Introduction to multivariate analysis : linear and nonlinear modeling (Book, 2014) [WorldCat.org]
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Introduction to multivariate analysis : linear and nonlinear modeling
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Introduction to multivariate analysis : linear and nonlinear modeling

Author: Sadanori Konishi
Publisher: Boca Raton : CRC Press, Taylor & Francis Group, [2014]
Series: Texts in statistical science.
Edition/Format:   Print book : EnglishView all editions and formats
Summary:
"Multivariate techniques are used to analyze data that arise from more than one variable in which there are relationships between the variables. Mainly based on the linearity of observed variables, these techniques are useful for extracting information and patterns from multivariate data as well as for the understanding the structure of random phenomena. This book describes the concepts of linear and nonlinear
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Document Type: Book
All Authors / Contributors: Sadanori Konishi
ISBN: 9781466567283 1466567287
OCLC Number: 878953459
Description: xxv, 312 pages : illustrations ; 24 cm.
Contents: Machine generated contents note: 1.1. Regression Modeling --
1.1.1. Regression Models --
1.1.2. Risk Models --
1.1.3. Model Evaluation and Selection --
1.2. Classification and Discrimination --
1.2.1. Discriminant Analysis --
1.2.2. Bayesian Classification --
1.2.3. Support Vector Machines --
1.3. Dimension Reduction --
1.4. Clustering --
1.4.1. Hierarchical Clustering Methods --
1.4.2. Nonhierarchical Clustering Methods --
2.1. Relationship between Two Variables --
2.1.1. Data and Modeling --
2.1.2. Model Estimation by Least Squares --
2.1.3. Model Estimation by Maximum Likelihood --
2.2. Relationships Involving Multiple Variables --
2.2.1. Data and Models --
2.2.2. Model Estimation --
2.2.3. Notes --
2.2.4. Model Selection --
2.2.5. Geometric Interpretation --
2.3. Regularization --
2.3.1. Ridge Regression --
2.3.2. Lasso --
2.3.3. L1 Norm Regularization --
3.1. Modeling Phenomena --
3.1.1. Real Data Examples --
3.2. Modeling by Basis Functions --
3.2.1. Splines --
3.2.2. B-splines --
3.2.3. Radial Basis Functions --
3.3. Basis Expansions --
3.3.1. Basis Function Expansions --
3.3.2. Model Estimation --
3.3.3. Model Evaluation and Selection --
3.4. Regularization --
3.4.1. Regularized Least Squares --
3.4.2. Regularized Maximum Likelihood Method --
3.4.3. Model Evaluation and Selection --
4.1. Risk Prediction Models --
4.1.1. Modeling for Proportional Data --
4.1.2. Binary Response Data --
4.2. Multiple Risk Factor Models --
4.2.1. Model Estimation --
4.2.2. Model Evaluation and Selection --
4.3. Nonlinear Logistic Regression Models --
4.3.1. Model Estimation --
4.3.2. Model Evaluation and Selection --
5.1. Criteria Based on Prediction Errors --
5.1.1. Prediction Errors --
5.1.2. Cross-Validation --
5.1.3. Mallows' Cp --
5.2. Information Criteria --
5.2.1. Kullback-Leibler Information --
5.2.2. Information Criterion AIC --
5.2.3. Derivation of Information Criteria --
5.2.4. Multimodel Inference --
5.3. Bayesian Model Evaluation Criterion --
5.3.1. Posterior Probability and BIC --
5.3.2. Derivation of the BIC --
5.3.3. Bayesian Inference and Model Averaging --
6.1. Fisher's Linear Discriminant Analysis --
6.1.1. Basic Concept --
6.1.2. Linear Discriminant Function --
6.1.3. Summary of Fisher's Linear Discriminant Analysis --
6.1.4. Prior Probability and Loss --
6.2. Classification Based on Mahalanobis Distance --
6.2.1. Two-Class Classification --
6.2.2. Multiclass Classification --
6.2.3. Example: Diagnosis of Diabetes --
6.3. Variable Selection --
6.3.1. Prediction Errors --
6.3.2. Bootstrap Estimates of Prediction Errors --
6.3.3. The .632 Estimator --
6.3.4. Example: Calcium Oxalate Crystals --
6.3.5. Stepwise Procedures --
6.4. Canonical Discriminant Analysis --
6.4.1. Dimension Reduction by Canonical Discriminant Analysis --
7.1. Bayes' Theorem --
7.2. Classification with Gaussian Distributions --
7.2.1. Probability Distributions and Likelihood --
7.2.2. Discriminant Functions --
7.3. Logistic Regression for Classification --
7.3.1. Linear Logistic Regression Classifier --
7.3.2. Nonlinear Logistic Regression Classifier --
7.3.3. Multiclass Nonlinear Logistic Regression Classifier --
8.1. Separating Hyperplane --
8.1.1. Linear Separability --
8.1.2. Margin Maximization --
8.1.3. Quadratic Programming and Dual Problem --
8.2. Linearly Nonseparable Case --
8.2.1. Soft Margins --
8.2.2. From Primal Problem to Dual Problem --
8.3. From Linear to Nonlinear --
8.3.1. Mapping to Higher-Dimensional Feature Space --
8.3.2. Kernel Methods --
8.3.3. Nonlinear Classification --
9.1. Principal Components --
9.1.1. Basic Concept --
9.1.2. Process of Deriving Principal Components and Properties --
9.1.3. Dimension Reduction and Information Loss --
9.1.4. Examples --
9.2. Image Compression and Decompression --
9.3. Singular Value Decomposition --
9.4. Kernel Principal Component Analysis --
9.4.1. Data Centering and Eigenvalue Problem --
9.4.2. Mapping to a Higher-Dimensional Space --
9.4.3. Kernel Methods --
10.1. Hierarchical Clustering --
10.1.1. Interobject Similarity --
10.1.2. Intercluster Distance --
10.1.3. Cluster Formation Process --
10.1.4. Ward's Method --
10.2. Nonhierarchical Clustering --
10.2.1. K-Means Clustering --
10.2.2. Self-Organizing Map Clustering --
10.3. Mixture Models for Clustering --
10.3.1. Mixture Models --
10.3.2. Model Estimation by EM Algorithm --
A.1. Bootstrap Error Estimation --
A.2. Regression Models --
A.3. Bootstrap Model Selection Probability --
B.1. Equality-Constrained Optimization Problem --
B.2. Inequality-Constrained Optimization Problem --
B.3. Equality/Inequality-Constrained Optimization --
C.1. General EM Algorithm --
C.2. EM Algorithm for Mixture Model.
Series Title: Texts in statistical science.
Responsibility: Sadanori Konishi, Chuo University, Tokyo, Japan.

Abstract:

"Multivariate techniques are used to analyze data that arise from more than one variable in which there are relationships between the variables. Mainly based on the linearity of observed variables, these techniques are useful for extracting information and patterns from multivariate data as well as for the understanding the structure of random phenomena. This book describes the concepts of linear and nonlinear multivariate techniques, including regression modeling, classification, discrimination, dimension reduction, and clustering"--

"The aim of statistical science is to develop the methodology and the theory for extracting useful information from data and for reasonable inference to elucidate phenomena with uncertainty in various fields of the natural and social sciences. The data contain information about the random phenomenon under consideration and the objective of statistical analysis is to express this information in an understandable form using statistical procedures. We also make inferences about the unknown aspects of random phenomena and seek an understanding of causal relationships. Multivariate analysis refers to techniques used to analyze data that arise from multiple variables between which there are some relationships. Multivariate analysis has been widely used for extracting useful information and patterns from multivariate data and for understanding the structure of random phenomena. Techniques would include regression, discriminant analysis, principal component analysis, clustering, etc., and are mainly based on the linearity of observed variables. In recent years, the wide availability of fast and inexpensive computers enables us to accumulate a huge amount of data with complex structure and/or high-dimensional data. Such data accumulation is also accelerated by the development and proliferation of electronic measurement and instrumentation technologies. Such data sets arise in various fields of science and industry, including bioinformatics, medicine, pharmaceuticals, systems engineering, pattern recognition, earth and environmental sciences, economics and marketing."--

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"The presentation is always clear and several examples and figures facilitate an easy understanding of all the techniques. The book can be used as a textbook in advanced undergraduate courses in Read more...

 
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