sommaire:

Preface.- 1 Linear Algebra and Optimization: An Introduction.- 2 Linear Transformations and Linear Systems.- 3 Eigenvectors and Diagonalizable Matrices.- 4 Optimization Basics: A Machine Learning View.- 5 Advanced Optimization Solutions.- 6 Constrained Optimization and Duality.- 7 Singular Value Decomposition.- 8 Matrix Factorization.- 9 The Linear Algebra of Similarity.- 10 The Linear Algebra of Graphs.- 11 Optimization in Computational Graphs.- Index.