Statistical Methods For Clustering And High Dimensional Time Series Analysis
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Statistical Methods For Clustering And High Dimensional Time Series Analysis
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Author : Kunhui Zhang
language : en
Publisher:
Release Date : 2022
Statistical Methods For Clustering And High Dimensional Time Series Analysis written by Kunhui Zhang and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022 with categories.
This dissertation mainly explores two statistical tasks, namely clustering and analysis of high-dimensional time series. Clustering, a very important unsupervised learning problem, studies the structure of unlabeled datasets. The goal of clustering is to partition the data points into subsets such that data points in the same subset are similar and different from those in other subsets. Mode-clustering is a clustering analysis method that partitions the data into groups by the local modes of the underlying density function. Sometimes, finding clusters is not the ultimate goal. The connectivity among clusters may yield valuable information for scientists. This dissertation presents a new clustering method inspired by mode-clustering that not only finds clusters but also assigns each cluster with an attribute label. Clusters obtained from our method show connectivity of the underlying distribution. We also design a local two-sample test based on the clustering result that has more power than a conventional method. We apply our method to the Astronomy and GvHD data and show that our method finds meaningful clusters. In addition, we derive the statistical and computational theory of our method. Motivated by the challenges of modeling time series data sets that exhibit non-linear patterns, especially in high dimensions, this dissertation also considers the threshold Auto-Regressive (TAR) process. The TAR process provides a family of non-linear auto-regressive time series models in which the process dynamics are specific step functions of a thresholding variable. While estimation and inference for low-dimensional TAR models have been investigated, high-dimensional TAR models have received less attention. In this dissertation, we develop a new framework for estimating high-dimensional TAR models and propose two different sparsity-inducing penalties. The first penalty corresponds to a natural extension of the classical TAR model to high-dimensional settings, where the same threshold is enforced for all model parameters. Our second penalty develops a more flexible TAR model, where different thresholds are allowed for different auto-regressive coefficients. We show that both penalized estimation strategies can be utilized in a three-step procedure that consistently learns both the thresholds and the corresponding auto-regressive coefficients. However, our theoretical and empirical investigations show that the direct extension of the TAR model is not appropriate for high-dimensional settings and is better suited for moderate dimensions. In contrast, the more flexible extension of the TAR model leads to consistent estimation and superior empirical performance in high dimensions. In addition to the three-step procedure, the dynamic programming approach can successfully handle high dimensions with diverging number of thresholds as well. In particular, extensive numerical analysis and theoretical results demonstrate the advantages of the dynamic programming approach. Finally, we also discuss a method to select the optimal thresholding variable automatically.
Data Clustering
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Author : Charu C. Aggarwal
language : en
Publisher: CRC Press
Release Date : 2018-09-03
Data Clustering written by Charu C. Aggarwal and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-09-03 with Business & Economics categories.
Research on the problem of clustering tends to be fragmented across the pattern recognition, database, data mining, and machine learning communities. Addressing this problem in a unified way, Data Clustering: Algorithms and Applications provides complete coverage of the entire area of clustering, from basic methods to more refined and complex data clustering approaches. It pays special attention to recent issues in graphs, social networks, and other domains. The book focuses on three primary aspects of data clustering: Methods, describing key techniques commonly used for clustering, such as feature selection, agglomerative clustering, partitional clustering, density-based clustering, probabilistic clustering, grid-based clustering, spectral clustering, and nonnegative matrix factorization Domains, covering methods used for different domains of data, such as categorical data, text data, multimedia data, graph data, biological data, stream data, uncertain data, time series clustering, high-dimensional clustering, and big data Variations and Insights, discussing important variations of the clustering process, such as semisupervised clustering, interactive clustering, multiview clustering, cluster ensembles, and cluster validation In this book, top researchers from around the world explore the characteristics of clustering problems in a variety of application areas. They also explain how to glean detailed insight from the clustering process—including how to verify the quality of the underlying clusters—through supervision, human intervention, or the automated generation of alternative clusters.
Time Series Clustering And Classification
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Author : Elizabeth Ann Maharaj
language : en
Publisher: CRC Press
Release Date : 2019-03-19
Time Series Clustering And Classification written by Elizabeth Ann Maharaj and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-03-19 with Mathematics categories.
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
Advances In Time Series Analysis And Forecasting
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Author : Ignacio Rojas
language : en
Publisher: Springer
Release Date : 2017-07-31
Advances In Time Series Analysis And Forecasting written by Ignacio Rojas and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-07-31 with Business & Economics categories.
This volume of selected and peer-reviewed contributions on the latest developments in time series analysis and forecasting updates the reader on topics such as analysis of irregularly sampled time series, multi-scale analysis of univariate and multivariate time series, linear and non-linear time series models, advanced time series forecasting methods, applications in time series analysis and forecasting, advanced methods and online learning in time series and high-dimensional and complex/big data time series. The contributions were originally presented at the International Work-Conference on Time Series, ITISE 2016, held in Granada, Spain, June 27-29, 2016. The series of ITISE conferences provides a forum for scientists, engineers, educators and students to discuss the latest ideas and implementations in the foundations, theory, models and applications in the field of time series analysis and forecasting. It focuses on interdisciplinary and multidisciplinary research encompassing the disciplines of computer science, mathematics, statistics and econometrics.
Time Series Clustering And Classification
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Author : Elizabeth Ann Maharaj
language : en
Publisher: CRC Press
Release Date : 2019-03-19
Time Series Clustering And Classification written by Elizabeth Ann Maharaj and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-03-19 with Mathematics categories.
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
Data Clustering
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Author : Charu C. Aggarwal
language : en
Publisher: CRC Press
Release Date : 2016-03-29
Data Clustering written by Charu C. Aggarwal and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-03-29 with Business & Economics categories.
Research on the problem of clustering tends to be fragmented across the pattern recognition, database, data mining, and machine learning communities. Addressing this problem in a unified way, Data Clustering: Algorithms and Applications provides complete coverage of the entire area of clustering, from basic methods to more refined and complex data clustering approaches. It pays special attention to recent issues in graphs, social networks, and other domains. The book focuses on three primary aspects of data clustering: Methods, describing key techniques commonly used for clustering, such as feature selection, agglomerative clustering, partitional clustering, density-based clustering, probabilistic clustering, grid-based clustering, spectral clustering, and nonnegative matrix factorization Domains, covering methods used for different domains of data, such as categorical data, text data, multimedia data, graph data, biological data, stream data, uncertain data, time series clustering, high-dimensional clustering, and big data Variations and Insights, discussing important variations of the clustering process, such as semisupervised clustering, interactive clustering, multiview clustering, cluster ensembles, and cluster validation In this book, top researchers from around the world explore the characteristics of clustering problems in a variety of application areas. They also explain how to glean detailed insight from the clustering process—including how to verify the quality of the underlying clusters—through supervision, human intervention, or the automated generation of alternative clusters.
Clustering
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Author : Rui Xu
language : en
Publisher: John Wiley & Sons
Release Date : 2008-11-03
Clustering written by Rui Xu and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-11-03 with Mathematics categories.
This is the first book to take a truly comprehensive look at clustering. It begins with an introduction to cluster analysis and goes on to explore: proximity measures; hierarchical clustering; partition clustering; neural network-based clustering; kernel-based clustering; sequential data clustering; large-scale data clustering; data visualization and high-dimensional data clustering; and cluster validation. The authors assume no previous background in clustering and their generous inclusion of examples and references help make the subject matter comprehensible for readers of varying levels and backgrounds.
Model Based Clustering And Classification For Data Science
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Author : Charles Bouveyron
language : en
Publisher: Cambridge University Press
Release Date : 2019-07-25
Model Based Clustering And Classification For Data Science written by Charles Bouveyron and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-07-25 with Business & Economics categories.
Colorful example-rich introduction to the state-of-the-art for students in data science, as well as researchers and practitioners.
Handbook Of Cluster Analysis
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Author : Christian Hennig
language : en
Publisher: CRC Press
Release Date : 2015-12-16
Handbook Of Cluster Analysis written by Christian Hennig and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-12-16 with Business & Economics categories.
Handbook of Cluster Analysis provides a comprehensive and unified account of the main research developments in cluster analysis. Written by active, distinguished researchers in this area, the book helps readers make informed choices of the most suitable clustering approach for their problem and make better use of existing cluster analysis tools.The
Foundations Of Computational Intelligence
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Author : Ajith Abraham
language : en
Publisher: Springer
Release Date : 2009-05-01
Foundations Of Computational Intelligence written by Ajith Abraham and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-05-01 with Technology & Engineering categories.
Foundations of Computational Intelligence Volume 6: Data Mining: Theoretical Foundations and Applications Finding information hidden in data is as theoretically difficult as it is practically important. With the objective of discovering unknown patterns from data, the methodologies of data mining were derived from statistics, machine learning, and artificial intelligence, and are being used successfully in application areas such as bioinformatics, business, health care, banking, retail, and many others. Advanced representation schemes and computational intelligence techniques such as rough sets, neural networks; decision trees; fuzzy logic; evolutionary algorithms; arti- cial immune systems; swarm intelligence; reinforcement learning, association rule mining, Web intelligence paradigms etc. have proved valuable when they are - plied to Data Mining problems. Computational tools or solutions based on intel- gent systems are being used with great success in Data Mining applications. It is also observed that strong scientific advances have been made when issues from different research areas are integrated. This Volume comprises of 15 chapters including an overview chapter providing an up-to-date and state-of-the research on the applications of Computational Int- ligence techniques for Data Mining. The book is divided into 3 parts: Part-I: Data Click Streams and Temporal Data Mining Part-II: Text and Rule Mining Part-III: Applications Part I on Data Click Streams and Temporal Data Mining contains four chapters that describe several approaches in Data Click Streams and Temporal Data Mining.