Recognition of Patterns Using the Frequencies of Occurrence of Binary Words
Peter W. Becker, L. F. Pau · IEEE Transactions on Systems Man and Cybernetics · 1977
1. Problems in the Design of Pattern Recognizers.- 1.1 Introduction.- 1.1.1 About this Book.- 1.1.2 Two Phases in the Existence of a PR.- 1.2 Three Areas of Application.- 1.2.1 Certain Acts of Identification.- 1.2.2 Decisions Regarding Complex Situations.- 1.2.3 Imitation of Human Pattern Recognition.- 1.3 Configuration of a PR.- 1.4 Factors which Influence the Design of a PR.- 1.4.1 Factors Associated with the Pattern Classes.- 1.4.2 Estimation of the PR's Performance.- 1.4.3 Four Major Problem Areas.- 1.5 Selection of the 1.5.1 Preliminary Processing.- 1.5.2 Generation of Sets of Attributes in Practice.- 1.5.3 Effective Set of 1.5.3.1 A Definition of An Effective Set of Attributes.- 1.5.3.2 A Definition of The Incremental Effectiveness of an 1.5.4 One Attribute.- 1.5.5 Templet Matching.- 1.5.6 Selection of a Set of p 1.6 Decision Procedures and Indices of Performance.- 1.6.1 Some Functions Related to the Micro-Regions.- 1.6.2 Bayes' Procedure.- 1.6.3 Minimaxing Classification Procedure.- 1.6.4 Likelihood Method.- 1.6.5 Neyman-Pearson Method.- 1.6.6 Three Practical Difficulties.- 1.7 Categorizer Design.- 1.7.1 Estimation of a Multivariate Density Function.- 1.7.2 Explicit Partitioning of Pattern Space.- 1.7.2.1 Separation Surfaces of Simple Shape.- 1.7.2.2 Need for Surfaces of Simple Shape.- 1.7.2.3 Parametric Training Methods.- 1.7.2.4 Non-Parametric Training Methods.- 1.7.3 Implicit Partitioning of the Pattern Space.- 1.7.3.1 Nearest-Neighbor-Pattern Classifier.- 1.7.3.2 Discriminant Functions and Separation Surfaces.- 1.7.3.3 Categorization Using NC Discriminants.- 1.7.3.4 ?-Machine.- 1.7.3.5 Nonlinear Generalized Discriminant.- 1.7.3.6 Parametric Training of Discriminants.- 1.7.4 Categorization of Members from More than Two Classes.- 1.8 Hardware Implementation.- 2. Design of a Pattern Recognizer Using the Frequency of Occurrence of Binary Words Method.- 2.1 Introduction.- 2.2 A Step by Step Description of the FOBW Design Procedure.- 2.3 Ordered Array of 2.4 Generation of New Sets of NH 2.5 Detection of Effective 3. Computational Rules for Binary Word Frequencies of Occurrence.- 3.1 Binary Word Probabilities, Frequencies of Occurrence and Sequence Length.- 3.2 Redundant Information in N-Gram Frequencies.- 3.2.1 Problem.- 3.2.2 Important Relationship.- 3.2.3 Four Digram Frequencies Described by Two Pieces of Information.- 3.2.4 2N N-Gram Frequencies Described by 2N?1 Pieces of Information.- 3.3 Other Sets of 2N?1 Pieces of Information.- 3.4 Bounds on the Binary Word Frequencies of Occurrence.- 3.5 Redundancy in Delayed N-Gram Frequencies.- 3.6 Eight Delayed Trigram Frequencies contain Five Pieces of Information.- 3.7 A Special Relationship between Delayed Digrams and Delayed Trigrams.- 3.8 Frequencies of Symmetrical and Unsymmetrical Binary Words.- 4. S, A Measure of Separability.- 4.1 Four Statistics.- 4.2 Some Features of the S-Measure.- 4.3 A Conjecture Later Proven by Chernoff.- 5. Modeling of Pattern Generating Stochastic Processes.- 5.1 Importance of a Model.- 5.2 Transition Matrix Model.- 5.2.1 A Machine for Random Generation of Binits.- 5.2.2 N-Gram Frequencies Determine All Other Binary Word Frequencies.- 5.2.3 Testing the Applicability of the Model.- 5.3 Gaussian Process Model.- 5.3.1 Examination of the Bivariate Distribution.- 5.3.2 Gaussian Bivariate Distribution.- 5.3.3 Relationship between m/?, ?, and the Delayed Digram Frequencies.- 5.3.4 Case with Zero Mean.- 5.3.5 Estimation of the Normalized Autocorrelation Function.- 5.3.6 Delayed Digram Frequencies Determine All Other Binary Word Frequencies.- 5.4 Processes Related to the Gaussian Process.- 5.4.1 A Special Type of Transmission Path.- 5.4.2 Additive Gaussian Noise.- 5.4.3 A Carrier Wave Modulated by a Gaussian Process.- 5.5 ?0 and ?m Concepts.- 6. Heuristic Search Procedure.- 6.1 Search Rule.- 6.2 First Example of the FOBW Search Procedure.- 6.2.1 Three Diagram Frequencies and One Trigram Frequency.- 6.2.2 Some Linear Relationships.- 6.2.3 Strongly Correlated and Uncorrelated 6.2.4 Geometric Argument.- 6.3 A Case Study.- 6.3.1 Some Background Information.- 6.3.2 First Attribute.- 6.3.3 Second Attribute.- 6.4 Second Example of the FOBW Search Procedure.- 6.4.1 Two N-Gram Frequencies and One (N+1)-Gram Frequency.- 6.4.2 Correlation between N-Gram Frequencies.- 6.4.3 Values of the S-Measure.- 6.4.4 A Geometric Construction.- 6.4.5 Realistic Parameter Values.- 6.4.6 A Related Conclusion.- 6.4.7 (N+l)-Gram Frequency Suggested by Two N-Gram Frequencies.- 7. Hardware Implementation.- 7.1 Two Applications.- 7.2 Simple Hardware.- 7.3 Sonic Analysis Demonstrator.- 7.3.1 Jet Engine Sound Simulator.- 7.3.2 Pattern Recognizer.- 7.3.3 Hardware Realization.- 7.4 Word Recognizer.- 7.4.1 On Automated Recognition of Speech.- 8. Summary.- Appendix 1. Some Recent Books.- Appendix 2. ?-Transformation.