Fuzzy Relational Clustering Algorithm Research Articles

Cophenetic-based fuzzy clustering of time series by linear dependency

In this work, a new approach to cluster large sets of time series is presented. The proposed methodology takes into account the dependency among the time series to obtain a fuzzy partition of the set of observations. A two-step procedure to accomplish this is presented. First, the cophenetic distances, based on a time series linear cross-dependency measure, are obtained. Second, these distances are used as an input of a non-Euclidean fuzzy relational clustering algorithm. As a result, we obtain a robust fuzzy procedure capable of detecting groups of time series with different types of cross-dependency. We illustrate the usefulness of the stated methodology through some Monte Carlo experiments and a real data example. Our results show that the methodology proposed in this work substantially improves the hard partitioning clustering alternative.

Automatic Determination of the Number of Clusters for Semi-Supervised Relational Fuzzy Clustering

Semi-supervised clustering relies on both labeled and unlabeled data to steer the clustering process towards optimal categorization and escape from local minima. In this paper, we propose a novel fuzzy relational semi-supervised clustering algorithm based on an adaptive local distance measure (SSRF-CA). The proposed clustering algorithm utilizes side-information and formulates it as a set of constraints to supervise the learning task. These constraints are expressed using reward and penalty terms, which are integrated into a novel objective function. In particular, we formulate the clustering task as an optimization problem through the minimization of the proposed objective function. Solving this optimization problem provides the optimal values of different objective function parameters and yields the proposed semi-supervised clustering algorithm. Along with its ability to perform data clustering and learn the underlying dissimilarity measure between the data instances, our algorithm determines the optimal number of clusters in an unsupervised manner. Moreover, the proposed SSRF-CA is designed to handle relational data. This makes it appropriate for applications where only pairwise similarity (or dissimilarity) information between data instances is available. In this paper, we proved the ability of the proposed algorithm to learn the appropriate local distance measures and the optimal number of clusters while partitioning the data using various synthetic and real-world benchmark datasets that contain varying numbers of clusters with diverse shapes. The experimental results revealed that the proposed SSRF-CA accomplished the best performance among other state-of-the-art algorithms and confirmed the outperformance of our clustering approach.

New automatic fuzzy relational clustering algorithms using multi-objective NSGA-II

Most of the fuzzy clustering methods use only centroid information and cannot differentiate the geometric structures of clusters due to the cohesion and separation measures of the fuzzy partition. Moreover, conventional clustering methods confine the search space of automatic fuzzy clustering as it shows a tendency to fall into local minima as well as the number of clusters is required to be provided as prior knowledge. In this paper, combining fuzzy relational clustering (FRC) with multi-objective genetic algorithm NSGA-II, we propose two new fuzzy relational clustering methods, referred to as FRCNSGA and IFRCNSGA. In IFRCNSGA, NSGA-II is used to adjust the parameters of FRC algorithm dynamically such as the appropriate number of clusters and the initial membership values. Thus this proposed model handles the intricacy of automatic clustering a dataset, at the same time, avoids the problem of falling into local minima quickly. For both of the proposed models, NSGA-II is used to optimize two cluster validity indices named, separation, and cohesion, simultaneously, whereas, FRC is used to handle the overlapping properties of clusters. In this case, fuzzy membership degrees are used to compute the overlap-separation. To eliminate the impediment of automatic fuzzy clustering, it is necessary to optimize one or more criteria. Therefore, we consider NSGA-II as an optimization algorithm to optimize more than single criterion. The experimental results have exhibited that the intended methods provide competitive results in the compound, overlapped, high-dimensional gene expression and non-gene expression datasets. The proposed methods are able to determine well-separated, hyperspherical, noncompact and overlapping clusters compared to other existing methods.

Optimal Sentence Clustering for Web Database using Hierarchical Fuzzy Relational Clustering Integrated with Artificial Bee Colony Algorithm

Sentence clustering plays a vital role in text mining and text processing activities. The proposed work is a novel hierarchical fuzzy relational clustering algorithm (HFRECA) capable of identifying sub clusters. It has features of both hierarchical clustering and fuzzy clustering in which it uses page rank to form multiple clusters present in text documents containing hierarchical structure. To enhance the quality of the clusters formed, an optimisation algorithm which is called artificial bee colony (ABC) algorithm is used along with it. The proposed algorithm identifies the sub clusters and finely tunes the cluster to show a better optimised result.

A fuzzy similarity measure based on equivalence relation with application in cluster analysis

We propose a novel notion of fuzzy similarity measure between fuzzy sets by using fuzzy equivalence. Furthermore, a similarity base fuzzy relational clustering algorithm is formulated. Applications are given to illustrate the usefulness of the chosen fuzzy equivalence and similarity measure in a partition algorithm.

A Discounted Fuzzy Relational Clustering of Web Users’ Using Intuitive Augmented Sessions Dissimilarity Metric

Relational fuzzy clustering (RFC) algorithms prove very useful in Web user session clustering because Web user sessions may contain fuzzy, conflicting and imprecise information. Though RFC algorithms are very sensitive to cluster initialization and works only if the numbers of clusters are specified in advance. However, at all times, the prior initialization of a number of clusters is not feasible due to the dynamically evolving nature of user sessions. Therefore, estimating the number of clusters and initializing suitable cluster prototype are a significant performance bottleneck in this method. In this paper, the discounted fuzzy relational clustering (DFRC) algorithm is proposed to address the major constraint of RFC. The DFRC algorithm identifies Web user session clusters from Web server access logs, without initializing the number of clusters and prototypes of initial clusters. The DFRC algorithm works in two stages. In the first stage, DFRC automatically identifies the number of potential clusters based on the successively discounted potential density function value of each relational data and their respective centres. In the second stage, DFRC assigns fuzzy membership values to each data point and forms fuzzy clusters from the relational matrix. The DFRC algorithm is applied on an augmented session dissimilarity matrix obtained from a publicly accessed NASA Web server log data. The experimental results are evaluated using different fuzzy validity measures. The extensive experiments are performed to test the effect of various parameters, including accept/reject ratio and neighbourhood radius on the performance of DFRC algorithm. The results were also compared with fuzzy relational clustering algorithm using cluster quality measures. It is observed that the quality of generated clusters using DFRC is superior as compared with that of RFC.

Fuzzy Distance Measure and Fuzzy Clustering Algorithm

A modified dissimilarity measure for fuzzy data is proposed and is applied to real data with mixed feature variables of symbolic and fuzzy data. We also proposed an improved version of fuzzy relational clustering algorithm. Numerical examples and comparison are given between mixed variable fuzzy C-means and fuzzy relational clustering algorithm.

Aggregated Probabilistic Fuzzy Relational Sentence Level Expectation Maximization Clustering Algorithm for Efficient Text Categorization

Now a days, Text clustering becomes an important application to organize the data and to extract useful information from the available corpus. Many previous clustering techniques have difficulties in handling extreme outliers but fuzzy clustering algorithms tend to give them very small membership degree in surrounding clusters. In this paper we proposed an aggregated probabilistic Fuzzy relational sentence level expectation maximization clustering algorithm for efficient text categorization. It will give the accurate and maximum similarity by finding the relevance of sentences which belongs to a particular cluster. This technique leads to a fuzzy partition of the sentences and find out the accurate probability of the words belongs to a cluster. This algorithm is particularly used in finding maximum likelihood estimates of words in a given sentence. It gives the low search results with highest accuracy. The practical results show that the proposed method obtains better and accurate results for getting best sentence-wise text classification when compared with the existing methods.

Cell formation using fuzzy relational clustering algorithm

Cellular manufacturing is a useful way to improve overall manufacturing performance. Group technology is used to increase the productivity for manufacturing high quality products and improving the flexibility of manufacturing systems. Cell formation is an important step in group technology. It is used in designing good cellular manufacturing systems. The key step in designing any cellular manufacturing system is the identification of part families and machine groups for the creation of cells that uses the similarities between parts in relation to the machines in their manufacture. There are two basic procedures for cell formation in group technology. One is part-family formation and the other is machine–cell formation. In this paper, we apply a fuzzy relational data clustering algorithm to form part families and machine groups. A real data study shows that the proposed approach performs well based on the grouping efficiency proposed by Chandrasekharan and Rajagopalan.

A novel approach to fuzzy clustering based on a dissimilarity relation extracted from data using a TS system

Clustering refers to the process of unsupervised partitioning of a data set based on a dissimilarity measure, which determines the cluster shape. Considering that cluster shapes may change from one cluster to another, it would be of the utmost importance to extract the dissimilarity measure directly from the data by means of a data model. On the other hand, a model construction requires some kind of supervision of the data structure, which is exactly what we look for during clustering. So, the lower the supervision degree used to build the data model, the more it makes sense to resort to a data model for clustering purposes. Conscious of this, we propose to exploit very few pairs of patterns with known dissimilarity to build a TS system which models the dissimilarity relation. Among other things, the rules of the TS system provide an intuitive description of the dissimilarity relation itself. Then we use the TS system to build a dissimilarity matrix which is fed as input to an unsupervised fuzzy relational clustering algorithm, denoted any relation clustering algorithm (ARCA), which partitions the data set based on the proximity of the vectors containing the dissimilarity values between each pattern and all the other patterns in the data set. We show that combining the TS system and the ARCA algorithm allows us to achieve high classification performance on a synthetic data set and on two real data sets. Further, we discuss how the rules of the TS system represent a sort of linguistic description of the dissimilarity relation.

Combining supervised and unsupervised learning for data clustering

Clustering aims to partition a data set into homogenous groups which gather similar objects. Object similarity, or more often object dissimilarity, is usually expressed in terms of some distance function. This approach, however, is not viable when dissimilarity is conceptual rather than metric. In this paper, we propose to extract the dissimilarity relation directly from the available data. To this aim, we train a feedforward neural network with some pairs of points with known dissimilarity. Then, we use the dissimilarity measure generated by the network to guide a new unsupervised fuzzy relational clustering algorithm. An artificial data set and a real data set are used to show how the clustering algorithm based on the neural dissimilarity outperforms some widely used (possibly partially supervised) clustering algorithms based on spatial dissimilarity.

A new fuzzy relational clustering algorithm based on the fuzzy C-means algorithm

In this paper, we show how one can take advantage of the stability and effectiveness of object data clustering algorithms when the data to be clustered are available in the form of mutual numerical relationships between pairs of objects. More precisely, we propose a new fuzzy relational algorithm, based on the popular fuzzy C-means (FCM) algorithm, which does not require any particular restriction on the relation matrix. We describe the application of the algorithm to four real and four synthetic data sets, and show that our algorithm performs better than well-known fuzzy relational clustering algorithms on all these sets.

A fuzzy relational clustering algorithm based on a dissimilarity measure extracted from data.

One of the critical aspects of clustering algorithms is the correct identification of the dissimilarity measure used to drive the partitioning of the data set. The dissimilarity measure induces the cluster shape and therefore determines the success of clustering algorithms. As cluster shapes change from a data set to another, dissimilarity measures should be extracted from data. To this aim, we exploit some pairs of points with known dissimilarity value to teach a dissimilarity relation to a feed-forward neural network. Then, we use the neural dissimilarity measure to guide an unsupervised relational clustering algorithm. Experiments on synthetic data sets and on the Iris data set show that the relational clustering algorithm based on the neural dissimilarity outperforms some popular clustering algorithms (with possible partial supervision) based on spatial dissimilarity.

Robust fuzzy clustering of relational data

Popular relational-data clustering algorithms, relational dual of fuzzy c-means (RFCM), non-Euclidean RFCM (NERFCM) (both by Hathaway et al), and FANNY (by Kaufman and Rousseeuw) are examined. A new algorithm, which is a generalization of FANNY, called the fuzzy relational data clustering (FRC) algorithm, is introduced, having an identical objective functional as RFCM. However, the FRC does not have the restriction of RFCM, which is that the relational data is derived from Euclidean distance as the measure of dissimilarity between the objects, and it also does not have limitations of FANNY, including the use of a fixed membership exponent, or a fuzzifier exponent, m. The FRC algorithm is further improved by incorporating the concept of Dave's object data noise clustering (NC) algorithm, done by proposing a concept of noise-dissimilarity. Next, based on the constrained minimization, which includes an inequality constraint for the memberships and corresponding Kuhn-Tucker conditions, a noise resistant, FRC algorithm is derived which works well for all types of non-Euclidean dissimilarity data. Thus it is shown that the extra computations for data expansion (/spl beta/-spread transformation) required by the NERFCM algorithm are not necessary. This new algorithm is called robust non-Euclidean fuzzy relational data clustering (robust-NE-FRC), and its robustness is demonstrated through several numerical examples. Advantages of this new algorithm are: faster convergence, robustness against outliers, and ability to handle all kinds of relational data, including non-Euclidean. The paper also presents a new and better interpretation of the noise-class.