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E-raamat: Time Series Clustering and Classification

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The beginning of the age of artificial intelligence and machine learning has created new challenges and opportunities for data analysts, statisticians, mathematicians, econometricians, computer scientists and many others. At the root of these techniques are algorithms and methods for clustering and classifying different types of large datasets, including time series data.

Time Series Clustering and Classification includes relevant developments on observation-based, feature-based and model-based traditional and fuzzy clustering methods, feature-based and model-based classification methods, and machine learning methods. It presents a broad and self-contained overview of techniques for both researchers and students.

Features





Provides an overview of the methods and applications of pattern recognition of time series





Covers a wide range of techniques, including unsupervised and supervised approaches





Includes a range of real examples from medicine, finance, environmental science, and more





R and MATLAB code, and relevant data sets are available on a supplementary website

Arvustused

"The book represents 20 years of research by the authors. They have achieved the goal of gathering in one place a broad spectrum of clustering and classification techniques for time series, which have attracted substantial attention for the last few decades...The book contains a number of examples of clustering, which are intended to highlight the main theoretical models on real data...The book contains a large amount of theoretical information and practical examples and may be recommended as a desk book for young scientists and applied mathematicians." - Maria Ivanchuk, ISCB News, July 2020

"The authors of this book have more than 20 years of experience on the topic of time series clustering and classification. They consolidate many important methods and algorithms commonly used in time series clustering and classification practices published by various scientific journals. In addition, they provide Matlab and R code and corresponding datasets to reproduce the examples in the book...This book covers most classical and common techniques for time series clustering and classification. It consolidates different methods into an extensive coherent framework. This makes the book a good reference for students and researchers." - Ming Chen, JASA, August 2020

Preface xiii
Authors xv
1 Introduction
1(8)
1.1 Overview
1(1)
1.2 Examples
2(5)
1.3 Structure of the book
7(2)
2 Time series features and models
9(18)
2.1 Introduction
9(1)
2.2 Stochastic processes
10(2)
2.3 Autocorrelation and partial autocorrelation functions
12(3)
2.4 Time series models
15(2)
2.4.1 Stationary models
15(1)
2.4.2 Non-stationary models
16(1)
2.4.3 Some other models
17(1)
2.5 Spectral representation of time series
17(3)
2.5.1 Periodogram
18(2)
2.5.2 Smoothed periodogram
20(1)
2.6 Wavelet representation of time series
20(5)
2.6.1 Discrete wavelet transform (DWT)
21(1)
2.6.2 Modified discrete wavelet transform (MODWT)
22(1)
2.6.3 Wavelet variance
22(2)
2.6.4 Wavelet correlation
24(1)
2.7 Conclusion
25(2)
I Unsupervised Approaches: Clustering Techniques for Time Series 27(136)
3 Traditional cluster analysis
29(8)
3.1 Introduction
29(1)
3.2 Distance measures
30(1)
3.3 Hierarchical clustering
31(2)
3.4 Non-hierarchical clustering (partitioning clustering)
33(2)
3.4.1 c-Means clustering method
33(1)
3.4.2 c-Medoids clustering method
34(1)
3.5 Some cluster validity criteria
35(2)
3.5.1 Calinski and Harabasz criterion
35(1)
3.5.2 Silhouette criterion
35(2)
4 Fuzzy clustering
37(12)
4.1 Introduction
37(1)
4.2 Fuzzy c-Means (FcM) clustering
38(1)
4.3 Cluster validity criteria
39(2)
4.3.1 Criteria based on partition coefficient and partition entropy
39(1)
4.3.2 The Xie-Beni criterion
40(1)
4.3.3 The Silhouette criterion
40(1)
4.4 Fuzzy c-Medoids (FcMd) clustering
41(2)
4.5 Fuzzy clustering with entropy regularization
43(1)
4.6 Robust fuzzy clustering
44(5)
4.6.1 Fuzzy clustering with noise cluster
44(1)
4.6.2 Fuzzy clustering with exponential distance
45(1)
4.6.3 Trimmed fuzzy clustering
46(3)
5 Observation-based clustering
49(18)
5.1 Introduction
49(1)
5.2 Observation-based distance measures
49(5)
5.2.1 Dynamic time warping
51(3)
5.3 Clustering methods
54(13)
6 Feature-based clustering
67(44)
6.1 Introduction
68(1)
6.2 Time domain features - Autocorrelations and partial autocorrelations
68(5)
6.2.1 Crisp clustering methods
68(3)
6.2.2 Fuzzy clustering methods
71(2)
6.3 Time domain features - Quantile autocovariances
73(4)
6.3.1 QAF-based fuzzy c-medoids clustering model (QAF-FcMdC model)
74(3)
6.4 Time domain features - Variance ratios
77(3)
6.4.1 Variance ratio tests
77(3)
6.4.2 Variance ratio-based metric
80(1)
6.5 Other time domain clustering methods
80(1)
6.6 Frequency domain features - Spectral ordinates
81(6)
6.6.1 Crisp clustering methods
81(2)
6.6.2 Fuzzy clustering methods
83(4)
6.7 Frequency domain clustering methods for time series of unequal lengths
87(9)
6.7.1 Hypothesis testing
89(1)
6.7.2 Comparison of processes with similar sample characteristics with simulated time series
89(3)
6.7.3 Clustering AR MA and ARIMA processes with simulated time series of unequal lengths
92(4)
6.8 Other frequency domain clustering methods
96(1)
6.9 Wavelet-based features
97(6)
6.10 Other feature-based applications
103(8)
6.10.1 Comparison between trend-stationary and difference-stationary processes
103(4)
6.10.2 Comparison of processes with different characteristics of persistence
107(4)
7 Model-based clustering
111(42)
7.1 Introduction
112(1)
7.2 Autoregressive expansions
113(7)
7.2.1 AR(infinity) and MA(infinity) coefficients-based distances
113(1)
7.2.2 AR coefficients-based distance
114(5)
7.2.3 ARMA(p,q) coefficents-based distance
119(1)
7.3 Fitted residuals
120(1)
7.4 Forecast densities
121(2)
7.4.1 Clustering based on forecast densities
121(1)
7.4.2 Clustering based on the polarization of forecast densities
122(1)
7.5 ARMA mixture models
123(1)
7.6 Generalized autoregressive conditional heteroskedasticity (GARCH) models
124(14)
7.6.1 Unconditional, Minimum and Time-varying Volatilities
126(2)
7.6.2 A GARCH-based metric for time series clustering
128(1)
7.6.3 A combined distance measure for heteroskedastic time series
129(2)
7.6.4 GARCH-based Fuzzy c-Medoids Clustering model (GARCH-FcMdC)
131(1)
7.6.5 GARCH-based Exponential Fuzzy c-Medoids Clustering model (GARCH-E-FcMdC)
131(1)
7.6.6 GARCH-based Fuzzy c-Medoids Clustering with Noise Cluster model (GARCH-NC-FcMdC)
132(2)
7.6.7 GARCH-based Trimmed Fuzzy c-Medoids Clustering model (GARCH-Tr-FcMdC)
134(4)
7.7 Generalized extreme value distributions
138(11)
7.8 Other model-based approaches
149(4)
8 Other time series clustering approaches
153(10)
8.1 Introduction
153(1)
8.2 Hidden Markov Models
153(1)
8.3 Support vector clustering
154(1)
8.4 Self-Organising Maps
155(6)
8.4.1 Wavelet-based Self-Organizing Map (W-SOM)
155(6)
8.5 Other data mining algorithms
161(2)
II Supervised Approaches: Classification Techniques for Time Series 163(34)
9 Feature-based approaches
165(26)
9.1 Introduction
165(1)
9.2 Discriminant Analysis
166(1)
9.3 Frequency domain approaches
167(3)
9.4 Wavelet feature approaches
170(13)
9.4.1 Classification using wavelet variances
170(2)
9.4.2 Classification using wavelet variances and correlations
172(10)
9.4.3 Classification using evolutionary wavelet spectra
182(1)
9.5 Time-domain approaches
183(8)
9.5.1 Classification using shapes
183(1)
9.5.2 Classification using complex demodulation
184(7)
10 Other time series classification approaches
191(6)
10.1 Introduction
191(1)
10.2 Classification trees
191(1)
10.3 Gaussian mixture models
192(1)
10.4 Bayesian approach
193(1)
10.5 Nearest neighbours methods
193(1)
10.6 Support vector machines
194(3)
III Software and Data Sets 197(8)
11 Software and data sets
199(6)
11.1 Introduction
199(1)
11.2
Chapter 5 Application
200(1)
11.2.1 Application 5.1
200(1)
11.3
Chapter 6 Applications
200(1)
11.3.1 Application 6.1
200(1)
11.3.2 Application 6.2
200(1)
11.3.3 Application 6.3
200(1)
11.3.4 Application 6.4
201(1)
11.3.5 Application 6.5
201(1)
11.3.6 Application 6.6
201(1)
11.3.7 Application 6.7
201(1)
11.3.8 Application 6.8
201(1)
11.4
Chapter 7 Applications
201(1)
11.4.1 Application 7.1
201(1)
11.4.2 Application 7.2
202(1)
11.4.3 Application 7.3
202(1)
11.5
Chapter 8 Application
202(1)
11.5.1 Application 8.1
202(1)
11.6
Chapter 9 Applications
202(1)
11.6.1 Application 9.1
202(1)
11.6.2 Application 9.2
203(1)
11.6.3 Application 9.3
203(1)
11.7 Software packages
203(2)
Bibliography 205(20)
Subject index 225
Elizabeth Ann Maharaj is an Associate Professor in the Department of Econometrics and Business Statistics at Monash University, Australia. She has a Ph.D. from Monash University on the Pattern Recognition of Time Series. Ann is an elected member of the International Statistical Institute (ISI), a member of the International Association of Statistical Computing (IASC) and of the Statistical Society of Australia (SSA). She is also an accredited statistician with the SSA. Anns main research interests are in time series classification, wavelets analysis, fuzzy classification and interval time series analysis. She has also worked on research projects in climatology, environmental science, labour markets, human mobility and finance.

Pierpaolo D'Urso is a Full Professor of Statistics at Sapienza - University of Rome. He is the chair of the Department of Social and Economic Sciences, Sapienza - University of Rome. He received his Ph.D. in Statistics and his bachelor's degree in Statistics both from Sapienza. He is an associate editor and a member of the editorial board of several journals. He has been member of several program committees of international conferences and guest editor of special issues. His recent research activity is focus on fuzzy clustering, clustering and classification of time series, clustering of complex structures of data, and statistical methods for marketing, local labour systems, electoral studies and environmental monitoring.

Jorge Caiado has a Ph.D. in Applied Mathematics to Economics and Management. He is a Professor of Econometrics and Forecasting Methods at the Lisbon School of Economics and Management (ISEG) and a Researcher at the Centre for Applied Mathematics and Economics. His research in econometrics, finance, time series analysis, forecasting methods and statistical software has led to numerous publications in scientific journals and books. He serves as an econometric and statistical consultant and trainer for numerous companies and organizations including central banks, commercial and investment banks, bureau of statistics, bureau of economic analysis, transportation and logistics companies, health companies and insurance companies. He is also a co-founder and partner of GlobalSolver.
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