Rough Set-based Clustering Research Articles

Clustering Categorical Data: A Survey

Clustering is a complex unsupervised method used to group most similar observations of a given dataset within the same cluster. To guarantee high efficiency, the clustering process should ensure high accuracy and low complexity. Many clustering methods were developed in various fields depending on the type of application and the data type considered. Categorical clustering considers segmenting a dataset in which the data are categorical and were widely used in many real-world applications. Thus several methods were developed including hard, fuzzy and rough set-based methods. In this survey, more than 30 categorical clustering algorithms were investigated. These methods were classified into hierarchical and partitional clustering methods and classified in terms of their accuracy, precision and recall to identify the most prominent ones. Experimental results show that rough set-based clustering methods provided better efficiency than hard and fuzzy methods. Besides, methods based on the initialization of the centroids also provided good results.

Rough Set-Based Clustering Utilizing Probabilistic Memberships

Representing the positive, possible, and boundary regions of clusters, rough set-based C-means clustering methods, such as generalized rough C-means (GRCM) and rough set C-means (RSCM), are promising for analyzing vague cluster shapes and realizing reliable classification. In this study, we consider rough set-based clustering approaches that utilize probabilistic memberships as variants of GRCM and RSCM, including π generalized rough C-means (πGRCM), π rough set C-means (πRSCM), and rough membership C-means (RMCM). πGRCM and πRSCM assign equal probabilities of cluster belonging according to Laplace’s principle of indifference, whereas RMCM assigns the probabilities according to rough memberships, which represent conditional probabilities based on the object’s neighborhood derived from a binary relation. In addition, we discuss the theoretical validity of our RMCM approach and compare it with other methods considered in this study. Furthermore, we conducted numerical experiments for evaluating the classification performances of the abovementioned methods. Based on our experimental results, the methods were found to be effective.

Informational Paradigm, management of uncertainty and theoretical formalisms in the clustering framework: A review

Fifty years have gone by since the publication of the first paper on clustering based on fuzzy sets theory. In 1965, L.A. Zadeh had published “Fuzzy Sets” [335]. After only one year, the first effects of this seminal paper began to emerge, with the pioneering paper on clustering by Bellman, Kalaba, Zadeh [33], in which they proposed a prototypal of clustering algorithm based on the fuzzy sets theory. Starting from this paper, several uncertain clustering methods based on different theoretical approaches for modeling the uncertainty have been proposed. The present paper presents a systematic literature review of these clustering approaches. In particular, with respect to the Statistical Reasoning System, we first illustrate the connection between Information and Uncertainty from the perspective of the so-called Informational Paradigm, according to which Information is constituted by “Informational ingredients”, specifically the “Empirical Information,” represented by statistical data, and “Theoretical information” consisting of background knowledge and basic modeling assumptions. We then describe different kinds of uncertainty affecting the Information. Focusing on the uncertainty associated with a particular statistical methodology, i.e. Cluster Analysis, and adopting as theoretical platform the Informational Paradigm, we present a systematic literature review of different uncertainty-based clustering approaches -i.e. Fuzzy clustering, Possibilistic clustering, Shadowed clustering, Rough sets-based clustering, Intuitionistic fuzzy clustering, Evidential clustering, Credibilistic clustering, Type-2 fuzzy clustering, Neutrosophic clustering, Hesitant fuzzy clustering, Interval-based fuzzy clustering, and Picture fuzzy clustering. We thus show how all these clustering approaches are able of managing in different ways the uncertainty associated with the two components of the Informational Paradigm, i.e. the Empirical and Theoretical Information.

Similarity upper approximation-based clustering for recommendation system

The web has evolved enormously in the past few years resulting in a rapid increase in the number of web users and web pages. Web personalisation has become a challenging task for e-commerce-based companies due to information overload on the web and increase in the number of web users. Recommendation systems generate recommendations to users for various products as per their requirements. Recommendation systems have been widely used in e-commerce websites and have become an integral part of the ecommerce business process. Developers try to customise websites to suit the needs of specific users utilising the knowledge acquired from users' navigational behaviour. The current study focuses on development of a framework for a web recommendation system on the basis of sequential information present in web logs. Rough set-based clustering using similarity upper approximation has been utilised to generate soft clusters to capture the multiple interests of users. The proposed recommendation system can predict the next possible page visit of the user based on the sequential information present in their navigation pattern.

Uncertain clustering algorithms based on rough and fuzzy sets for real-time image segmentation

In real pattern recognition applications, the complete and accurate information of a given set is not always easy to get. Such incomplete knowledge may lead to imperfect expressions of the set using many pattern recognition methods. Rough sets theory is designed to approximately describe an imprecise set by a pair of lower and upper approximations which are weighted by different parameters. As the distributive character varies from one set to another, it is undesirable to employ a constant weighted parameter for controlling the importance of the lower and upper approximations on describing various given sets. This paper presents an improved rough-fuzzy c-means clustering algorithm in which a parameter selection strategy is designed to adaptively adjust the weighted parameter depending on the distributive character of each cluster instead of manually choosing a constant parameter. Such an online-decision method enables the formed prototype to get close to the desirable location. Experimental results on synthetic datasets, real-life datasets, and image segmentation problems confirm the effectiveness of the proposed adaptive parameter selection strategy. With the introduction of adaptive parameter selection strategy, the improved rough sets-based clustering algorithm outperforms its counterparts in certain cases.

Rough set-based regionalisation in air quality monitoring

Regionalisation is to organise a large set of spatial objects into spatially contiguous regions despite optimising the homogeneity of the derived regions, while representing social and economic geography. To confront this problem, it is necessary to classify the regions to form groups that are homogeneous in air quality attributes. It is to develop a system that applies data mining techniques to study the distribution of air pollutants in Chennai, a metro city in India using vehicular ad hoc networking and map the distribution on the geographical map for effective policy making. In conventional regionalisation methods, the data points are assigned to a single region in a multidimensional attribute space affecting air pollution response. However, some data points, having distributed membership to more than one region, could not be justified and allocated to a single region. Rough set-based clustering technique is applied to regionalisation problem to resolve vague or overlapping regions. The overlapping regions are restructured to guarantee the homogeneity of the regions formed or altered. The investigations of the cluster validity tests confirm the effectiveness of rough set-based regionalisation in air quality modelling.

Shadowed sets in the characterization of rough-fuzzy clustering

In this study, we develop a technique of an automatic selection of a threshold parameter, which determines approximation regions in rough set-based clustering. The proposed approach exploits a concept of shadowed sets. All patterns (data) to be clustered are placed into three categories assuming a certain perspective established by an optimization process. As a result, a lack of knowledge about global relationships among objects caused by the individual absolute distance in rough C-means clustering or individual membership degree in rough-fuzzy C-means clustering can be circumvented. Subsequently, relative approximation regions of each cluster are detected and described. By integrating several technologies of Granular Computing including fuzzy sets, rough sets, and shadowed sets, we show that the resulting characterization leads to an efficient description of information granules obtained through the process of clustering including their overlap regions, outliers, and boundary regions. Comparative experimental results reported for synthetic and real-world data illustrate the essence of the proposed idea.

A New Fuzzy DSS/ES for Stock Portfolio Selection using Technical and Fundamental Approaches in Parallel

A Decision Support System/Expert System for stock portfolio selection presented where at first step, both technical and fundamental data used to estimate technical and fundamental return and risk (1 phase); Then, the estimated values are aggregated with the investor preferences (2 phase) to produce convenient stock portfolio. In the 1 phase, there are two expert systems, each of which is responsible for technical or fundamental estimation. In the technical expert system, for each stock, twenty seven candidates are identified and with using rough sets-based clustering method (RC) the effective variables have been selected. Next, for each stock two fuzzy rulebases are developed with fuzzy C-Mean method and Takai-SugenoKang (TSK) approach; one for return estimation and the other for risk. Thereafter, the parameters of the rule-bases are tuned with backpropagation method. In parallel, for fundamental expert systems, fuzzy rule-bases have been identified in the form of “IF-THEN” rules through brainstorming with the stock market experts and the input data have been derived from financial statements; as a result two fuzzy rule-bases have been generated for all the stocks, one for return and the other for risk. In the 2 phase, user preferences represented by four criteria and are obtained by questionnaire. Using an expert system, four estimated values of return and risk have been aggregated with the respective values of user preference. At last, a fuzzy rule base having four rules, treats these values and produce a ranking score for each stock which will lead to a satisfactory portfolio for the user. The stocks of six manufacturing companies and the period of 2003-2006 selected for data gathering. Keywords—Stock Portfolio Selection, Fuzzy Rule-Base Expert Systems, Financial Decision Support Systems, Technical Analysis, Fundamental Analysis.

Rough Set-Based Clustering with Refinement Using Shannon's Entropy Theory

Lots of clustering algorithms have been developed, while most of them cannot process objects in hybrid numerical/nominal attribute space or with missing values. In most of them, the number of clusters should be manually determined and the clustering results are sensitive to the input order of the objects to be clustered. These limit applicability of the clustering and reduce the quality of clustering. To solve this problem, an improved clustering algorithm based on rough set (RS) and entropy theory was presented. It aims at avoiding the need to prespecify the number of clusters, and clustering in both numerical and nominal attribute space with the similarity introduced to replace the distance index. At the same time, the RS theory endows the algorithm with the function to deal with vagueness and uncertainty in data analysis. Shannon's entropy was used to refine the clustering results by assigning relative weights to the set of attributes according to the mutual entropy values. A novel measure of clustering quality was also presented to evaluate the clusters. This algorithm was analyzed and applied later to cluster the data set of one industrial product. The experimental results confirm that performances of efficiency and clustering quality of this algorithm are improved.