Advanced Mathematical Applications in Data Science

Advanced Mathematical Applications in Data Science comprehensively explores the crucial role mathematics plays in the field of data science. Each chapter is contributed by scientists, researchers, and academicians. The 13 chapters cover a range of mathematical concepts utilized in data science, enabling readers to understand the intricate connection between mathematics and data analysis. The book covers diverse topics, including, machine learning models, the Kalman filter, data modeling, artificial neural networks, clustering techniques, and more, showcasing the application of advanced mathematical tools for effective data processing and analysis. With a strong emphasis on real-world applications, the book offers a deeper understanding of the foundational principles behind data analysis and its numerous interdisciplinary applications. This reference is an invaluable resource for graduate students, researchers, academicians, and learners pursuing a research career in mathematical computing or completing advanced data science courses. Key Features: - Comprehensive coverage of advanced mathematical concepts and techniques in data science - Contributions from established scientists, researchers, and academicians - Real-world case studies and practical applications of mathematical methods - Focus on diverse areas, such as image classification, carbon emission assessment, customer churn prediction, and healthcare data analysis - In-depth exploration of data science's connection with mathematics, computer science, and artificial intelligence - Scholarly references for each chapter - Suitable for readers with high school-level mathematical knowledge, making it accessible to a broad audience in academia and industry. Cover Title Copyright 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 Back Cover