From Curve Fitting to Machine Learning An Illustrative Guide to Scientific Data Analysis and Computational Intelligence

✍ Scribed by Zielesny, Achim

• Publisher: Springer International Publishing
• Year: 2016
• Tongue: English
• Leaves: 509
• Series: Intelligent systems reference library 109
• Edition: 2nd ed. 2016
• Category: Library

✦ Synopsis

This successful book provides in its second edition an interactive and illustrative guide from two-dimensional curve fitting to multidimensional clustering and machine learning with neural networks or support vector machines. Along the way topics like mathematical optimization or evolutionary algorithms are touched. All concepts and ideas are outlined in a clear cut manner with graphically depicted plausibility arguments and a little elementary mathematics.The major topics are extensively outlined with exploratory examples and applications. The primary goal is to be as illustrative as possible without hiding problems and pitfalls but to address them. The character of an illustrative cookbook is complemented with specific sections that address more fundamental questions like the relation between machine learning and human intelligence.All topics are completely demonstrated with the computing platform Mathematica and the Computational Intelligence Packages (CIP), a high-level function library developed with Mathematica's programming language on top of Mathematica's algorithms. CIP is open-source and the detailed code used throughout the book is freely accessible.The target readerships are students of (computer) science and engineering as well as scientific practitioners in industry and academia who deserve an illustrative introduction. Readers with programming skills may easily port or customize the provided code. "'From curve fitting to machine learning' is ... a useful book. ... It contains the basic formulas of curve fitting and related subjects and throws in, what is missing in so many books, the code to reproduce the results.All in all this is an interesting and useful book both for novice as well as expert readers. For the novice it is a good introductory book and the expert will appreciate the many examples and working code." Leslie A. Piegl (Review of the first edition, 2012).

✦ Table of Contents

Cover......Page 1
Intelligent Systems Reference Library Volume 109......Page 2
About this Series......Page 3
From Curve Fitting to Machine Learning......Page 4
Library of Congress Control Number: 2016936957......Page 5
Dedication......Page 6
Preface to the first edition......Page 7
Preface to the second edition......Page 9
Acknowledgements to the first edition......Page 10
Acknowledgements to the second edition......Page 11
Contents......Page 12
1Introduction......Page 15
1.1 Motivation: Data, models and molecular sciences......Page 16
1.2 Optimization......Page 20
1.2.1 Calculus......Page 24
1.2.2 Iterative optimization......Page 28
1.2.3 Iterative local optimization......Page 30
1.2.4 Iterative global optimization......Page 34
1.2.5 Constrained iterative optimization......Page 45
1.3 Model functions......Page 51
1.3.1 Linear model functions with one argument......Page 52
1.3.2 Non-linear model functions with one argument......Page 54
1.3.3 Linear model functions with multiple arguments......Page 55
1.3.4 Non-linear model functions with multiple arguments......Page 57
1.3.6 Summary......Page 58
1.4.2 Data for machine learning......Page 59
1.4.3 Inputs for clustering......Page 61
1.4.4 Inspection, cleaning and splitting of data......Page 62
1.5 Scaling of data......Page 68
1.6 Data errors......Page 69
1.7 Regression versus classification tasks......Page 70
1.8 The structure of CIP calculations......Page 72
1.9 A note on reproducibility......Page 73
2Curve Fitting......Page 74
2.1.1 Fitting data......Page 78
2.1.2 Useful quantities......Page 79
2.1.3 Smoothing data......Page 81
2.2 Evaluating the goodness of fit......Page 83
2.3 How to guess a model function......Page 89
2.4 Problems and pitfalls......Page 101
2.4.1 Parameters’ start values......Page 102
2.4.2 How to search for parameters’ start values......Page 106
2.4.3 More difficult curve fitting problems......Page 110
2.4.4 Inappropriate model functions......Page 120
2.5.1 Correction of parameters’ errors......Page 125
2.5.2 Confidence levels of parameters’ errors......Page 126
2.5.3 Estimating the necessary number of data......Page 127
2.5.4 Large parameters’ errors and educated cheating......Page 131
2.5.5 Experimental errors and data transformation......Page 145
2.6 Empirical enhancement of theoretical model functions......Page 148
2.7 Data smoothing with cubic splines......Page 156
2.8 Cookbook recipes for curve fitting......Page 167
3Clustering......Page 169
3.1 Basics......Page 172
3.2 Intuitive clustering......Page 175
3.3 Clustering with a fixed number of clusters......Page 190
3.4 Getting representatives......Page 197
3.5 Cluster occupancies and the iris flower example......Page 206
3.6 White-spot analysis......Page 218
3.7 Alternative clustering with ART-2a......Page 221
3.8 Clustering and class predictions......Page 232
3.9 Cookbook recipes for clustering......Page 240
4Machine Learning......Page 241
4.1 Basics......Page 249
4.2 Machine learning methods......Page 254
4.2.1 Multiple linear and polynomial regression (MLR, MPR)......Page 255
4.2.2 Three-layer feed-forward neural networks......Page 258
4.2.3 Support vector machines (SVM)......Page 263
4.3 Evaluating the goodness of regression......Page 268
4.4 Evaluating the goodness of classification......Page 272
4.5 Regression: Entering non-linearity......Page 276
4.6 Classification: Non-linear decision surfaces......Page 294
4.7 Ambiguous classification......Page 298
4.8 Training and test set partitioning......Page 310
4.8.1 Cluster representatives based selection......Page 311
4.8.2 Iris flower classification revisited......Page 316
4.8.3 Adhesive kinetics regression revisited......Page 328
4.8.4 Design of experiment......Page 332
4.8.5 Concluding remarks......Page 347
4.9 Comparative machine learning......Page 348
4.10 Relevance of input components and minimal models......Page 361
4.11 Pattern recognition......Page 367
4.12 Technical optimization problems......Page 385
4.13 Cookbook recipes for machine learning......Page 390
4.14 Appendix - Collecting the pieces......Page 392
5.1 Computers are about speed......Page 419
5.2 Isn’t it just ...?......Page 429
5.2.2 ... data smoothing?......Page 430
5.3 Computational intelligence......Page 441
5.4 Final remark......Page 446
A.1 Basics......Page 448
A.2.1 Temperature dependence of the viscosity of water......Page 450
A.2.2 Potential energy surface of hydrogen fluoride......Page 451
A.2.3 Kinetics data from time dependent IR spectra of the hydrolysis of acetanhydride......Page 452
A.2.4 Iris flowers......Page 459
A.2.5 Adhesive kinetics......Page 460
A.2.6 Intertwined spirals......Page 462
A.2.7 Faces......Page 463
A.2.8 Wisconsin Diagnostic Breast Cancer (WDBC) data......Page 466
A.2.9 Wisconsin Prognostic Breast Cancer (WPBC) data......Page 467
A.2.10 QSPR data......Page 468
A.3 Parallelized calculations......Page 469
References......Page 472
Index......Page 478