Mathematical Problems in Data Science: Theoretical and Practical Methods

This book describes current problems in data science and Big Data. Key topics are data classification, Graph Cut, the Laplacian Matrix, Google Page Rank, efficient algorithms, hardness of problems, different types of big data, geometric data structures, topological data processing, and various learning methods. For unsolved problems such as incomplete data relation and reconstruction, the book includes possible solutions and both statistical and computational methods for data analysis. Initial chapters focus on exploring the properties of incomplete data sets and partial-connectedness among data points or data sets. Discussions also cover the completion problem of Netflix matrix; machine learning method on massive data sets; image segmentation and video search. This book introduces software tools for data science and Big Data such MapReduce, Hadoop, and Spark. This book contains three parts. The first part explores the fundamental tools of data science. It includes basic graph theoretical methods, statistical and AI methods for massive data sets. In second part, chapters focus on the procedural treatment of data science problems including machine learning methods, mathematical image and video processing, topological data analysis, and statistical methods. The final section provides case studies on special topics in variational learning, manifold learning, business and financial data rec overy, geometric search, and computing models. Mathematical Problems in Data Science is a valuable resource for researchers and professionals working in data science, information systems and networks. Advanced-level students studying computer science, electrical engineering and mathematics will also find the content helpful.

5.2.3 Image Recognition.

Preface; Contents; Acronyms; Part I Basic Data Science; 1 Introduction: Data Science and BigData Computing; 1.1 Data Mining and Cloud Computing: The Prelude of BigData and Data Science; 1.2 BigData Era; 1.3 The Meaning of Data Sciences; 1.4 Problems Related to Data Science; 1.5 Mathematical Problems in Data Science; 1.6 Mathematics, Data Science, and Data Scientists in Industry; 1.7 Remark: Discussion on the Future Problems in Data Science; References; 2 Overview of Basic Methods for Data Science; 2.1 ``Hardware'' and ``Software'' of Data Science; 2.1.1 Searching and Optimization.

2.1.2 Decision Making2.1.3 Classification; 2.1.4 Learning; 2.2 Graph-Theoretic Methods; 2.2.1 Review of Graphs; 2.2.2 Breadth First Search and Depth First Search; 2.2.3 Dijkstra's Algorithm for the Shortest Path; 2.2.4 Minimum Spanning Tree; 2.3 Statistical Methods; 2.4 Classification, Clustering, and Pattern Recognition; 2.4.1 k-Nearest Neighbor Method; 2.4.2 k-Means Method ; 2.5 Numerical Methods and Data Reconstruction in Science and Engineering; 2.6 Algorithm Design and Computational Complexity; 2.6.1 Concepts of Data Structures and Databases; 2.6.2 Queues, Stacks, and Linked Lists.

Part II Data Sc…