Fuzzy cluster analysis

In order to reduce incomparabilities and to facilitate the interpretation of Hasse diagrams, pre-processing by two strategies of fuzzy cluster analysis has been applied to sediment data ... 

We have already discussed an example iot grouping data on the basis of unsupervised learning with respect to fuzzy cluster analysis by the c-means algorithm (Section 5.2). 

Most of the applications of fuzzy cluster analysis in chemistry apply the fuzzy-c-means algorithm. It relies on the general least-squares error functional... 

Miyamoto, S. (1990) Fuzzy sets in information retrieval and cluster analysis. Kluwer Academic Publishers, Dordrecht, The Netherlands. 

Fuzzy clustering methods that have recently become popular are distinct from traditional clustering techniques in that molecules are permitted to belong to multiple clusters or have fractional membership in all clusters. A potential advantage of such classification schemes is that more than one similarity relationship can be established by cluster analysis. 

Technische Universitat Wien Does latent class analysis, short-time Fourier transform, fuzzy clustering, support vector machines, shortest path computation, bagged clustering, naive Bayes classifier, etc. (http //cran.r-project.org/ web/packages/el071/index.html)... 

Similarity Search. A type of "fuzzy" structure searching in which molecules are compared with respect to the degree of overlap they share in terms of topological and/or physicochemical properties. Topological descriptors usually consist of substructure keys or fingerprints, in which case a similarity coefficient like the Tanimoto coefficient is computed. In the case of calculated properties, a simple correlation coefficient may be used. The similarity coefficient used in a similarity search can also be used in various types of cluster analysis to group similar structures. 

Factor analysis, 79 0-mode, 84 / -mode, 85 target transform, 91 Feature extraction, 54 Feature selection, 54 Filtering, 41 Flicker noise, 31 Fourier integral 41 Fourier pairs 42 Fourier transform 28 Furthest neighbours clustering, 103, 107 Fuzzy clustering, 104, 115... 

To demonstrate the use and application of fuzzy clustering, a simple set of data will be analysed manually. The data in Table 4.9 represent 15 objects (A. .. O) characterized by two variables X and X2, and these data are plotted in the scatter diagram of Figure 4.15. It is perhaps not unreasonable to assume that these data represent two classes or clusters. The means of the clusters are well separated but the clusters touch about points G, H, and I. Because the apparent groups are not well separated, the results using conventional cluster analysis schemes can be misleading or ambiguous. With the data from Table... 

Sarbu, C Mot, AC. (2011). Ecosystem discrimination and fingerprinting of Romain propolis by hierarchical fuzzy clustering and image analysis of TLC patterns. Talanta, Vol. 85, pp.1112-1117. ISSN 0039-9140... 

Commonly in nonhierarchical cluster analysis, one starts with an initial partitioning of objects to the different clusters. After that, the membership of the objects to the clusters, for example, to the cluster centroids, is determined and the objects are newly partitioned. We consider here a general method for nonhierarchical clustering that can be used for both crisp (classical) and fuzzy clustering, the c-means algorithm. 

Miyamoto S. Fuzzy Sets in Information Retrieval and Cluster Analysis. Dordrecht Kluwer Academic Publishers 1990. 

Hert J, Willett P, Wilton DJ, Acklin P, Azzaoui K, Jacoby E, Schuffenhauer A(2006)New methods for ligand-based virtual screening use of data-fusion and machine-learning techniques to enhance the effectiveness of similarity searching. J Chem Inf Model 46 462-470 Miyamoto S (1990) Fuzzy sets in information retrieval and cluster analysis. Kluwer Academic, Dordrecht... 

As is well known, Cluster Analysis involves the classification of objects into categories. Since most categories have vague boundaries, and may even overlap, the necessity of introducing fuzzy sets is obvious. A discussion of Fuzzy Clustering must refer to the following issues ... 

A broken line separates the two classes of light lanthanides, including Yb and the heavier lanthanides, together with Sc and Y. The clusters are framed by solid borders. Going along the series of lanthanides in the direction of the arrows we find all the clusters given by the fuzzy PCA analysis. 

The outcome of agglomerative hierarchical cluster analysis is a crisp cluster membership function, which can take only the values 0 (no membership) or 1 (membership). Other non-hierarchical clustering techniques such as k-means cluster (KMC) analysis still follow this concept, whereas fuzzy C-means (FCM) clustering returns fuzzy class memberships. The latter method thus departs from the classical (0 or 1) two-valued logic and uses soft linguistic system variables, i.e. degrees of class membership values varying between 0 and 1. 

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