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Discrete geometry --- Geometry --- Data processing. --- Combinatorial geometry --- Computer vision. --- Computer graphics. --- Discrete groups. --- Biometrics. --- Computational complexity. --- Database management. --- Image Processing and Computer Vision. --- Computer Graphics. --- Convex and Discrete Geometry. --- Discrete Mathematics in Computer Science. --- Database Management. --- Data base management --- Data services (Database management) --- Database management services --- DBMS (Computer science) --- Generalized data management systems --- Services, Database management --- Systems, Database management --- Systems, Generalized database management --- Electronic data processing --- Complexity, Computational --- Machine theory --- Groups, Discrete --- Infinite groups --- Automatic drafting --- Graphic data processing --- Graphics, Computer --- Computer art --- Graphic arts --- Engineering graphics --- Image processing --- Machine vision --- Vision, Computer --- Artificial intelligence --- Pattern recognition systems --- Digital techniques --- Discrete mathematics --- Optical data processing. --- Convex geometry . --- Discrete geometry. --- Biometrics (Biology). --- Computer science—Mathematics. --- Biological statistics --- Biology --- Biometrics (Biology) --- Biostatistics --- Biomathematics --- Statistics --- Optical computing --- Visual data processing --- Bionics --- Integrated optics --- Photonics --- Computers --- Statistical methods --- Optical equipment

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Digital Functions and Data Reconstruction: Digital-Discrete Methods provides a solid foundation to the theory of digital functions and its applications to image data analysis, digital object deformation, and data reconstruction. This new method has a unique feature in that it is mainly built on discrete mathematics with connections to classical methods in mathematics and computer sciences. Digitally continuous functions and gradually varied functions were developed in the late 1980s. A. Rosenfeld (1986) proposed digitally continuous functions for digital image analysis, especially to describe the “continuous” component in a digital image, which usually indicates an object. L. Chen (1989) invented gradually varied functions to interpolate a digital surface when the boundary appears to be continuous. In theory, digitally continuous functions are very similar to gradually varied functions. Gradually varied functions are more general in terms of being functions of real numbers; digitally continuous functions are easily extended to the mapping from one digital space to another.  This will be the first book about digital functions, which is an important modern research area for digital images and digitalized data processing, and provides an introduction and comprehensive coverage of digital function methods. Digital Functions and Data Reconstruction: Digital-Discrete Methods offers scientists and engineers who deal with digital data a highly accessible, practical, and mathematically sound introduction to the powerful theories of digital topology and functional analysis, while avoiding the more abstruse aspects of these topics.

Discrete mathematics --- Computer science --- Artificial intelligence. Robotics. Simulation. Graphics --- Computer. Automation --- computervisie --- beeldverwerking --- discrete wiskunde --- computers --- grafische vormgeving --- KI (kunstmatige intelligentie) --- computerkunde --- signaalverwerking --- AI (artificiële intelligentie)

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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.

Computer Science --- Engineering & Applied Sciences --- Quantitative research. --- Big data. --- Cloud computing. --- Data sets, Large --- Large data sets --- Data analysis (Quantitative research) --- Exploratory data analysis (Quantitative research) --- Quantitative analysis (Research) --- Quantitative methods (Research) --- Computer science. --- Computer communication systems. --- Computer science --- Computers. --- Computer Science. --- Information Systems and Communication Service. --- Computer Communication Networks. --- Mathematics of Computing. --- Mathematics. --- Research --- Electronic data processing --- Web services --- Distributed processing --- Data sets --- Information systems. --- Informatics --- Science --- Computer science—Mathematics. --- Communication systems, Computer --- Computer communication systems --- Data networks, Computer --- ECNs (Electronic communication networks) --- Electronic communication networks --- Networks, Computer --- Teleprocessing networks --- Data transmission systems --- Digital communications --- Electronic systems --- Information networks --- Telecommunication --- Cyberinfrastructure --- Network computers --- Automatic computers --- Automatic data processors --- Computer hardware --- Computing machines (Computers) --- Electronic brains --- Electronic calculating-machines --- Electronic computers --- Hardware, Computer --- Computer systems --- Cybernetics --- Machine theory --- Calculators --- Cyberspace