DeepDyve eBooks - A Matrix Algebra Approach to Artificial Intelligence

Basic Matrix Computation

Zhang, Xian-Da

Pages: 3 –54

[In science and engineering, we often encounter the problem of solving a system of linear equations. Matrices provide the most basic and useful mathematical tool for describing and solving such systems. As the introduction to matrix algebra, this chapter presents the basic operations and...

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Matrix Differential

Zhang, Xian-Da

Pages: 55 –87

[The matrix differential is a generalization of the multivariate function differential. The matrix differential (including the matrix partial derivative and gradient) is an important operation tool in matrix algebra and optimization in machine learning, neural networks, support vector machine and...

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Gradient and Optimization

Zhang, Xian-Da

Pages: 89 –155

[Many machine learning methods involve solving complex optimization problems, e.g., neural networks, support vector machines, and evolutionary computation. Optimization theory mainly considers (1) the existence conditions for an extremum value (gradient analysis); (2) the design of optimization...

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Solution of Linear Systems

Zhang, Xian-Da

Pages: 157 –201

[One of the most common problems in science and engineering is to solve the matrix equation Ax = b for finding x when the data matrix A and the data vector b are given.]

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Eigenvalue Decomposition

Zhang, Xian-Da

Pages: 203 –220

[This chapter is devoted to another core subject of matrix algebra: the eigenvalue decomposition (EVD) of matrices, including various generalizations of EVD such as the generalized eigenvalue decomposition, the Rayleigh quotient, and the generalized Rayleigh quotient.]

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Machine Learning

Zhang, Xian-Da

Pages: 223 –440

[Machine learning is a subset of artificial intelligence. This chapter presents first a machine learning tree, and then focuses on the matrix algebra methods in machine learning including single-objective optimization, feature selection, principal component analysis, and canonical correlation...

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Neural Networks

Zhang, Xian-Da

Pages: 441 –615

[Neural networks can be viewed as a kind of cognitive intelligence. This chapter presents a neural network tree, and then deals with the optimization problem in neural networks, activation functions, and basic neural networks from the perspective of matrix algebra. The topical subjects of this...

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Support Vector Machines

Zhang, Xian-Da

Pages: 617 –679

[Supervised regression/classification methods learn a model of relation between the target vectors {yi}i=1N\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs}...

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Evolutionary Computation

Zhang, Xian-Da

Pages: 681 –803

[From the perspective of artificial intelligence, evolutionary computation belongs to computation intelligence. The origins of evolutionary computation can be traced back to the late 1950s (see, e.g., the influencing works (Friedberg, IBM J 2(1):2–13, 1958; Friedberg, et al. IBM J 3(7):282–287,...

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A Matrix Algebra Approach to Artificial Intelligence

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A Matrix Algebra Approach to Artificial Intelligence

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