By Thomas A. Runkler
This e-book is a finished creation to the tools and algorithms and methods of recent information analytics. It covers information preprocessing, visualization, correlation, regression, forecasting, type, and clustering. It offers a valid mathematical foundation, discusses benefits and downsides of alternative techniques, and allows the reader to layout and enforce facts analytics options for real-world functions. The textual content is designed for undergraduate and graduate classes on facts analytics for engineering, desktop technological know-how, and math scholars. it's also compatible for practitioners engaged on facts analytics initiatives. This ebook has been used for greater than ten years in different classes on the Technical college of Munich, Germany, briefly classes at numerous different universities, and in tutorials at clinical meetings. a lot of the content material is predicated at the result of commercial study and improvement tasks at Siemens.
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Additional info for Data Analytics: Models and Algorithms for Intelligent Data Analysis
On lines and planes of closest ﬁt to systems of points in space. Philosophical Magazine, 2(6):559–572, 1901. 5. T. A. Runkler. Fuzzy histograms and fuzzy chi–squared tests for independence. In IEEE International Conference on Fuzzy Systems, volume 3, pages 1361–1366, Budapest, July 2004. 6. J. W. Sammon. A nonlinear mapping for data structure analysis. IEEE Transactions on Computers, C-18(5):401–409, 1969. 7. D. W. Scott. On optimal and data–based histograms. Biometrika, 66(3):605–610, 1979. 8.
Every datum between the lower and upper bounds of a histogram interval is counted for the respective bin, whether it is close to the interval center or close to the border. A fuzzy histogram  partially counts data for several neighboring bins. 50 4 Data Visualization μ ξ1 ξ2 ξ3 ξm-1 ξm x Fig. 14 Triangular membership functions. For example, a datum at the border between two bins may be counted as half for one and half for the other bin. More generally, fuzzy histograms use data counts in fuzzy intervals deﬁned by membership functions μ : X → [0, 1].
The ﬁltering methods presented in this section speciﬁcally consider series data, and they typically change all values of the series. The goal is not only to remove outliers but also to remove noise. Fig. 3 shows a categorization of the different ﬁlter types presented here. A widely used class of ﬁlters uses statistical measures over moving windows. To compute the ﬁltering result for each value xk , k = 1, . . , n, all series values in a local window around xk are considered and the ﬁlter output yk is the value of a statistical measure of the data in this window.