Recognition of Patterns: Using the Frequencies of Occurrence of Binary Words

'1. Problems in the Design of Pattern Recognizers.- 1.1 Introduction.- 1.1.1 About this Book.- 1.1.2 The 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 The 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 The Selection of the Attributes.- 1.5.1 Preliminary Processing.- 1.5.2 Generation of Sets of Attributes in Practice.- 1.5.3 An Effective Set of Attributes.- 1.5.3.1 A Definition of "An Effective Set of Attributes".- 1.5.3.2 A Definition of "The Incremental Effectiveness of an Attribute".- 1.5.4 One Attribute.- 1.5.5 Templet Matching.- 1.5.6 Selection of a Set of p Attributes.- 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 The Minimaxing Classification Procedure.- 1.6.4 The Likelihood Method.- 1.6.5 The 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 The 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 The ?-Machine.- 1.7.3.5 The 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 The Ordered Array of Attributes.- 2.4 The Generation of New Sets of NH Attributes.- 2.5 Detection of Effective Attributes.- 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 The Problem.- 3.2.2 An 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 The 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 The Importance of a Model.- 5.2 The Transition Matrix Model.- 5.2.1 A Machine for Random Generation of Binits.- 5.2.2 The N-Gram Frequencies Determine All Other Binary Word Frequencies.- 5.2.3 Testing the Applicability of the Model.- 5.3 The Gaussian Process Model.- 5.3.1 The Examination of the Bivariate Distribution.- 5.3.2 The Gaussian Bivariate Distribution.- 5.3.3 The Relationship between m/?, ?, and the Delayed Digram Frequencies.- 5.3.4 The Case with Zero Mean.- 5.3.5 Estimation of the Normalized Autocorrelation Function.- 5.3.6 The 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