Mathematical foundations

2019 ◽  
pp. 1-40
Author(s):  
Max A. Little
Keyword(s):  
Mathematical Modeling ◽  
Machine Learning ◽  
Signal Processing ◽  
Mathematical Models ◽  
Applied Mathematics ◽  
Statistical Machine Learning ◽  
Mathematical Concepts ◽  
The Subject ◽  
Mathematical Foundations

Statistical machine learning and signal processing are topics in applied mathematics, which are based upon many abstract mathematical concepts. Defining these concepts clearly is the most important first step in this book. The purpose of this chapter is to introduce these foundational mathematical concepts. It also justifies the statement that much of the art of statistical machine learning as applied to signal processing, lies in the choice of convenient mathematical models that happen to be useful in practice. Convenient in this context means that the algebraic consequences of the choice of mathematical modeling assumptions are in some sense manageable. The seeds of this manageability are the elementary mathematical concepts upon which the subject is built.

Machine Learning for Signal Processing

2019 ◽  
Author(s):  
Max A. Little
Keyword(s):  
Machine Learning ◽  
Signal Processing ◽  
Applied Mathematics ◽  
Digital Signal ◽  
Statistical Modelling ◽  
Modern World ◽  
Statistical Machine Learning ◽  
Contemporary World ◽  
Mp3 Players ◽  
Intelligent Information

Digital signal processing (DSP) is one of the ‘foundational’ engineering topics of the modern world, without which technologies such the mobile phone, television, CD and MP3 players, WiFi and radar, would not be possible. A relative newcomer by comparison, statistical machine learning is the theoretical backbone of exciting technologies such as automatic techniques for car registration plate recognition, speech recognition, stock market prediction, defect detection on assembly lines, robot guidance and autonomous car navigation. Statistical machine learning exploits the analogy between intelligent information processing in biological brains and sophisticated statistical modelling and inference. DSP and statistical machine learning are of such wide importance to the knowledge economy that both have undergone rapid changes and seen radical improvements in scope and applicability. Both make use of key topics in applied mathematics such as probability and statistics, algebra, calculus, graphs and networks. Intimate formal links between the two subjects exist and because of this many overlaps exist between the two subjects that can be exploited to produce new DSP tools of surprising utility, highly suited to the contemporary world of pervasive digital sensors and high-powered and yet cheap, computing hardware. This book gives a solid mathematical foundation to, and details the key concepts and algorithms in, this important topic.

Random sampling

2019 ◽  
pp. 71-92
Author(s):  
Max A. Little
Keyword(s):  
Machine Learning ◽  
Signal Processing ◽  
Statistical Model ◽  
Random Sampling ◽  
Joint Distribution ◽  
Optimization Problems ◽  
Viable Alternative ◽  
Statistical Machine Learning ◽  
Digital Signals ◽  
Large Numbers

This chapter provides an overview of generating samples from random variables with a given (joint) distribution, and using these samples to find quantities of interest from digital signals. This task plays a fundamental role in many problems in statistical machine learning and signal processing. For example, effectively simulating the behaviour of the statistical model offers a viable alternative to optimization problems arising from some models for signals with large numbers of variables.

Rays, Waves, and Scattering

2017 ◽  
Author(s):  
John A. Adam
Keyword(s):  
Graduate Students ◽  
Seismic Waves ◽  
Applied Mathematics ◽  
Ocean Waves ◽  
Theoretical Physics ◽  
Mathematical Concepts ◽  
Light Waves ◽  
Technical Material ◽  
The Subject ◽  
Ptolemy’S Theorem

This book presents many of the mathematical concepts, structures, and techniques used in the study of rays, waves, and scattering. It includes discussions of how ocean waves are refracted around islands and underwater ridges, how seismic waves are refracted in the earth's interior, how atmospheric waves are scattered by mountains and ridges, how the scattering of light waves produces the blue sky, and meteorological phenomena such as rainbows and coronas. This book is a valuable resource for practitioners, graduate students, and advanced undergraduates in applied mathematics, theoretical physics, and engineering. Bridging the gap between advanced treatments of the subject written for specialists and less mathematical books aimed at beginners, this unique mathematical compendium features problems and exercises throughout that are geared to various levels of sophistication, covering everything from Ptolemy's theorem to Airy integrals (as well as more technical material), and several informative appendixes.

Statistical modelling and inference

2019 ◽  
pp. 93-132
Author(s):  
Max A. Little
Keyword(s):  
Machine Learning ◽  
Signal Processing ◽  
Joint Distribution ◽  
Probabilistic Models ◽  
Optimal Parameter ◽  
Statistical Modelling ◽  
Statistical Machine Learning ◽  
Central Task ◽  
Parameter Values

The modern view of statistical machine learning and signal processing is that the central task is one of finding good probabilistic models for the joint distribution over all the variables in the problem. We can then make `queries' of this model, also known as inferences, to determine optimal parameter values or signals. Hence, the importance of statistical methods to this book cannot be overstated. This chapter is an in-depth exploration of what this probabilistic modeling entails, the origins of the concepts involved, how to perform inferences and how to test the quality of a model produced this way.

scholarly journals ANALISIS KESULITAN BELAJAR ABK (TUNA RUNGU) DALAM MENYELESAIKAN SOAL CERITA MATEMATIKA

2020 ◽  
Vol 5 (2) ◽  
pp. 183-194
Author(s):  
Nungki Anditiasari
Keyword(s):  
Data Analysis ◽  
Problem Solving ◽  
Mathematical Models ◽  
Learning Difficulties ◽  
Role Playing ◽  
Hearing Impairments ◽  
Story Problems ◽  
Mathematical Concepts ◽  
The Subject ◽  
Research Students

This study aims to determine the learning difficulties of students with hearing impairments in solving story problems using the role playing method and using problem solving learning according to Polya, namely: understanding problems, determining problem strategy plans, solving problem strategies, and checking the answers obtained to understand story question are seen from four aspects, namely understanding story problems, making mathematical models, computations, and drawing conclusions. The subject of this study used 2 ABK students. The data were collected by means of interviews, tests and documentations. Data analysis was carried and by drawing conclusions. Based on the results of the research students can understand story problems by applying role playing and problem solving methods, because learning becomes very fun and students can easily solve story problems. Based on the research results, students can understand story problems by applying role playing and problem solving methods, because learning becomes very fun and students can easily solve story problems. In addition, students experience some learning difficulties, namely difficulties in understanding the questions, difficulties in basic mathematical concepts, and difficulties in understanding the language that is conveyed.

scholarly journals Hysteresis Compensation in Force/Torque Sensors Using Time Series Information

Sensors ◽  
2019 ◽  
Vol 19 (19) ◽  
pp. 4259 ◽  
Author(s):  
Ryuichiro Koike ◽  
Sho Sakaino ◽  
Toshiaki Tsuji
Keyword(s):  
Machine Learning ◽  
Time Series ◽  
Signal Processing ◽  
Linear Regression ◽  
Mathematical Models ◽  
High Precision ◽  
Previous History ◽  
Force Sensor ◽  
Force Sensing ◽  
Hysteresis Compensation

The purpose of this study is to compensate for the hysteresis in a six-axis force sensor using signal processing, thereby achieving high-precision force sensing. Although mathematical models of hysteresis exist, many of these are one-axis models and the modeling is difficult if they are expanded to multiple axes. Therefore, this study attempts to resolve this problem through machine learning. Since hysteresis is dependent on the previous history, this study investigates the effect of using time series information in machine learning. Experimental results indicate that the performance is improved by including time series information in the linear regression process generally utilized to calibrate six-axis force sensors.

scholarly journals Mathematical modeling as a bridge between pure and applied mathematics

2015 ◽  
Vol 1 (1) ◽  
Author(s):  
Nelson Hein
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Model ◽  
Applied Mathematics ◽  
The Other ◽  
Real Situation ◽  
Mathematical Concepts ◽  
Precise Identification ◽  
The One ◽  
Teaching Situations

It is very common to find systems that include mathematical concepts that can be interpreted in real ones. When it is possible to establish some precise identification of the elements of a system on the one hand, and the phenomena or objects of a real situation, on the other, there is a mathematical model of a real situation. The objective of this paper is to present how this can be built to teaching situations, highlighting the possibilities and limits of technical modeling

Review of classification studies for machine learning in the development of intelligent management decision support systems

2020 ◽  
Vol 89 ◽  
pp. 20-29
Author(s):  
Sh. K. Kadiev ◽  
◽  
R. Sh. Khabibulin ◽  
P. P. Godlevskiy ◽  
V. L. Semikov ◽  
...  
Keyword(s):  
Machine Learning ◽  
Decision Support ◽  
Mathematical Models ◽  
Decision Support Systems ◽  
Support Systems ◽  
Management Decision ◽  
Classification Methods ◽  
Advantages And Disadvantages ◽  
Intelligent Management ◽  
Management Decision Support

Introduction. An overview of research in the field of classification as a method of machine learning is given. Articles containing mathematical models and algorithms for classification were selected. The use of classification in intelligent management decision support systems in various subject areas is also relevant. Goal and objectives. The purpose of the study is to analyze papers on the classification as a machine learning method. To achieve the objective, it is necessary to solve the following tasks: 1) to identify the most used classification methods in machine learning; 2) to highlight the advantages and disadvantages of each of the selected methods; 3) to analyze the possibility of using classification methods in intelligent systems to support management decisions to solve issues of forecasting, prevention and elimination of emergencies. Methods. To obtain the results, general scientific and special methods of scientific knowledge were used - analysis, synthesis, generalization, as well as the classification method. Results and discussion thereof. According to the results of the analysis, studies with a mathematical formulation and the availability of software developments were identified. The issues of classification in the implementation of machine learning in the development of intelligent decision support systems are considered. Conclusion. The analysis revealed that enough algorithms were used to perform the classification while sorting the acquired knowledge within the subject area. The implementation of an accurate classification is one of the fundamental problems in the development of management decision support systems, including for fire and emergency prevention and response. Timely and effective decision by officials of operational shifts for the disaster management is also relevant. Key words: decision support, analysis, classification, machine learning, algorithm, mathematical models.

PENINGKATAN KEMAMPUAN PEMAHAMAN KONSEP MATEMATIKA SISWA DENGAN PENERAPAN MEDIA KARTU PERMAINAN BILANGAN DI SDIT DELI INSANI TANJUNG MORAWA

2019 ◽  
Vol 8 (2) ◽  
Author(s):  
Dwi Novita Sari ◽  
Putri Juwita
Keyword(s):  
Elementary School Students ◽  
Fifth Grade ◽  
School Students ◽  
Mathematical Concepts ◽  
Class V ◽  
Fifth Grade Students ◽  
Learning Mathematics ◽  
Comprehension Ability ◽  
The Subject ◽  
Number Game

This study aims to improve the results of learning mathematics of elementary school students SDIT Deli Insani of class V on the subject matter of fractions by using number playing card media. The from of this study is classroom action research conducted in 2 cycles, using number playing cards at SDIT Deli Insani in class V Tanjung Morawa. The subjects of this study were the fifth grade students of SDIT Deli Insani, amounting to 30 students. This action was carried out in April 2018. Methods of collecting data using observation and documentation. The data analysis used is quantitative and qualitative analysis. The results of the study showed an increase in students' ability to understand concepts from the first cycle and second cycle. Percentage of increase in pre-action results, cycle I and cycle II students' concept comprehension ability that is 13.04% for indicators identifying number forms using number game cards (dominoes) and indicators solving problems in fractional form operations using dominoes 27.26%. the success indicator in cycle II reaches 80%. Thus the application of number game cards can improve students' understanding of mathematical concepts at SDIT Deli Insani in Class V.

Predicting the citation and impact factor of terms for scientific publications using machine learning algorithms

2020 ◽  
Author(s):  
Aleksey Klokov ◽  
Evgenii Slobodyuk ◽  
Michael Charnine
Keyword(s):  
Machine Learning ◽  
Semantic Processing ◽  
The Body ◽  
Machine Learning Algorithms ◽  
Scientific Publications ◽  
Text Data ◽  
Semantic Relationships ◽  
Subject Areas ◽  
The Subject ◽  
Scientific Environment

The object of the research when writing the work was the body of text data collected together with the scientific advisor and the algorithms for processing the natural language of analysis. The stream of hypotheses has been tested against computer science scientific publications through a series of simulation experiments described in this dissertation. The subject of the research is algorithms and the results of the algorithms, aimed at predicting promising topics and terms that appear in the course of time in the scientific environment. The result of this work is a set of machine learning models, with the help of which experiments were carried out to identify promising terms and semantic relationships in the text corpus. The resulting models can be used for semantic processing and analysis of other subject areas.

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