Pattern Theory
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Pattern Theory
Pattern theory is a distinctive approach to the analysis of all forms of real-world signals. At its core is the design of a large variety of probabilistic models whose samples reproduce the look and feel of the real signals, their patterns, and their variability. Bayesian statistical inference then allows you to apply these models in the analysis of new signals. This book treats the mathematical tools, the models themselves, and the computational algorithms for applying statistics to analyze six representative classes of signals of increasing complexity. The book covers patterns in text, sound, and images. Discussions of images include recognizing characters, textures, nature scenes, and human faces. The text includes onlineaccess to thematerials (data, code, etc.) needed for the exercises.
Pattern Theory
Pattern Theory provides a comprehensive and accessible overview of the modern challenges in signal, data, and pattern analysis in speech recognition, computational linguistics, image analysis and computer vision. Aimed at graduate students in biomedical engineering, mathematics, computer science, and electrical engineering with a good background in mathematics and probability, the text includes numerous exercises and an extensive bibliography. Additional resources including extended proofs, selected solutions and examples are available on a companion website. The book commences with a short overview of pattern theory and the basics of statistics and estimation theory. Chapters 3-6 discuss the role of representation of patterns via condition structure. Chapters 7 and 8 examine the second central component of pattern theory: groups of geometric transformation applied to the representation of geometric objects. Chapter 9 moves into probabilistic structures in the continuum, studying random processes and random fields indexed over subsets of Rn. Chapters 10 and 11 continue with transformations and patterns indexed over the continuum. Chapters 12-14 extend from the pure representations of shapes to the Bayes estimation of shapes and their parametric representation. Chapters 15 and 16 study the estimation of infinite dimensional shape in the newly emergent field of Computational Anatomy. Finally, Chapters 17 and 18 look at inference, exploring random sampling approaches for estimation of model order and parametric representing of shapes.
Pattern Theory
Author: Rachel H. Ellaway
language: en
Publisher: Taylor & Francis
Release Date: 2024-12-30
Pattern Theory is a groundbreaking exploration of the concept of pattern across a range of disciplines, including science, neuroscience, psychology, and social sciences. This book examines the meaning and implications of pattern, presenting a comprehensive body of theory that unifies concepts of form, order, and regularity and connects them to memory and perception. By challenging existing orthodoxies and linking evidence from brain and mind function, it outlines a robust theoretical framework around pattern searching and matching, pattern activation, and the continuity of pattern nexuses. This in-depth study of pattern theory and pattern thinking delves into the cognitive basis of patterns, their impact on reasoning and learning, and the social and collaborative nature of pattern recognition, expression, and representation. It also addresses philosophical issues and implications surrounding shared pattern thinking and introduces a broad conceptual basis for "pattern inquiry", providing a range of questions and methodologies for applying pattern theory. The book culminates in a manifesto for pattern theory and its application in pattern inquiry, offering 50 key principles that can be applied across various settings. Researchers, scholars, and practitioners are encouraged to explore and critique this unified theory as a lens for examining social and cognitive phenomena. Ideal for academics and professionals seeking to challenge their understanding of the connections between mind and society, as well as for those looking to deepen their understanding of pattern as a cognitive phenomenon, as a theoretical lens, and as a meta-methodology for inquiry, this text provides a substantive foundation for ongoing development and application of pattern science across multiple fields.