Data mining essentially relies on several mathematical disciplines, many of which are presented in this second edition of this book. Topics include partially ordered sets, combinatorics, general topology, metric spaces, linear spaces, graph theory. To motivate the reader a significant number of applications of these mathematical tools are included ranging from association rules, clustering algorithms, classification, data constraints, logical data analysis, etc. The book is intended as a reference for researchers and graduate students. The current edition is a significant expansion of the first edition. We strived to make the book self-contained and only a general knowledge of mathematics is required. More than 700 exercises are included and they form an integral part of the material. Many exercises are in reality supplemental material and their solutions are included.
1 WorkshopTheme Digital multimedia di?ers from previous forms of combined media in that the bits that represent text, images, animations, and audio, video and other signals can be treated as data by computer programs. One facet of this diverse data in termsofunderlyingmodelsandformatsisthatitissynchronizedandintegrated, hence it can be treated as integral data records. Such records can be found in a number of areas of human endeavour. Modern medicine generates huge amounts of such digital data. Another - ample is architectural design and the related architecture, engineering and c- struction (AEC) industry. Virtual communities (in the broad sense of this word, which includes any communities mediated by digital technologies) are another example where generated data constitutes an integral data record. Such data may include data about member pro?les, the content generated by the virtual community, and communication data in di?erent formats, including e-mail, chat records, SMS messages, videoconferencing records. Not all multimedia data is so diverse. An example of less diverse data, but data that is larger in terms of the collected amount, is that generated by video surveillance systems, where each integral data record roughly consists of a set of time-stamped images – the video frames. In any case, the collection of such in- gral data records constitutes a multimedia data set. The challenge of extracting meaningful patterns from such data sets has led to the research and devel- ment in the area of multimedia data mining.
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