Algebraic approach to data processing : techniques and applications / / Julio C. Urenda and Vladik Kreinovich

• Autore: Urenda Julio C.
• Pubblicazione: Cham, Switzerland : , : Springer, , [2022]; ©2022
• Descrizione fisica: 1 online resource (246 pages)
• Disciplina: 005.7
• Soggetto topico: Big data; Computational intelligence; Computer science - Mathematics
• Persona (resp. second.): KreinovichVladik
• Nota di bibliografia: Includes bibliographical references and index.
• Nota di contenuto: Intro -- Preface -- Contents -- 1 Introduction -- 1.1 What Is Data Processing and Why Do We Need It? -- 1.2 Why Algebraic Approach? -- 1.3 What We Do in This Book: An Overview -- 1.4 Thanks -- References -- 2 What Are the Most Natural and the Most Frequent Transformations -- 2.1 Main Idea: Numerical Values Change When We Change a Measuring Unit and/or Starting Point -- 2.2 Scaling Transformations -- 2.3 Shifts -- 2.4 Linear Transformations -- 2.5 Geometric Transformations -- 2.6 Beyond Linear Transformations -- 2.7 Permutations -- References -- 3 Which Functions and Which Families of Functions Are Invariant -- 3.1 Why Do We Need Invariant Functions -- 3.2 What Does It Mean for a Function to Be Invariant -- 3.3 Example: Scale-Invariant Functions of One Variable -- 3.4 What If We Have Both Shift- and Scale-Invariance? -- 3.5 Which Families of Functions Are Invariant: Case of Shift-Invariance -- 3.6 Which Families of Functions Are Invariant: Case of Scale-Invariance -- 3.7 What If We Have Both Shift- and Scale-Invariance -- 3.8 Which Linear Transformations Are Shift-Invariant -- References -- 4 What Is the General Relation Between Invariance and Optimality -- 4.1 What Is an Optimality Criterion -- 4.2 We Need a Final Optimality Criterion -- 4.3 It Is Often Reasonable to Require That the Optimality Criterion Be Invariant -- 4.4 Main Result of This Chapter -- 5 General Application: Dynamical Systems -- 5.1 Problem: Why a Linear-Based Classification Often Works in Nonlinear Cases -- 5.2 Our Explanation -- References -- 6 First Application to Physics: Why Liquids? -- 6.1 Two Applications to Physics: Summary -- 6.2 Problem: Why Liquids? -- 6.3 Towards a Formulation of the Problem in Precise Terms -- 6.4 Main Result of This Chapter -- References -- 7 Second Application to Physics: Warping of Our Galaxy -- 7.1 Formulation of the Problem. ; 7.2 Analysis of the Problem and the Resulting Explanation -- References -- 8 Application to Electrical Engineering: Class-D Audio Amplifiers -- 8.1 Applications to Engineering: Summary -- 8.2 Problem: Why Class-D Audio Amplifiers Work Well? -- 8.3 Why Pulses -- 8.4 Why the Pulse's Duration Should Linearly Depend … -- References -- 9 Application to Mechanical Engineering: Wood Structures -- 9.1 Problem: Need for a Theoretical Explanation of an Empirical Fact -- 9.2 Our Explanation: Main Idea -- 9.3 Our Explanation: Details -- 9.4 Proof -- References -- 10 Medical Application: Prevention -- 10.1 Problem: How to Best Maintain Social Distance -- 10.2 Towards Formulating This Problem in Precise Terms -- 10.3 Solution -- Reference -- 11 Medical Application: Testing -- 11.1 Problem: Optimal Group Testing -- 11.2 What Was Proposed -- 11.3 Resulting Problem -- 11.4 Let Us Formulate This Problem in Precise Terms -- 11.5 Solution -- References -- 12 Medical Application: Diagnostics, Part 1 -- 12.1 Problem: Diagnosing Lung Disfunctions in Children -- 12.2 First Pre-processing Stage: Scale-Invariant Smoothing -- 12.3 Which Order Polynomials Should We Use? -- 12.4 Second Pre-processing Stage: Using the Approximating Polynomials to Distinguish Between Different Diseases -- 12.5 Third Pre-processing Stage: Scale-Invariant Similarity/Dissimilarity Measures -- 12.6 How to Select α: Need to Have Efficient and Robust Estimates -- 12.7 Scale-Invariance Helps to Take Into Account That Signal Informativeness Decreases with Time -- 12.8 Pre-processing Summarized: What Information Serves as An Input to a Neural Network -- 12.9 The Results of Training Neural Networks on These Pre-processed Data -- References -- 13 Medical Application: Diagnostics, Part 2 -- 13.1 Problem: Why Hierarchical Multiclass Classification Works Better Than Direct Classification -- 13.2 Our Explanation. ; References -- 14 Medical Application: Diagnostics, Part 3 -- 14.1 Problem: Which Fourier Components Are Most Informative -- 14.2 Main Idea -- 14.3 First Case Study: Human Color Vision -- 14.4 Second Case Study: Classifying Lung Dysfunctions -- References -- 15 Medical Application: Treatment -- 15.1 Problem: Geometric Aspects of Wound Healing -- 15.2 What Are Natural Symmetries Here and What Are the Resulting Cell Shapes: Case of Undamaged Skin -- 15.3 What If the Skin Is Damaged: Resulting Symmetries and Cell Shapes -- 15.4 Geometric Symmetries Also Explain Observed Cell Motions -- References -- 16 Applications to Economics: How Do People Make Decisions, Part 1 -- References -- 17 Application to Economics: How Do People Make Decisions, Part 2 -- 17.1 Problem: Need to Consider Multiple Scenarios -- 17.2 Our Explanation -- References -- 18 Application to Economics: How Do People Make Decisions, Part 3 -- 18.1 Problem: Using Experts -- 18.2 Towards an Explanation -- References -- 19 Application to Economics: How Do People Make Decisions, Part 4 -- 19.1 Why Should We Play Down Emotions -- 19.2 Towards Explanation -- References -- 20 Application to Economics: Stimuli, Part 1 -- 20.1 Problem: Why Rewards Work Better Than Punishment -- 20.2 Analysis of the Problem -- 20.3 Our Explanation -- References -- 21 Application to Economics: Stimuli, Part 2 -- 21.1 Problem: Why Top Experts Are Paid So Much -- 21.2 Our Explanation -- References -- 22 Application to Economics: Investment -- 22.1 1/n Investment: Formulation of the Problem -- 22.2 Our Explanation -- 22.3 Discussion -- References -- 23 Application to Social Sciences: When Revolutions Happen -- 23.1 Formulation of the Problem -- 23.2 Analysis of the Problem -- References -- 24 Application to Education: General -- 24.1 Problem: Is Immediate Repetition Good for Learning?. ; 24.2 Analysis of the Problem and the Resulting Explanation -- References -- 25 Application to Education: Specific -- 25.1 Problem: Why Derivative -- 25.2 Invariance Naturally Leads to the Derivative -- Reference -- 26 Application to Mathematics: Why Necessary Conditions Are Often Sufficient -- 26.1 Formulation of the Problem -- 26.2 Analysis of the Problem -- 26.3 How Can We Formalize What Is Not Abnormal -- 26.4 Resulting Explanation of the TONCAS Phenomenon -- References -- 27 Data Processing: Neural Techniques, Part 1 -- 27.1 Machine Learning Is Needed to Analyze Complex Systems -- 27.2 Neural Networks and Deep Learning: A Brief Reminder -- 27.3 Why Traditional Neural Networks -- 27.4 Why Sigmoid Activation Function: Idea -- 27.5 Why Sigmoid-Derivation -- 27.6 Limit Cases -- 27.7 We Need Multi-layer Neural Networks -- 27.8 Which Activation Function Should We Use -- 27.9 This Leads Exactly to Squashing Functions -- 27.10 Why Rectified Linear Functions -- References -- 28 Data Processing: Neural Techniques, Part 2 -- 28.1 Problem: Spiking Neural Networks -- 28.2 Analysis of the Problem and the First Result -- 28.3 Main Result: Spikes Are, in Some Reasonable Sense, Optimal -- References -- 29 Data Processing: Fuzzy Techniques, Part 1 -- 29.1 Why Fuzzy Techniques -- 29.2 Fuzzy Techniques: Main Ideas -- 29.3 Fuzzy Techniques: Logic -- References -- 30 Data Processing: Neural and Fuzzy Techniques -- 30.1 Problem: Computations Should Be Fast and Understandable -- 30.2 Definitions and the Main Results -- 30.3 Auxiliary Result: What Can We Do with Two-Layer Networks -- References -- 31 Data Processing: Fuzzy Techniques, Part 2 -- 31.1 Problem: Which Fuzzy Techniques to Use? -- 31.2 Analysis of the Problem -- 31.3 Which Symmetric Membership Functions Should We … -- 31.4 Which Hedge Operations and Negation Operations Should We Select -- 31.5 Proofs. ; References -- 32 Data Processing: Fuzzy Techniques, Part 3 -- 32.1 Problem: Which Fuzzy Degrees to Use? -- 32.2 Definitions and the Main Result -- 32.3 How General Is This Result? -- 32.4 What If We Allow Unlimited Number of ``And''-Operations and Negations: Case Study -- References -- 33 Data Processing: Fuzzy Techniques, Part 4 -- 33.1 Problem: How to Explain Commonsense Reasoning -- 33.2 Our Explanation -- 33.3 Auxiliary Result: Why the Usual Quantifiers? -- References -- 34 Data Processing: Probabilistic Techniques, Part 1 -- 34.1 Problem: How to Represent Interval Uncertainty -- 34.2 Analysis of the Problem -- 34.3 Our Results -- References -- 35 Data Processing: Probabilistic Techniques, Part 2 -- 35.1 Problem: How to Represent General Uncertainty -- 35.2 Definitions and the Main Result -- 35.3 Consequence -- References -- 36 Data Processing: Probabilistic Techniques, Part 3 -- 36.1 Problem: Experts Don't Perform Well in Unusual Situations -- 36.2 Our Explanation -- References -- 37 Data Processing: Beyond Traditional Techniques -- 37.1 DNA Computing: Introduction -- 37.2 Computing Without Computing-Quantum Version: A Brief Reminder -- 37.3 Computing Without Computing-Version Involving Acausal Processes: A Reminder -- 37.4 Computing Without Computing-DNA Version -- 37.5 DNA Computing Without Computing Is Somewhat Less … -- 37.6 First Related Result: Security Is More Difficult to Achieve than Privacy -- 37.7 Second Related Result: Data Storage Is More Difficult Than Data Transmission -- References -- Appendix References -- -- Index.
• Titolo autorizzato: Algebraic approach to data processing
• ISBN: 3-031-16780-5
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910617307203321
• Lo trovi qui: Univ. Federico II
• Serie: Studies in big data ; ; Volume 115.