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The Resource Data Science Foundations : Geometry and Topology of Complex Hierarchic Systems and Big Data Analytics

Data Science Foundations : Geometry and Topology of Complex Hierarchic Systems and Big Data Analytics

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Data Science Foundations : Geometry and Topology of Complex Hierarchic Systems and Big Data Analytics
Title
Data Science Foundations
Title remainder
Geometry and Topology of Complex Hierarchic Systems and Big Data Analytics
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Subject
Language
eng
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Cataloging source
MiAaPQ
Literary form
non fiction
Nature of contents
dictionaries
Series statement
Chapman & Hall/CRC Computer Science & Data Analysis
Data Science Foundations : Geometry and Topology of Complex Hierarchic Systems and Big Data Analytics
Label
Data Science Foundations : Geometry and Topology of Complex Hierarchic Systems and Big Data Analytics
Link
http://libproxy.rpi.edu/login?url=https://ebookcentral.proquest.com/lib/rpi/detail.action?docID=5056392
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Copyright
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Carrier category
online resource
Carrier category code
cr
Carrier MARC source
rdacarrier
Color
multicolored
Content category
text
Content type code
txt
Content type MARC source
rdacontent
Contents
  • Cover -- Half Title -- Title Page -- Copyright Page -- Table of Contents -- Preface -- I: Narratives from Film and Literature, from Social Media and Contemporary Life -- 1: The Correspondence Analysis Platform for Mapping Semantics -- 1.1 The Visualization and Verbalization of Data -- 1.2 Analysis of Narrative from Film and Drama -- 1.2.1 Introduction -- 1.2.2 The Changing Nature of Movie and Drama -- 1.2.3 Correspondence Analysis as a Semantic Analysis Platform -- 1.2.4 Casablanca Narrative: Illustrative Analysis -- 1.2.5 Modelling Semantics via the Geometry and Topology of Information -- 1.2.6 Casablanca Narrative: Illustrative Analysis Continued -- 1.2.7 Platform for Analysis of Semantics -- 1.2.8 Deeper Look at Semantics of Casablanca: Text Mining -- 1.2.9 Analysis of a Pivotal Scene -- 1.3 Application of Narrative Analysis to Science and Engineering Research -- 1.3.1 Assessing Coverage and Completeness -- 1.3.2 Change over Time -- 1.3.3 Conclusion on the Policy Case Studies -- 1.4 Human Resources Multivariate Performance Grading -- 1.5 Data Analytics as the Narrative of the Analysis Processing -- 1.6 Annex: The Correspondence Analysis and Hierarchical Clustering Platform -- 1.6.1 Analysis Chain -- 1.6.2 Correspondence Analysis: Mapping X2 Distances into Euclidean Distances -- 1.6.3 Input: Cloud of Points Endowed with the Chi-Squared Metric -- 1.6.4 Output: Cloud of Points Endowed with the Euclidean Metric in Factor Space -- 1.6.5 Supplementary Elements: Information Space Fusion -- 1.6.6 Hierarchical Clustering: Sequence-Constrained -- 2: Analysis and Synthesis of Narrative: Semantics of Interactivity -- 2.1 Impact and Effect in Narrative: A Shock Occurrence in Social Media -- 2.1.1 Analysis -- 2.1.2 Two Critical Tweets in Terms of Their Words -- 2.1.3 Two Critical Tweets in Terms of Twitter Sub-narratives
  • 2.2 Analysis and Synthesis, Episodization and Narrativization -- 2.3 Storytelling as Narrative Synthesis and Generation -- 2.4 Machine Learning and Data Mining in Film Script Analysis -- 2.5 Style Analytics: Statistical Significance of Style Features -- 2.6 Typicality and Atypicality for Narrative Summarization and Transcoding -- 2.7 Integration and Assembling of Narrative -- II: Foundations of Analytics through the Geometry and Topology of Complex Systems -- 3: Symmetry in Data Mining and Analysis through Hierarchy -- 3.1 Analytics as the Discovery of Hierarchical Symmetries in Data -- 3.2 Introduction to Hierarchical Clustering, p-Adic and m-Adic Numbers -- 3.2.1 Structure in Observed or Measured Data -- 3.2.2 Brief Look Again at Hierarchical Clustering -- 3.2.3 Brief Introduction to p-Adic Numbers -- 3.2.4 Brief Discussion of p-Adic and m-Adic Numbers -- 3.3 Ultrametric Topology -- 3.3.1 Ultrametric Space for Representing Hierarchy -- 3.3.2 Geometrical Properties of Ultrametric Spaces -- 3.3.3 Ultrametric Matrices and Their Properties -- 3.3.4 Clustering through Matrix Row and Column Permutation -- 3.3.5 Other Data Symmetries -- 3.4 Generalized Ultrametric and Formal Concept Analysis -- 3.4.1 Link with Formal Concept Analysis -- 3.4.2 Applications of Generalized Ultrametrics -- 3.5 Hierarchy in a p-Adic Number System -- 3.5.1 p-Adic Encoding of a Dendrogram -- 3.5.2 p-Adic Distance on a Dendrogram -- 3.5.3 Scale-Related Symmetry -- 3.6 Tree Symmetries through the Wreath Product Group -- 3.6.1 Wreath Product Group for Hierarchical Clustering -- 3.6.2 Wreath Product Invariance
  • 3.6.3 Wreath Product Invariance: Haar Wavelet Transform of Dendrogram -- 3.7 Tree and Data Stream Symmetries from Permutation Groups -- 3.7.1 Permutation Representation of a Data Stream -- 3.7.2 Permutation Representation of a Hierarchy -- 3.8 Remarkable Symmetries in Very High-Dimensional Spaces -- 3.9 Short Commentary on This Chapter -- 4: Geometry and Topology of Data Analysis: in p-Adic Terms -- 4.1 Numbers and Their Representations -- 4.1.1 Series Representations of Numbers -- 4.1.2 Field -- 4.2 p-Adic Valuation, p-Adic Absolute Value, p-Adic Norm -- 4.3 p-Adic Numbers as Series Expansions -- 4.4 Canonical p-Adic Expansion -- p-Adic Integer or Unit Ball -- 4.5 Non-Archimedean Norms as p-Adic Integer Norms in the Unit Ball -- 4.5.1 Archimedean and Non-Archimedean Absolute Value Properties -- 4.5.2 A Non-Archimedean Absolute Value, or Norm, is Less Than or Equal to One, and an Archimedean Absolute Value, or Norm, is Unbounded -- 4.6 Going Further: Negative p-Adic Numbers, and p-Adic Fractions -- 4.7 Number Systems in the Physical and Natural Sciences -- 4.8 p-Adic Numbers in Computational Biology and Computer Hardware -- 4.9 Measurement Requires a Norm, Implying Distance and Topology -- 4.10 Ultrametric Topology -- 4.11 Short Review of p-Adic Cosmology -- 4.12 Unbounded Increase in Mass or Other Measured Quantity -- 4.13 Scale-Free Partial Order or Hierarchical Systems -- 4.14 p-Adic Indexing of the Sphere -- 4.15 Diffusion and Other Dynamic Processes in Ultrametric Spaces -- III: New Challenges and New Solutions for Information Search and Discovery -- 5: Fast, Linear Time, m-Adic Hierarchical Clustering -- 5.1 Pervasive Ultrametricity: Computational Consequences -- 5.1.1 Ultrametrics in Data Analytics -- 5.1.2 Quantifying Ultrametricity -- 5.1.3 Pervasive Ultrametricity -- 5.1.4 Computational Implications
  • 5.2 Applications in Search and Discovery using the Baire Metric -- 5.2.1 Baire Metric -- 5.2.2 Large Numbers of Observables -- 5.2.3 High-Dimensional Data -- 5.2.4 First Approach Based on Reduced Precision of Measurement -- 5.2.5 Random Projections in High-Dimensional Spaces, Followed by the Baire Distance -- 5.2.6 Summary Comments on Search and Discovery -- 5.3 m-Adic Hierarchy and Construction -- 5.4 The Baire Metric, the Baire Ultrametric -- 5.4.1 Metric and Ultrametric Spaces -- 5.4.2 Ultrametric Baire Space and Distance -- 5.5 Multidimensional Use of the Baire Metric through Random Projections -- 5.6 Hierarchical Tree Defined from m-Adic Encoding -- 5.7 Longest Common Prefix and Hashing -- 5.7.1 From Random Projection to Hashing -- 5.8 Enhancing Ultrametricity through Precision of Measurement -- 5.8.1 Quantifying Ultrametricity -- 5.8.2 Pervasiveness of Ultrametricity -- 5.9 Generalized Ultrametric and Formal Concept Analysis -- 5.9.1 Generalized Ultrametric -- 5.9.2 Formal Concept Analysis -- 5.10 Linear Time and Direct Reading Hierarchical Clustering -- 5.10.1 Linear Time, or O(N) Computational Complexity, Hierarchical Clustering -- 5.10.2 Grid-Based Clustering Algorithms -- 5.11 Summary: Many Viewpoints, Various Implementations -- 6: Big Data Scaling through Metric Mapping -- 6.1 Mean Random Projection, Marginal Sum, Seriation -- 6.1.1 Mean of Random Projections as A Seriation -- 6.1.2 Normalization of the Random Projections -- 6.2 Ultrametric and Ordering of Rows, Columns -- 6.3 Power Iteration Clustering -- 6.4 Input Data for Eigenreduction
  • 6.4.1 Implementation: Equivalence of Iterative Approximation and Batch Calculation -- 6.5 Inducing a Hierarchical Clustering from Seriation -- 6.6 Short Summary of All These Methodological Underpinnings -- 6.6.1 Trivial First Eigenvalue, Eigenvector in Correspondence Analysis -- 6.7 Very High-Dimensional Data Spaces: Data Piling -- 6.8 Recap on Correspondence Analysis for Following Applications -- 6.8.1 Clouds of Points, Masses and Inertia -- 6.8.2 Relative and Absolute Contributions -- 6.9 Evaluation 1: Uniformly Distributed Data Cloud Points -- 6.9.1 Computation Time Requirements -- 6.10 Evaluation 2: Time Series of Financial Futures -- 6.11 Evaluation 3: Chemistry Data, Power Law Distributed -- 6.11.1 Data and Determining Power Law Properties -- 6.11.2 Randomly Generating Power Law Distributed Data in Varying Embedding Dimensions -- 6.12 Application 1: Quantifying Effectiveness through Aggregate Outcome -- 6.12.1 Computational Requirements, from Original Space and Factor Space Identities -- 6.13 Application 2: Data Piling as Seriation of Dual Space -- 6.14 Brief Concluding Summary -- 6.15 Annex: R Software Used in Simulations and Evaluations -- 6.15.1 Evaluation 1: Dense, Uniformly Distributed Data -- 6.15.2 Evaluation 2: Financial Futures -- 6.15.3 Evaluation 3: Chemicals of Specified Marginal Distribution -- IV: New Frontiers: New Vistas on Information, Cognition and the Human Mind -- 7: On Ultrametric Algorithmic Information -- 7.1 Introduction to Information Measures -- 7.2 Wavelet Transform of a Set of Points Endowed with an Ultrametric -- 7.3 An Object as a Chain of Successively Finer Approximations -- 7.3.1 Approximation Chain using a Hierarchy -- 7.3.2 Dendrogram Wavelet Transform of Spherically Complete Space -- 7.4 Generating Faces: Case Study Using a Simplified Model -- 7.4.1 A Simplified Model of Face Generation
  • 7.4.2 Discussion of Psychological and Other Consequences
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1st ed.
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1 online resource (224 pages)
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online
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9781315350493
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computer
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rdamedia
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c
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