Computational Methods for Data Analysis

Book Description

This graduate text covers a variety of mathematical and statistical tools for the analysis of big data coming from biology, medicine and economics. Neural networks, Markov chains, tools from statistical physics and wavelet analysis are used to develop efficient computational algorithms, which are then used for the processing of real-life data using Matlab.

Table of Contents

  1. Cover
  2. Title Page
  3. Copyright
  4. Preface
  5. Acknowledgment
  6. Contents
  7. 1 Introduction
    1. 1.1 Objectives
    2. 1.2 Intended audience
    3. 1.3 Features of the chapters
    4. 1.4 Content of the chapters
    5. 1.5 Text supplements
      1. 1.5.1 Datasets
  8. 2 Dataset
    1. 2.1 Big data and data science
    2. 2.2 Data objects, attributes and types of attributes
      1. 2.2.1 Nominal attributes and numeric attributes
    3. 2.3 Basic definitions of real and synthetic data
      1. 2.3.1 Real dataset
      2. 2.3.2 Synthetic dataset
    4. 2.4 Real and synthetic data from the fields of economy and medicine
      1. 2.4.1 Economy data: Economy (U.N.I.S.) dataset
      2. 2.4.2 MS data and content (neurology and radiology data): MS dataset
      3. 2.4.3 Clinical psychology data: WAIS-R dataset
    5. 2.5 Basic statistical descriptions of data
      1. 2.5.1 Central tendency: Mean, median and mode
      2. 2.5.2 Spread of data
      3. 2.5.3 Measures of data dispersion
      4. 2.5.4 Graphic displays
    6. 2.6 Data matrix versus dissimilarity matrix
    7. References
  9. 3 Data preprocessing and model evaluation
    1. 3.1 Data quality
    2. 3.2 Data preprocessing: Major steps involved
      1. 3.2.1 Data cleaning and methods
      2. 3.2.2 Data cleaning as a process
      3. 3.2.3 Data integration and methods
    3. 3.3 Data value conflict detection and resolution
    4. 3.4 Data smoothing and methods
    5. 3.5 Data reduction
    6. 3.6 Data transformation
    7. 3.7 Attribute subset selection
    8. 3.8 Classification of data
      1. 3.8.1 Definition of classification
    9. 3.9 Model evaluation and selection
      1. 3.9.1 Metrics for evaluating classifier performance
    10. References
  10. 4 Algorithms
    1. 4.1 What is an algorithm?
      1. 4.1.1 What is the flowchart of an algorithm?
      2. 4.1.2 Fundamental concepts of programming
      3. 4.1.3 Expressions and repetition statements
    2. 4.2 Image on coordinate systems
      1. 4.2.1 Pixel coordinates
      2. 4.2.2 Color models
    3. 4.3 Statistical application with algorithms: Image on coordinate systems
      1. 4.3.1 Statistical application with algorithms: BW image on coordinate systems
      2. 4.3.2 Statistical application with algorithms: RGB image on coordinate systems
    4. References
  11. 5 Linear model and multilinear model
    1. 5.1 Linear model analysis for various data
      1. 5.1.1 Application of economy dataset based on linear model
      2. 5.1.2 Linear model for the analysis of MS
      3. 5.1.3 Linear model for the analysis of mental functions
    2. 5.2 Multilinear model algorithms for the analysis of various data
      1. 5.2.1 Multilinear model for the analysis of economy (U.N.I.S.) dataset
      2. 5.2.2 Multilinear model for the analysis of MS
      3. 5.2.3 Multilinear model for the analysis of mental functions
    3. References
  12. 6 Decision Tree
    1. 6.1 Decision tree induction
    2. 6.2 Attribute selection measures
    3. 6.3 Iterative dichotomiser 3 (ID3) algorithm
      1. 6.3.1 ID3 algorithm for the analysis of various data
    4. 6.4 C4.5 algorithm
      1. 6.4.1 C4.5 Algorithm for the analysis of various data
    5. 6.5 CART algorithm
      1. 6.5.1 CART algorithm for the analysis of various data
    6. References
  13. 7 Naive Bayesian classifier
    1. 7.1 Naive Bayesian classifier algorithm (and its types) for the analysis of various data
      1. 7.1.1 Naive Bayesian classifier algorithm for the analysis of economy (U.N.I.S.)
      2. 7.1.2 Algorithms for the analysis of multiple sclerosis
      3. 7.1.3 Naive Bayesian classifier algorithm for the analysis of mental functions
    2. References
  14. 8 Support vector machines algorithms
    1. 8.1 The case with data being linearly separable
    2. 8.2 The case when the data are linearly inseparable
    3. 8.3 SVM algorithm for the analysis of various data
      1. 8.3.1 SVM algorithm for the analysis of economy (U.N.I.S.) Data
      2. 8.3.2 SVM algorithm for the analysis of multiple sclerosis
      3. 8.3.3 SVM algorithm for the analysis of mental functions
    4. References
  15. 9 k-Nearest neighbor algorithm
    1. 9.1 k-Nearest algorithm for the analysis of various data
      1. 9.1.1 k-Nearest algorithm for the analysis of Economy (U.N.I.S.)
      2. 9.1.2 k-Nearest algorithm for the analysis of multiple sclerosis
      3. 9.1.3 k-Nearest algorithm for the analysis of mental functions
    2. References
  16. 10 Artificial neural networks algorithm
    1. 10.1 Classification by backpropagation
      1. 10.1.1 A multilayer feed-forward neural network
    2. 10.2 Feed-forward backpropagation (FFBP) algorithm
      1. 10.2.1 FFBP algorithm for the analysis of various data
    3. 10.3 LVQ algorithm
      1. 10.3.1 LVQ algorithm for the analysis of various data
    4. References
  17. 11 Fractal and multifractal methods with ANN
    1. 11.1 Basic descriptions of fractal
    2. 11.2 Fractal dimension
    3. 11.3 Multifractal methods
      1. 11.3.1 Two-dimensional fractional Brownian motion
      2. 11.3.2 Hölder regularity
      3. 11.3.3 Fractional Brownian motion
    4. 11.4 Multifractal analysis with LVQ algorithm
      1. 11.4.1 Polynomial Hölder function with LVQ algorithm for the analysis of various data
      2. 11.4.2 Exponential Hölder function with LVQ algorithm for the analysis of various data
    5. References
  18. Index

Product Information

  • Title: Computational Methods for Data Analysis
  • Author(s): Yeliz Karaca, Carlo Cattani
  • Release date: December 2018
  • Publisher(s): De Gruyter
  • ISBN: 9783110493603