Visualization of Fuzzy Clustering Result in Metric Space

AbstractThis paper presents a visualization of a result of fuzzy clustering. The feature of fuzzy clustering is to obtain the degree of belongingness of objects to fuzzy clusters so the result will be more commensurate with reality. In addition, the number of clusters requires less and the solution of the result will be more robust when compared with conventional hard clustering. In contrast, the fuzzy clustering result interpretation tends to be more complicated. Therefore, measuring the similarity (or dissimilarity) between a pair of fuzzy classification status of objects is important. In order to measure the similarity (or dissimilarity) mathematically, it is necessary to introduce a scale to the fuzzy clustering result. That is, the obtained solutions as a fuzzy clustering result must be in a metric space. In order to implement this, we have proposed multidimensional joint scale and cluster analysis. In this analysis, we exploit a scale obtained by multidimensional scaling. This paper clarifies that the multidimensional joint scale and cluster analysis introduces scale to the fuzzy clustering result and then the visualization of the fuzzy clustering result in the metric vector space has a theoretical mathematical meaning through the Euclidean distance structure. In this paper, this is shown by using several numerical comparisons with ordinary visualizations of the fuzzy clustering result

Conceptual clustering using relational informatio

Work in conceptual clustering has focused on creating classes from objects with a fixed set of features, such as color or size. In this paper we describe a system which uses relations between the objects being clustered as well as features of the objects to form a hierarchy tree of classes. Unlike previous conceptual clustering systems, this algorithm can define new attributes. Using relational information the system is able to find object classifications not possible with conventional conceptual clustering methods

Methods of conceptual clustering and their relation to numerical taxonomy

Artificial Intelligence (AI) methods for machine learning can be viewed as forms of exploratory data analysis, even though they differ markedly from the statistical methods generally connoted by the term. The distinction between methods of machine learning and statistical data analysis is primarily due to differences in the way techniques of each type represent data and structure within data. That is, methods of machine learning are strongly biased toward symbolic (as opposed to numeric) data representations. We explore this difference within a limited context, devoting the bulk of our paper to the explication of conceptual clustering, an extension to the statistically based methods of numerical taxonomy. In conceptual clustering the formation of object clusters is dependent on the quality of 'higher-level' characterizations, termed concepts, of the clusters. The form of concepts used by existing conceptual clustering systems (sets of necessary and sufficient conditions) is described in some detail. This is followed by descriptions of several conceptual clustering techniques, along with sample output. We conclude with a discussion of how alternative concept representations might enhance the effectiveness of future conceptual clustering systems

Soft clustering analysis of galaxy morphologies: A worked example with SDSS

Context: The huge and still rapidly growing amount of galaxies in modern sky surveys raises the need of an automated and objective classification method. Unsupervised learning algorithms are of particular interest, since they discover classes automatically. Aims: We briefly discuss the pitfalls of oversimplified classification methods and outline an alternative approach called "clustering analysis". Methods: We categorise different classification methods according to their capabilities. Based on this categorisation, we present a probabilistic classification algorithm that automatically detects the optimal classes preferred by the data. We explore the reliability of this algorithm in systematic tests. Using a small sample of bright galaxies from the SDSS, we demonstrate the performance of this algorithm in practice. We are able to disentangle the problems of classification and parametrisation of galaxy morphologies in this case. Results: We give physical arguments that a probabilistic classification scheme is necessary. The algorithm we present produces reasonable morphological classes and object-to-class assignments without any prior assumptions. Conclusions: There are sophisticated automated classification algorithms that meet all necessary requirements, but a lot of work is still needed on the interpretation of the results.Comment: 18 pages, 19 figures, 2 tables, submitted to A

Concept Extraction and Clustering for Topic Digital Library Construction

This paper is to introduce a new approach to build topic digital library using concept extraction and document clustering. Firstly, documents in a special domain are automatically produced by document classification approach. Then, the keywords of each document are extracted using the machine learning approach. The keywords are used to cluster the documents subset. The clustered result is the taxonomy of the subset. Lastly, the taxonomy is modified to the hierarchical structure for user navigation by manual adjustments. The topic digital library is constructed after combining the full-text retrieval and hierarchical navigation function