Coding the Matrix

Author: Philip N. Klein
Publisher:
ISBN: 9780615856735
Category : Algebras, Linear
Languages : en
Pages : 530

Book Description
An engaging introduction to vectors and matrices and the algorithms that operate on them, intended for the student who knows how to program. Mathematical concepts and computational problems are motivated by applications in computer science. The reader learns by "doing," writing programs to implement the mathematical concepts and using them to carry out tasks and explore the applications. Examples include: error-correcting codes, transformations in graphics, face detection, encryption and secret-sharing, integer factoring, removing perspective from an image, PageRank (Google's ranking algorithm), and cancer detection from cell features. A companion web site, codingthematrix.com provides data and support code. Most of the assignments can be auto-graded online. Over two hundred illustrations, including a selection of relevant "xkcd" comics. Chapters: "The Function," "The Field," "The Vector," "The Vector Space," "The Matrix," "The Basis," "Dimension," "Gaussian Elimination," "The Inner Product," "Special Bases," "The Singular Value Decomposition," "The Eigenvector," "The Linear Program" A new edition of this text, incorporating corrections and an expanded index, has been issued as of September 4, 2013, and will soon be available on Amazon.

Coding the Matrix

Author: Philip N. Klein
Publisher:
ISBN: 9780615880990
Category : Algebras, Linear
Languages : en
Pages : 0

Book Description
An engaging introduction to vectors and matrices and the algorithms that operate on them, intended for the student who knows how to program. Mathematical concepts and computational problems are motivated by applications in computer science. The reader learns by doing, writing programs to implement the mathematical concepts and using them to carry out tasks and explore the applications. Examples include: error-correcting codes, transformations in graphics, face detection, encryption and secret-sharing, integer factoring, removing perspective from an image, PageRank (Google's ranking algorithm), and cancer detection from cell features. A companion web site, codingthematrix.com provides data and support code. Most of the assignments can be auto-graded online. Over two hundred illustrations, including a selection of relevant xkcd comics. Chapters: The Function, The Field, The Vector, The Vector Space, The Matrix, The Basis, Dimension, Gaussian Elimination, The Inner Product, Special Bases, The Singular Value Decomposition, The Eigenvector, The Linear Program

Introduction to Applied Linear Algebra

Author: Stephen Boyd
Publisher: Cambridge University Press
ISBN: 1316518965
Category : Business & Economics
Languages : en
Pages : 477

Book Description
A groundbreaking introduction to vectors, matrices, and least squares for engineering applications, offering a wealth of practical examples.

Multivariate General Linear Models

Author: Richard F. Haase
Publisher: SAGE Publications
ISBN: 1483303721
Category : Mathematics
Languages : en
Pages : 225

Book Description
Multivariate General Linear Models is an integrated introduction to multivariate multiple regression analysis (MMR) and multivariate analysis of variance (MANOVA). Beginning with an overview of the univariate general linear model, this volume defines the key steps in analyzing linear model data, and introduces multivariate linear model analysis as a generalization of the univariate model. The author focuses on multivariate measures of association for four common multivariate test statistics, presents a flexible method for testing hypotheses on models, and emphasizes the multivariate procedures attributable to Wilks, Pillai, Hotelling, and Roy. The volume concludes with a discussion of canonical correlation analysis that is shown to subsume all the multivariate procedures discussed in previous chapters. The analyses are illustrated throughout the text with three running examples drawing from several disciples, including personnel psychology, anthropology, environmental epidemiology, and neuropsychology.

A First Course in Coding Theory

Author: Raymond Hill
Publisher: Oxford University Press
ISBN: 9780198538035
Category : Computers
Languages : en
Pages : 268

Book Description
Algebraic coding theory is a new and rapidly developing subject, popular for its many practical applications and for its fascinatingly rich mathematical structure. This book provides an elementary yet rigorous introduction to the theory of error-correcting codes. Based on courses given by the author over several years to advanced undergraduates and first-year graduated students, this guide includes a large number of exercises, all with solutions, making the book highly suitable for individual study.

Linear Algebra Coding with Python

Author: Hyun-Seok Son
Publisher: Hyun-Seok Son
ISBN:
Category : Art
Languages : en
Pages : 304

Book Description
Python is one of the most popular languages for data analysis and prediction. What's more, tensorflow and torch, useful tools of recent deep learning, are fully implemented by Python. The basic form of data in these languages is an array, created by Python's important package numpy. In particular, arrays are the basis of data science because they have structures of vectors and matrices that give the meaning of direction and magnitude to each value in the data set. The matrix structure allows transformation to a simple form without losing the basic characteristics of a vast data set. These transformations are useful for efficient processing of data and for finding implicit characteristics. Linear Algebra, a field that provides a basic theory of vectors and matrices, provides many algorithms to increase the accuracy and speed of computation for analyzing data and to discover the characteristics of a data set. These algorithms are very useful for understanding the computing process of probability, statistics and the learning machine. This book introduces many basics of linear algebra using Python packages numpy, sympy, and so on. Chapters 1 and 2 introduce the creation and characteristics of vectors and matrices. Chapter 3 describes the linear system(linear combination) through the process finding the solution in a system of simultaneous equations. Vector space, a concept introduced in Chapter 4, is used to infer the collective characteristics and relationships of each vector of a linear system. Chapter 5 introduces the coordinate system to represent the linear system geometrically. Chapter 6 introduces the process of transforming while maintaining basic characteristics such as vectors and matrices. Finally, Chapter 7 describes several ways to decompose the original form into a simple form. In this process, we use a variety of Python functions.

A First Course in Random Matrix Theory

Author: Marc Potters
Publisher: Cambridge University Press
ISBN: 1108488080
Category : Computers
Languages : en
Pages : 371

Book Description
An intuitive, up-to-date introduction to random matrix theory and free calculus, with real world illustrations and Big Data applications.

Machine Learning with Python Cookbook

Author: Chris Albon
Publisher: "O'Reilly Media, Inc."
ISBN: 1491989335
Category : Computers
Languages : en
Pages : 305

Book Description
This practical guide provides nearly 200 self-contained recipes to help you solve machine learning challenges you may encounter in your daily work. If you’re comfortable with Python and its libraries, including pandas and scikit-learn, you’ll be able to address specific problems such as loading data, handling text or numerical data, model selection, and dimensionality reduction and many other topics. Each recipe includes code that you can copy and paste into a toy dataset to ensure that it actually works. From there, you can insert, combine, or adapt the code to help construct your application. Recipes also include a discussion that explains the solution and provides meaningful context. This cookbook takes you beyond theory and concepts by providing the nuts and bolts you need to construct working machine learning applications. You’ll find recipes for: Vectors, matrices, and arrays Handling numerical and categorical data, text, images, and dates and times Dimensionality reduction using feature extraction or feature selection Model evaluation and selection Linear and logical regression, trees and forests, and k-nearest neighbors Support vector machines (SVM), naïve Bayes, clustering, and neural networks Saving and loading trained models

Meschach

Author: David Edward Stewart
Publisher:
ISBN: 9780731519002
Category : C# (Computer program language)
Languages : en
Pages : 240

Book Description

Matrix Methods in Data Mining and Pattern Recognition

Author: Lars Elden
Publisher: SIAM
ISBN: 0898716268
Category : Computers
Languages : en
Pages : 226

Book Description
Several very powerful numerical linear algebra techniques are available for solving problems in data mining and pattern recognition. This application-oriented book describes how modern matrix methods can be used to solve these problems, gives an introduction to matrix theory and decompositions, and provides students with a set of tools that can be modified for a particular application.Matrix Methods in Data Mining and Pattern Recognition is divided into three parts. Part I gives a short introduction to a few application areas before presenting linear algebra concepts and matrix decompositions that students can use in problem-solving environments such as MATLAB®. Some mathematical proofs that emphasize the existence and properties of the matrix decompositions are included. In Part II, linear algebra techniques are applied to data mining problems. Part III is a brief introduction to eigenvalue and singular value algorithms. The applications discussed by the author are: classification of handwritten digits, text mining, text summarization, pagerank computations related to the GoogleÔ search engine, and face recognition. Exercises and computer assignments are available on a Web page that supplements the book.Audience The book is intended for undergraduate students who have previously taken an introductory scientific computing/numerical analysis course. Graduate students in various data mining and pattern recognition areas who need an introduction to linear algebra techniques will also find the book useful.Contents Preface; Part I: Linear Algebra Concepts and Matrix Decompositions. Chapter 1: Vectors and Matrices in Data Mining and Pattern Recognition; Chapter 2: Vectors and Matrices; Chapter 3: Linear Systems and Least Squares; Chapter 4: Orthogonality; Chapter 5: QR Decomposition; Chapter 6: Singular Value Decomposition; Chapter 7: Reduced-Rank Least Squares Models; Chapter 8: Tensor Decomposition; Chapter 9: Clustering and Nonnegative Matrix Factorization; Part II: Data Mining Applications. Chapter 10: Classification of Handwritten Digits; Chapter 11: Text Mining; Chapter 12: Page Ranking for a Web Search Engine; Chapter 13: Automatic Key Word and Key Sentence Extraction; Chapter 14: Face Recognition Using Tensor SVD. Part III: Computing the Matrix Decompositions. Chapter 15: Computing Eigenvalues and Singular Values; Bibliography; Index.