Data Mining Algorithms in C++ Data Patterns and Algorithms for M....pdf

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Cover

Table of Contents

About the Author

Introduction

1: Information and Entropy

Entropy

Entropy of a Continuous Random Variable

Partitioning a Continuous Variable for Entropy

An Example of Improving Entropy

Joint and Conditional Entropy

Code for Conditional Entropy

Mutual Information

Fano's Bound and Selection of Predictor Variables

Confusion Matrices and Mutual Information

Extending Fano's Bound for Upper Limits

Simple Algorithms for Mutual Information

The TEST_DIS Program

Continuous Mutual Information

The Parzen Window Method

Adaptive Partitioning

The TEST_CON Program

Asymmetric Information Measures

Uncertainty Reduction

Transfer Entropy: Schreiber's Information Transfer

2: Screening for Relationships

Simple Screening Methods

Univariate Screening

Bivariate Screening

Forward Stepwise Selection

Forward Selection Preserving Subsets

Backward Stepwise Selection

Criteria for a Relationship

Ordinary Correlation

Nonparametric Correlation

Accommodating Simple Nonlinearity

Chi-Square and Cramer's V

Mutual Information and Uncertainty Reduction

Multivariate Extensions

Permutation Tests

A Modestly Rigorous Statement of the Procedure

A More Intuitive Approach

Serial Correlation Can Be Deadly

Permutation Algorithms

Outline of the Permutation Test Algorithm

Permutation Testing for Selection Bias

Combinatorially Symmetric Cross Validation

The CSCV Algorithm

An Example of CSCV OOS Testing

Univariate Screening for Relationships

Three Simple Examples

Bivariate Screening for Relationships

Stepwise Predictor Selection Using Mutual Information

Maximizing Relevance While Minimizing Redundancy

Code for the Relevance Minus Redundancy Algorithm

An Example of Relevance Minus Redundancy

A Superior Selection Algorithm for Binary Variables

FREL for High-Dimensionality, Small Size Datasets

Regularization

Interpreting Weights

Bootstrapping FREL

Monte Carlo Permutation Tests of FREL

General Statement of the FREL Algorithm

Multithreaded Code for FREL

Some FREL Examples

3: Displaying Relationship Anomalies

Marginal Density Product

Actual Density

Marginal Inconsistency

Mutual Information Contribution

Code for Computing These Plots

Comments on Showing the Display

4: Fun with Eigenvectors

Eigenvalues and Eigenvectors

Principal Components (If You Really Must)

The Factor Structure Is More Interesting

A Simple Example

Rotation Can Make Naming Easier

Code for Eigenvectors and Rotation

Eigenvectors of a Real Symmetric Matrix

Factor Structure of a Dataset

Varimax Rotation

Horn's Algorithm for Determining Dimensionality

Code for the Modified Horn Algorithm

Clustering Variables in a Subspace

Code for Clustering Variables

Separating Individual from Common Variance

Log Likelihood the Slow, Definitional Way

Log Likelihood the Fast, Intelligent Way

The Basic Expectation Maximization Algorithm

Code for Basic Expectation Maximization

Accelerating the EM Algorithm

Code for Quadratic Acceleration with DECME-2s

Putting It All Together

Thoughts on My Version of the Algorithm

Measuring Coherence

Code for Tracking Coherence

Coherence in the Stock Market

5: Using the DATAMINE Program

File/Read Data File

File/Exit

Screen/Univariate Screen

Screen/Bivariate Screen

Screen/Relevance Minus Redundancy

Screen/FREL

Analyze/Eigen Analysis

Analyze/Factor Analysis

Analyze/Rotate

Analyze/Cluster Variables

Analyze/Coherence

Plot/Series

Plot/Histogram

Plot/Density

Index

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