Download Cluster analysis for data mining and system identification by János Abonyi, Balázs Feil PDF

By János Abonyi, Balázs Feil

The objective of this e-book is to demonstrate that complicated fuzzy clustering algorithms can be utilized not just for partitioning of the information. it could actually even be used for visualisation, regression, class and time-series research, consequently fuzzy cluster research is an efficient method of clear up complicated information mining and process identity difficulties. This ebook is orientated to undergraduate and postgraduate and is definitely fitted to instructing purposes.

Show description

Read Online or Download Cluster analysis for data mining and system identification PDF

Best mathematical & statistical books

Elimination Practice: Software Tools and Applications (With CD-Rom)

With a software program library incorporated, this e-book offers an ordinary advent to polynomial removing in perform. The library Epsilon, applied in Maple and Java, comprises greater than 70 well-documented features for symbolic removal and decomposition with polynomial platforms and geometric reasoning.

Mathematica(R) for Physics

A suitable complement for any undergraduate and graduate direction in physics, Mathematica® for Physics makes use of the ability of Mathematica® to imagine and reveal physics innovations and generate numerical and graphical ideas to physics difficulties. during the ebook, the complexity of either physics and Mathematica® is systematically prolonged to increase the variety of difficulties that may be solved.

Introduction to Scientific Computing: A Matrix-Vector Approach Using MATLAB

This e-book offers a distinct process for one semester numerical equipment and numerical research classes. good prepared yet versatile, the textual content is short and transparent adequate for introductory numerical research scholars to "get their toes wet," but complete adequate in its remedy of difficulties and purposes for higher-level scholars to enhance a deeper snatch of numerical instruments.

Cross Section and Experimental Data Analysis Using Eviews

A realistic consultant to picking and using the main acceptable version for research of move part info utilizing EViews. "This ebook is a mirrored image of the substantial event and data of the writer. it's a important reference for college students and practitioners facing go sectional information research . .

Additional info for Cluster analysis for data mining and system identification

Example text

Step 1 Calculate values for the model parameters θ i that minimize the cost function Em (U, {θ i }). Step 2 Update the partition matrix (l) µi,k = 1 , c 2/(m−1) j=1 (Ei,k /Ej,k ) 1 ≤ i ≤ c, 1 ≤ k ≤ N . 57) until ||U(l) − U(l−1) || < ǫ. The N data pairs and the membership degrees are matrices. ⎡ T ⎤ ⎡ ⎤ ⎡ xi,1 y1 µi,1 0 T ⎢ xi,2 ⎥ ⎢ y2 ⎥ ⎢ 0 µ i,2 ⎢ ⎢ ⎥ ⎥ ⎢ Xi = ⎢ . ⎥ , y = ⎢ . ⎥ , Φi = ⎢ . . . ⎣ . ⎦ ⎣ . ⎦ ⎣ . yN 0 0 xTi,N The optimal parameters θ i are then computed by: θ i = [XT Φi X]−1 XT Φi y .

The method has been included in the Fuzzy modelling and Identification Toolbox for MATLAB and can be downloaded from the website of the book. 21, the fuzzy clusters obtained by standard FCRM do not result in convex membership functions. 9 (a) Unconstrained (standard) case. 9 1 (b) FCRM with constrained prototypes. 21: Projected membership degrees to the u(k) domain obtained by fuzzy c-regression. Two types of prior knowledge were used to define constraints on the cluster prototypes. Both of them resulted in relative constraints.

In the following, a fuzzy clustering technique is introduced that is able to identify local models directly during the partitioning of the data. Fuzzy c-Regression Models Fuzzy c-regression models yield simultaneous estimates of parameters of c regression models together with a fuzzy c-partitioning of the data. 54) where xk = [xk,1 , . . , xk,n ] denotes the kth data sample and the functions fi are parameterized by θi ∈ Rpi . The membership degree µi,k ∈ U is interpreted as a weight representing the extent to which the value predicted by the model fi (xk , θi ) matches yk .

Download PDF sample

Rated 4.37 of 5 – based on 43 votes