Foreword to the Special Focus on Mathematics, Data and Knowledge
- 203 Downloads
There is a growing interest in applying mathematical theories and methods from topology, computational geometry, differential equations, fluid dynamics, quantum statistics, etc. to describe and to analyze scientific regularities of diverse, massive, complex, nonlinear, and fast changing data accumulated continuously around the world and in discovering and revealing valid, insightful, and valuable knowledge that data imply. With increasingly solid mathematical foundations, various methods and techniques have been studied and developed for data mining, modeling, and processing, and knowledge representation, organization, and verification; different systems and mechanisms have been designed to perform data-intensive tasks in many application fields for classification, predication, recommendation, ranking, filtering, etc. This special focus of Mathematics in Computer Science is organized to stimulate original research on the interaction of mathematics with data and knowledge, in particular the exploration of new mathematical theories and methodologies for data modeling and analysis and knowledge discovery and management, the study of mathematical models of big data and complex knowledge, and the development of novel solutions and strategies to enhance the performance of existing systems and mechanisms for data and knowledge processing. The present foreword provides a short review of some key ideas and techniques on how mathematics interacts with data and knowledge, together with a few selected research directions and problems and a brief introduction to the four papers published in the focus.
Unable to display preview. Download preview PDF.
- 9.Carette, J., Farmer, W.M.: A review of mathematical knowledge management. In: Carette, J., Dixon, L., Coen, C.S., Watt, S.M. (eds.) Intelligent Computer Mathematics, volume 5625 of Lecture Notes in Artificial Intelligence, pp. 233–246. Springer, Berlin (2009)Google Scholar
- 10.Carlsson, G.: Topology and data. Bull. Am. Math. Soc. 46(2), 255–308 (2009)Google Scholar
- 13.Chin, F.Y., Leung, H.C.: Voting algorithms for discovering long motifs. In: Chen, Y.-P.P., Wong, L. (eds.) Proceedings of the 3rd Asia-Pacific Bioinformatics Conference, volume 1 of Series on Advances in Bioinformatics and Computational Biology, pp. 261–271. World Scientific Publishing Company, Singapore (2005)Google Scholar
- 16.Diao, Y., Li, B., Liu, A., Peng, L., Sutton, C.A., Tran, T.T.L., Zink, M.: Capturing data uncertainty in high-volume stream processing. In: Proceedings of the 4th Biennial Conference on Innovative Data Systems Research, Asilomar, California, USA, January 4–7, 2009. (Online Proceedings)Google Scholar
- 18.Friedman, M., Last, M., Zaafrany, O., Schneider, M., Kandel, A.: A new approach for fuzzy clustering of web documents. In: Proceedings of IEEE International Conference on Fuzzy Systems, volume 1, pp. 377–381. IEEE Computational Intelligence Society (2004)Google Scholar
- 20.Kerber, M. (ed.): Management of Mathematical Knowledge—Special issue of Mathematics in Computer Science, vol 2. Birkhäuser, Basel (2008)Google Scholar
- 21.Lian, X., Chen, L.: A generic framework for handling uncertain data with local correlations. Proc. VLDB Endow. 4(1), 12–21 (2010)Google Scholar
- 22.Ropero J., Leun C., Carrasco A., Gumez A., Rivera O.: Fuzzy logic applications for knowledge discovery: a survey. Int. J. Adv. Comput. Technol. 3(6), 187–198 (2011)Google Scholar
- 24.Scheinberg, K., Peng, J., Terlaky, T., Shuurmans, D., Jordan, M., Poggio, T.: Mathematical programming in machine learning and data mining. In: 5-day Worksop Held by Banff International Research Station for Mathematical Innovation and Discovery, January 14–19 (2007)Google Scholar
- 25.Silva, V.D., Carlsson, G.: Topological estimation using witness complexes. In: Alexa, M., Gross, M., Pfister, H., Rusinkiewicz, S. (eds.) Proceedings of the First Eurographics Conference on Point-Based Graphics, pp. 157–166. Eurographics Association Aire-la-Ville (2004)Google Scholar
- 26.Simovici, D.A., Djeraba, C.: Mathematical Tools for Data Mining: Set Theory, Partial Orders, Combinatorics. Advanced Information and Knowledge Processing. Springer, London (2008)Google Scholar