Related Clustering Methods Research Articles

A method of relational fuzzy clustering based on producing feature vectors using FastMap

The first stage of organizing objects is to partition them into groups or clusters. The clustering is generally done on individual object data representing the entities such as feature vectors or on object relational data incorporated in a proximity matrix. This paper describes another method for finding a fuzzy membership matrix that provides cluster membership values for all the objects based strictly on the proximity matrix. This is generally referred to as relational data clustering. The fuzzy membership matrix is found by first finding a set of vectors that approximately have the same inter-vector Euclidian distances as the proximities that are provided. These vectors can be of very low dimension such as 5 or less. Fuzzy c-means (FCM) is then applied to these vectors to obtain a fuzzy membership matrix. In addition two-dimensional vectors are also created to provide a visual representation of the proximity matrix. This allows comparison of the result of automatic clustering to visual clustering. The method proposed here is compared to other relational clustering methods including NERFCM, Rouben’s method and Windhams A-P method. Various clustering quality indices are also calculated for doing the comparison using various proximity matrices as input. Simulations show the method to be very effective and no more computationally expensive than other relational data clustering methods. The membership matrices that are produced by the proposed method are less crisp than those produced by NERFCM and more representative of the proximity matrix that is used as input to the clustering process.

Fuzzy Relational Fixed Point Clustering

The proposed relational fuzzy clustering method, called FRFP (fuzzy relational fixed point), is based on determining a fixed point of a function of the desired membership matrix. The ethod is compared to other relational clustering methods. Simulations show the method to be very effective and less computationally expensive than other fuzzy relational data clustering methods. The membership matrices that are produced by the proposed method are less crisp than those produced by NERFCM and more representative of the proximity matrix that is used as input to the clustering process.

Fuzzy Relational Fixed Point Clustering

The proposed relational fuzzy clustering method, called FRFP (fuzzy relational fixed point), is based on determining a fixed point of a function of the desired membership matrix. The ethod is compared to other relational clustering methods. Simulations show the method to be very effective and less computationally expensive than other fuzzy relational data clustering methods. The membership matrices that are produced by the proposed method are less crisp than those produced by NERFCM and more representative of the proximity matrix that is used as input to the clustering process.

Fuzzy Clustering and Aggregation of Relational Data With Instance-Level Constraints

In this paper, we introduce a semisupervised approach for clustering and aggregating relational data (SS-CARD). We assume that data is available in a relational form, where information only about the degrees to which pairs of objects in the dataset are related is available. Moreover, we assume that the relational information is represented by multiple dissimilarity matrices. These matrices could have been generated using different features, different mappings, or even different sensors. SS-CARD is designed to aggregate pairwise distances from multiple relational matrices, partition the data into clusters, and learn a relevance weight for each matrix in each cluster simultaneously. These weights have two main advantages. First, they help in partitioning the data into more meaningful clusters. Second, they can be used as part of a more complex learning system to enhance its learning behavior. SS-CARD uses partial supervision information that consists of a small set of constraints on which instances (should link) or ( should not link) reside in the same cluster. This additional information can guide the algorithm in learning the optimal relevance weights and in generating a better partition. The performance of the proposed algorithm is illustrated by using it in two different applications. The first one consists of categorizing the discrete nominal-valued mushroom data. The second application consists of categorizing a collection of images where each image is represented by several continuous features. For both applications, we represent the pairwise image dissimilarities by multiple relational matrices extracted from different feature sets. The results are compared with those obtained by three traditional relational clustering methods. We show that the partial supervision information and the learned aggregation weights can improve the results significantly.

Dealing with non-metric dissimilarities in fuzzy central clustering algorithms

Clustering is the problem of grouping objects on the basis of a similarity measure among them. Relational clustering methods can be employed when a feature-based representation of the objects is not available, and their description is given in terms of pairwise (dis)similarities. This paper focuses on the relational duals of fuzzy central clustering algorithms, and their application in situations when patterns are represented by means of non-metric pairwise dissimilarities. Symmetrization and shift operations have been proposed to transform the dissimilarities among patterns from non-metric to metric. In this paper, we analyze how four popular fuzzy central clustering algorithms are affected by such transformations. The main contributions include the lack of invariance to shift operations, as well as the invariance to symmetrization. Moreover, we highlight the connections between relational duals of central clustering algorithms and central clustering algorithms in kernel-induced spaces. One among the presented algorithms has never been proposed for non-metric relational clustering, and turns out to be very robust to shift operations.

Fuzzy relational clustering based on comparing two proximity matrices with utilization of particle swarm optimization

The first stage of knowledge acquisition and reduction of complexity concerning a group of entities is to partition or divide the entities into groups or clusters based on their attributes or characteristics. Clustering algorithms normally require both a method of measuring proximity between patterns and prototypes and a method for aggregating patterns. However sometimes feature vectors or patterns may not be available for objects and only the proximities between the objects are known. Even if feature vectors are available some of the features may not be numeric and it may not be possible to find a satisfactory method of aggregating patterns for the purpose of determining prototypes. Clustering of objects however can be performed on the basis of data describing the objects in terms of feature vectors or on the basis of relational data. The relational data is in terms of proximities between objects. Clustering of objects on the basis of relational data rather than individual object data is called relational clustering. The premise of this paper is that the proximities between the membership vectors, which are obtained as the objective of clustering, should be proportional to the proximities between the objects. The values of the components of the membership vector corresponding to an object are the membership degrees of the object in the various clusters. The membership vector is just a type of feature vector. Based on this premise, this paper describes another fuzzy relational clustering method for finding a fuzzy membership matrix. The method involves solving a rather challenging optimization problem, since the objective function has many local minima. This makes the use of a global optimization method such as particle swarm optimization (PSO) attractive for determining the membership matrix for the clustering. To minimize computational effort, a Bayesian stopping criterion is used in combination with a multi-start strategy for the PSO. Other relational clustering methods generally find local optimum of their objective function.

Multiorder Neurons for Evolutionary Higher-Order Clustering and Growth

This letter proposes to use multiorder neurons for clustering irregularly shaped data arrangements. Multiorder neurons are an evolutionary extension of the use of higher-order neurons in clustering. Higher-order neurons parametrically model complex neuron shapes by replacing the classic synaptic weight by higher-order tensors. The multiorder neuron goes one step further and eliminates two problems associated with higher-order neurons. First, it uses evolutionary algorithms to select the best neuron order for a given problem. Second, it obtains more information about the underlying data distribution by identifying the correct order for a given cluster of patterns. Empirically we observed that when the correlation of clusters found with ground truth information is used in measuring clustering accuracy, the proposed evolutionary multiorder neurons method can be shown to outperform other related clustering methods. The simulation results from the Iris, Wine, and Glass data sets show significant improvement when compared to the results obtained using self-organizing maps and higher-order neurons. The letter also proposes an intuitive model by which multiorder neurons can be grown, thereby determining the number of clusters in data.

A genetic k-medoids clustering algorithm

We propose a hybrid genetic algorithm for k-medoids clustering. A novel heuristic operator is designed and integrated with the genetic algorithm to fine-tune the search. Further, variable length individuals that encode different number of medoids (clusters) are used for evolution with a modified Davies-Bouldin index as a measure of the fitness of the corresponding partitionings. As a result the proposed algorithm can efficiently evolve appropriate partitionings while making no a priori assumption about the number of clusters present in the datasets. In the experiments, we show the effectiveness of the proposed algorithm and compare it with other related clustering methods.

Relational mountain (density) clustering method and web log analysis

The mountain clustering method and the subtractive clustering method are useful methods for finding cluster centers based on local density in object data. These methods have been extended to shell clustering. In this article, we propose a relational mountain clustering method (RMCM), which produces a set of (proto) typical objects as well as a crisp partition of the objects generating the relation, using a new concept that we call relational density. We exemplify RMCM by clustering several relational data sets that come from object data. Finally, RMCM is applied to web log analysis, where it produces useful user profiles from web log data. © 2005 Wiley Periodicals, Inc. Int J Int Syst 20: 375–392, 2005.

Modified ART 2A growing network capable of generating a fixed number of nodes.

This paper introduces the Adaptive Resonance Theory under Constraint (ART-C 2A) learning paradigm based on ART 2A, which is capable of generating a user-defined number of recognition nodes through online estimation of an appropriate vigilance threshold. Empirical experiments compare the cluster validity and the learning efficiency of ART-C 2A with those of ART 2A, as well as three closely related clustering methods, namely online K-Means, batch K-Means, and SOM, in a quantitative manner. Besides retaining the online cluster creation capability of ART 2A, ART-C 2A gives the alternative clustering solution, which allows a direct control on the number of output clusters generated by the self-organizing process.

EVCLUS: evidential clustering of proximity data.

A new relational clustering method is introduced, based on the Dempster-Shafer theory of belief functions (or evidence theory). Given a matrix of dissimilarities between n objects, this method, referred to as evidential clustering (EVCLUS), assigns a basic belief assignment (or mass function) to each object in such a way that the degree of conflict between the masses given to any two objects reflects their dissimilarity. A notion of credal partition is introduced, which subsumes those of hard, fuzzy, and possibilistic partitions, allowing to gain deeper insight into the structure of the data. Experiments with several sets of real data demonstrate the good performances of the proposed method as compared with several state-of-the-art relational clustering techniques.

A Structured Family of Clustering and Tree Construction Methods

A cluster A is an Apresjan cluster if every pair of objects within A is more similar than either is to any object outside A. The criterion is intuitive, compelling, but often too restrictive for applications in classification. We therefore explore extensions of Apresjan clustering to a family of related hierarchical clustering methods. The extensions are shown to be closely connected with the well-known single and average linkage tree constructions. A dual family of methods for classification by splits is also presented. Splits are partitions of the set of objects into two disjoint blocks and are widely used in domains such as phylogenetics. Both the cluster and split methods give rise to progressively refined tree representations. We exploit dualities and connections between the various methods, giving polynomial time construction algorithms for most of the constructions and NP-hardness results for the rest.

Self-organization of pulse-coupled oscillators with application to clustering

We introduce an efficient synchronization model that organizes a population of integrate-and-fire oscillators into stable and structured groups. Each oscillator fires synchronously with all the others within its group, but the groups themselves fire with a constant phase difference. The structure of the synchronized groups depends on the choice of the coupling function. We show that by defining the interaction between oscillators according to the relative distance between them, our model can be used as a general clustering algorithm. Unlike existing models, our model incorporates techniques from relational and prototype-based clustering methods and results in a clustering algorithm that is simple, efficient, robust, unbiased by the size of the clusters, and that can find an arbitrary number of clusters. In addition to helping the model self-organize into stable groups, the synergy between clustering and synchronization reduces the computational complexity significantly. The resulting clustering algorithm has several advantages over conventional clustering techniques. In particular, it can generate a nested sequence of partitions and it can determine the optimum number of clusters in an efficient manner. Moreover, since our approach does not involve optimizing an objective function, it is not sensitive to initialization and it can incorporate nonmetric similarity measures. We illustrate the performance of our algorithms with several synthetic and real data sets.

5241652 System for performing rule partitioning in a rete networkWilliam Barabash, William Yerazunis assigned to Digital Equipment Corporation

Deng proposed grey clustering analysis (GCA) in 1987. Later, Jin presented a new method in 1993, called grey relational clustering (GRC) method that combined grey relational analysis with clustering. However, the GRC method cannot use a tree diagram to make appropriate classification decisions without re-computation. This study thus attempts to combine GRC and hierarchical clustering analysis. Given the existence of an excess of medical resources in the Taipei area, this study attempts to understand the degree of concentration of medical resources in this area. Specifically, this study applies a geographical information system (GIS) to present the geographical distribution of hospitals in Taipei. Additionally, a new-type of cluster analysis, known as hierarchical grey relation clustering analysis, is used to analyze the distribution of hospitals and understand how they compete with one another. The analytical results demonstrate that hierarchical grey relation clustering analysis is a suitable method of analyzing geographical position. Tree diagrams can help policymakers make appropriate classification decisions without re-computation. The study results can inform hospitals of their competitors and help them to develop appropriate responses. Additionally, the analytical results can also provide a reference to government or hospital policymakers to help them position hospitals in areas, thus achieving a better distribution of medical resources in Taipei.