Cluster analysis is an unsupervised process that divides a set of objects into homogeneous groups. This book starts with basic information on cluster analysis, including the classification of data and the corresponding similarity measures, followed by the presentation of over 50 clustering algorithms in groups according to some specific baseline methodologies such as hierarchical, centre-based, and search-based methods. As a result, readers and users can easily identify an appropriate algorithm for their applications and compare novel ideas with existing results. The book also provides examples of clustering applications to illustrate the advantages and shortcomings of different clustering architectures and algorithms. Application areas include pattern recognition, artificial intelligence, information technology, image processing, biology, psychology, and marketing. Suitable as a textbook for an introductory course in cluster analysis or as source material for a graduate-level introduction to data mining.

Data Clustering: Theory, Algorithms, and Applications (ASA-SIAM Series on Statistics and Applied Probability, Series Number 20)

Computers & Technology

Gan, Guojun

Wu, Jianhong

Ma, Chaoqun

Computer Science

Society for Industrial and Applied Mathematics

An introduction to the mathematical theory and financial models developed and used on Wall Street Providing both a theoretical and practical approach to the underlying mathematical theory behind financial models, Measure, Probability, and Mathematical Finance: A Problem-Oriented Approach presents important concepts and results in measure theory, probability theory, stochastic processes, and stochastic calculus. Measure theory is indispensable to the rigorous development of probability theory and is also necessary to properly address martingale measures, the change of numeraire theory, and LIBOR market models. In addition, probability theory is presented to facilitate the development of stochastic processes, including martingales and Brownian motions, while stochastic processes and stochastic calculus are discussed to model asset prices and develop derivative pricing models. The authors promote a problem-solving approach when applying mathematics in real-world situations, and readers are encouraged to address theorems and problems with mathematical rigor. In addition, Measure, Probability, and Mathematical Finance features: <ul>
<li>A comprehensive list of concepts and theorems from measure theory, probability theory, stochastic processes, and stochastic calculus</li> <li>Over 500 problems with hints and select solutions to reinforce basic concepts and important theorems</li> <li>Classic derivative pricing models in mathematical finance that have been developed and published since the seminal work of Black and Scholes</li> </ul>
Measure, Probability, and Mathematical Finance: A Problem-Oriented Approach is an ideal textbook for introductory quantitative courses in business, economics, and mathematical finance at the upper-undergraduate and graduate levels. The book is also a useful reference for readers who need to build their mathematical skills in order to better understand the mathematical theory of derivative pricing models.

Measure, Probability, and Mathematical Finance: A Problem-Oriented Approach

Business & Money

Xie, Hong

Finance

wiley

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