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A Matrix Algebra Approach to Artificial Intelligence

  • Book
  • © 2020

Overview

Authors:
  1. Xian-Da Zhang

    1. Department of Automation, Tsinghua University, Beijing, China

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  • Proposes the machine learning tree, the neural network tree and the evolutionary computation tree
  • Presents the solid matrix algebra theory and methods for machine learning, neural networks, support vector machines and evolutionary computation
  • Highlights selected topics and advances in machine learning, neural networks and evolutionary computation
  • Summarizes about 80 AI algorithms so that readers can further understand and implement relevant AI methods

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Table of contents (9 chapters)

  1. Front Matter

    Pages i-xxxiv
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  2. Introduction to Matrix Algebra

    1. Front Matter

      Pages 1-1
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    2. Basic Matrix Computation

      • Xian-Da Zhang
      Pages 3-54

    3. Matrix Differential

      • Xian-Da Zhang
      Pages 55-87

    4. Gradient and Optimization

      • Xian-Da Zhang
      Pages 89-155

    5. Solution of Linear Systems

      • Xian-Da Zhang
      Pages 157-201

    6. Eigenvalue Decomposition

      • Xian-Da Zhang
      Pages 203-220

  3. Artificial Intelligence

    1. Front Matter

      Pages 221-221
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    2. Machine Learning

      • Xian-Da Zhang
      Pages 223-440

    3. Neural Networks

      • Xian-Da Zhang
      Pages 441-615

    4. Support Vector Machines

      • Xian-Da Zhang
      Pages 617-679

    5. Evolutionary Computation

      • Xian-Da Zhang
      Pages 681-803

  4. Back Matter

    Pages 805-820
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Keywords

About this book

Matrix algebra plays an important role in many core artificial intelligence (AI) areas, including machine learning, neural networks, support vector machines (SVMs) and evolutionary computation. This book offers a comprehensive and in-depth discussion of matrix algebra theory and methods for these four core areas of AI, while also approaching AI from a theoretical matrix algebra perspective.

The book consists of two parts: the first discusses the fundamentals of matrix algebra in detail, while the second focuses on the applications of matrix algebra approaches in AI. Highlighting matrix algebra in graph-based learning and embedding, network embedding, convolutional neural networks and Pareto optimization theory, and discussing recent topics and advances, the book offers a valuable resource for scientists, engineers, and graduate students in various disciplines, including, but not limited to, computer science, mathematics and engineering.  


Reviews

“The book is of very high relevance for students, professors and researchers involved in artificial intelligence (AI), the work is also of very high relevance for the mathematics community in general since it addresses the importance of matrix algebra for the field of AI and how major approaches and state-of-the-art algorithms rely on matrix algebra.” (Carlos Pedro Gonçalves, zbMATH 1455.68010, 2021)

Authors and Affiliations

  • Department of Automation, Tsinghua University, Beijing, China

    Xian-Da Zhang

About the author

XIAN-DA ZHANG is a Professor Emeritus at the Department of Automation, Tsinghua University, China. He was a Distinguished Professor at Xidian University, Xi’an, China, as part of the Ministry of Education of China and Cheung Kong Scholars Programme, from 1999 to 2002. His areas of research include intelligent signal and information processing, pattern recognition, machine learning and neural networks, evolutional computation, and correlated applied mathematics. He has published over 120 international journal and conference papers. The Japanese translation of his book “Linear Algebra in Signal Processing” (published in Chinese by Science Press, Beijing, in 1997) was published by Morikita Press, Tokyo, in 2008. He also authored the book “Matrix Analysis and Applications” (Cambridge University Press, UK, 2017).

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