Advanced Mathematical Applications in Data Science

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End User License Agreement
Contents
Foreword
Preface
List of Contributors
The Role of Mathematics in Data Science: Methods, Algorithms, and Computer Programs
Rashmi Singh1,*, Neha Bhardwaj2 and Sardar M. N. Islam (Naz)3
INTRODUCTION
DATA SCIENCE
MAIN MATHEMATICAL PRINCIPLES AND METHODS IMPORTANT FOR DATA SCIENCE
Linear Algebra
Matrices
System of Linear Equation
The Number of Solutions
Vectors
Loss Function
Regularization
Support Vector Machine Classification
Statistics
Probability Theory
Normal Distribution
Z Scores
The Central Limit Theorem
Some Other Statistical Methods
Skewness
Kurtosis
Applications of Statistics in Data Science through Machine Learning Algorithms
Regression
Machine Learning Using Principal Component Analysis to Reduce Dimensionality
Mathematical Basis of PCA
Classification
K-Nearest Neighbor
Naive Bayes
Calculus
Optimization or Operational Research Methods
Dynamic Optimization Model
Stochastic Optimization Methods
Some Other Methods
Computer Programs
CONCLUDING REMARKS
REFERENCES
Kalman Filter: Data Modelling and Prediction
Arnob Sarkar1 and Meetu Luthra2,*
INTRODUCTION
Why Kalman Filter?
UNDERSTANDING THE KALMAN FILTER
What is Kalman Filter?
State Space Approach
Mean Squared Error
KALMAN FILTER EQUATIONS
GENERAL APPLICATIONS OF KALMAN FILTER
KALMAN FILTER EQUATIONS IN ONE DIMENSION
EXAMPLE 1: FINDING THE TRUE VALUE OF TEMPERATURE
First Iteration
Second Iteration
EXAMPLE 2: FINDING THE TRUE VALUE OF ACCELERATION DUE TO GRAVITY
EXAMPLE 3: VERIFYING HUBBLE’S LAW
LIMITATIONS OF KALMAN FILTER
OTHER FILTERS
FUTURE PROSPECTS
CONCLUDING REMARKS- KALMAN FILTER IN A NUTSHELL
APPENDIX – BASIC CONCEPTS
A.1. LINEAR DYNAMIC SYSTEMS
A.2. ERROR COVARIANCE MATRIX
A.3. TULLY FISHER RELATION
A.4. RED SHIFTS AND RECESSIONAL VELOCITY
REFERENCES
The Role of Mathematics and Statistics in the Field of Data Science and its Application
Sathiyapriya Murali1,* and Priya Panneer1
INTRODUCTION
Data Science
DATA SCIENCE IN MATHEMATICS
MATH AND DATA SCIENCE IN EDUCATION
TYPES OF DATA SCIENCE IN MATH
Linear Algebra
APPLICATION OF LINEAR ALGEBRA IN DATA SCIENCE
Loss Function
Mean Squared Error
MEAN ABSOLUTE ERROR
COMPUTER VISION
CALCULUS
CALCULUS IN MACHINE LEARNING
APPLICATIONS IN MEDICAL SCIENCE
APPLICATION IN ENGINEERING
APPLICATIONS IN RESEARCH ANALYSIS
APPLICATIONS IN PHYSICS
STATISTICS
Types of Statistics in Data Science
Descriptive Statistics
Inferential Statistics
Application of Statistics in the Field of Study
VITAL STATISTICS IDEAS OBTAINING STARTED
DISTRIBUTION OF DATA POINT
APPLIED MATH EXPERIMENTS AND SIGNIFICANCE TESTING
NONPARAMETRIC STATISTICAL METHODS
APPLICATION OF STATISTICS IN DATA SCIENCE ANALYZING AND CATEGORIZING DATA
NUMERIC DATA & CATEGORICAL DATA
EXPLORATORY KNOWLEDGE ANALYSIS
SIGNIFICANCE TESTS
Null Hypotheses
Alternative Hypotheses
CHI-SQUARED CHECK
STUDENT’S T-TEST
ANALYSIS OF VARIANCE CHECK (ANOVA)
Unidirectional
Two-ways
RESERVATION AND PREDICTION
Linear Regression
Logistic Regression
CLASSIFICATION OF KNOWLEDGE SCIENCE IN STATISTICS
Naive Mathematician
K-nearest Neighbors
PROBABILITY
FREQUENCY TABLES
HISTOGRAM
CONTINUOUS RANDOM VARIABLES
SKEWNESS DISTRIBUTION
RIGHT SKEW DISTRIBUTION
LEFT SKEW DISTRIBUTION
NORMAL DISTRIBUTION
EXPONENTIAL DISTRIBUTION
UNIFORM DISTRIBUTION
POISSON DISTRIBUTION
IMPORTANT OF INFORMATION SCIENCE
DATA WHILE NOT KNOWLEDGE SCIENCE
DATA CAN PRODUCE HIGHER CLIENT EXPERTISE
DATA USED ACROSS VERTICALS
POWER OF INFORMATION SCIENCE
FUTURE OF INFORMATION SCIENCE
DATA SCIENCE IN TRADE
BENEFITS OF KNOWLEDGE SCIENCE
STATISTICAL INFORMATION
DATA SCIENCE IS VERY IMPORTANT IN THE MODERN WORLD
DATA INDIVIDUAL
DATA SCIENCE WORKS
CONCLUDING REMARKS
REFERENCES
Bag of Visual Words Model - A Mathematical Approach
Maheswari K P 1,*
INTRODUCTION
HISTOGRAM REWEIGHTING – TF – IDF APPROACH
COST MATRIX GENERATION
EUCLIDEAN DISTANCE AND COSINE DISTANCE
MODEL DESCRIPTION
Histogram Generation for Image
Computation of Cost Matrix
Reweighting of Histogram using TF – IDF
Visualization of Original Euclidean, Reweighted Euclidean
Normalization of Original Histogram
Checking for Similarity of the Normalized Histogram
Visual Comparison of Histograms
CONCLUSION
REFERENCES
A Glance Review on Data Science and its Teaching: Challenges and Solutions
Srinivasa Rao Gundu1, Charanarur Panem2,* and J. Vijaylaxmi3
INTRODUCTION
THE IMPACT OF DATA SCIENCE ON THE SOCIETY
EDUCATIONAL GOALS OF DATA SCIENCE
DATA SCIENCE IN PRACTICE AS A PROBLEM SOLVING
LITERATURE REVIEW
DEMANDS OF THE DATA SCIENCE INDUSTRY AND THE DATA SCIENCE CURRICULUM
INHERENT PROBLEMS IN DATA SCIENCE CURRICULA DEVELOPMENT
TEACHING DATA SCIENCE
CONCLUDING REMARKS
REFERENCES
Optimization of Various Costs in Inventory Management using Neural Networks
Prerna Sharma1,* and Bhim Singh1
INTRODUCTION
RELATED WORK
ASSUMPTION AND NOTATIONS
MATHEMATICAL FORMULATION OF MODEL AND ANALYSIS
MULTILAYER-FEED FORWARD NEURAL NETWORKS
WORKING ON PROPOSED SYSTEM
EXPERIMENTAL RESULTS AND ANALYSIS
CONCLUDING REMARKS
REFERENCES
Cyber Security in Data Science and its Applications
M. Varalakshmi1,* and I. P. Thulasi1
INTRODUCTION
DATA SCIENCE TODAY
MOTIVE AND SIGNIFICANCE OF DATA SCIENCE
IMPORTANCE OF DATA
IMPORTANCE OF DATA SCIENCE
MOTIVATION OF DATA IMPORTANT INDUSTRIES
DATA SCIENCE FOR PREFERABLE TRADE
DATA ANALYTICS FOR CLIENT ACQUISITION
DATA ANALYTICS FOR REVOLUTION
DATA SCIENCE FOR ENHANCESURVIVAL
PART OF DATA SCIENCE IN CYBER SECURITY
CONNECTION ALLYING SUBSTANTIAL DATA AND CYBER SECURITY
DATA SCIENCE USED IN CYBER SECURITY
Negative Hoping on “Lab-based” Order
Utilize Entrance to Sufficient Data
Specialize in this Irregularity
Utilize Data Science in a Logical Approach
UPCOMING CHALLENGES IN CYBER SECURITY DATA SCIENCE
OPERATE CLASSIFICATION ISSUES IN CYBERSECURITY DATAFILE
RELIABILITY SCHEME RULE
AMBIENCE PERCEPTON IN CYBER SECURITY
ATTRIBUTE ENGINEERING IN CYBER SECURITY
PROMINENT SECURITY ACTIVE CREATION AND ARRAY
DISCUSSION
CONCLUDING REMARKS
REFERENCES
Artificial Neural Networks for Data Processing: A Case Study of Image Classification
Jayaraj Ramasamy1,*, R. N. Ravikumar2 and S. Shitharth3
INTRODUCTION
ARCHITECTURE OF ANN
Input Layer
Hidden Layer
Output Layer
BENEFITS OF ARTIFICIAL NEURAL NETWORK (ANN)
Ability for Processing
Network-based Data Storage
Capacity to Function Despite a Lack of Knowledge
Transmission of Memory
Acceptance for Faults
DISADVANTAGES
Ensure that the Network Structure is Correct
Network Activity that has Gone Unnoticed
Network's Life Expectancy is Unknown
WORKING OF ANN
TYPES OF ANN
Feedback ANN
Feed-Forward
SIMPLE NEURAL NETWORK
LITERATURE REVIEW
PROPOSED SYSTEM
RESULTS AND DISCUSSION
CONCLUSION
REFERENCES
Carbon Emission Assessment by Applying Clustering Technique to World’s Emission Datasets
Nitin Jaglal Untwal1,*
INTRODUCTION
Research Methodology
Limitations of the Study
Feature Extraction and Engineering
Data Extraction
Standardizing and Scaling
Identification of Clusters by Elbow Method
Cluster Formation
RESULTS AND ANALYSIS
Cluster One – High Rainfall
Cluster Two
Cluster Three
Cluster Four
Cluster Five
Cluster Six
CONCLUSION
REFERENCES
A Machine Learning Application to Predict Customer Churn: A Case in Indonesian Telecommunication Company
Agus Tri Wibowo1, Andi Chaerunisa Utami Putri1, Muhammad Reza Tribosnia1, Revalda Putawara1 and M. Mujiya Ulkhaq2,3,*
INTRODUCTION
LITERATURE REVIEW AND CONTRIBUTION
RESEARCH DESIGN
Dataset
Data Preparation
Exploratory Data Analysis
Features Selection
MACHINE LEARNING APPLICATION
Ridge Classifier
Gradient Booster
Adaptive Boosting
Bagging Classifier
k-Nearest Neighbor
Decision Tree
Logistic Regression
Random Forest
MODEL PERFORMANCE AND EVALUATION
RESULT
CONCLUDING REMARKS
REFERENCES
A State-Wise Assessment of Greenhouse Gases Emission in India by Applying K-mean Clustering Technique
Nitin Jaglal Untwal1,*
INTRODUCTION
Introduction to Cluster Analysis
Research Methodology
Data Source
Period of Study
Software used for Data Analysis
Model Applied
Limitations of the Study
Future Scope
Research is Carried Out in Five Steps
Feature Extraction and Engineering
Data Extraction
Standardizing and Scaling
Identification of Clusters by Elbow Method
Cluster formation
RESULTS AND ANALYSIS
Cluster One
Cluster Two
Cluster Three
CONCLUSION
REFERENCES
Data Mining Techniques: New Avenues for Heart
Disease Prediction
Data Science and Healthcare
Armel Djangone1,*
INTRODUCTION
So, What is Data Science?
Data Science Techniques vs. Data Mining
Now, Why is Data Essential?
What is an Ideal Data Scientist?
Technical and Soft Skills for Healthcare Data Scientists
Technical Skills
Soft Skills
Why is Data Science so Crucial for Organizations?
HEALTHCARE DATA: CHALLENGES AND OPPORTUNITIES
Opportunities
Defining Big Data
Challenges
Data Science Opportunities for Healthcare
HEALTHCARE LEADERSHIP
Transactional leader
Transformational leadership
CONCLUDING REMARKS
REFERENCES
Subject Index
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