Data Clustering Model Research Articles

Fuzzy C-means Model and Algorithm for Data Clustering

Fuzzy C-means Model and Algorithm for Data Clustering

Laplacian Regularized Gaussian Mixture Model for Data Clustering

Gaussian Mixture Models (GMMs) are among the most statistically mature methods for clustering. Each cluster is represented by a Gaussian distribution. The clustering process thereby turns to estimate the parameters of the Gaussian mixture, usually by the Expectation-Maximization algorithm. In this paper, we consider the case where the probability distribution that generates the data is supported on a submanifold of the ambient space. It is natural to assume that if two points are close in the intrinsic geometry of the probability distribution, then their conditional probability distributions are similar. Specifically, we introduce a regularized probabilistic model based on manifold structure for data clustering, called Laplacian regularized Gaussian Mixture Model (LapGMM). The data manifold is modeled by a nearest neighbor graph, and the graph structure is incorporated in the maximum likelihood objective function. As a result, the obtained conditional probability distribution varies smoothly along the geodesics of the data manifold. Experimental results on real data sets demonstrate the effectiveness of the proposed approach.

A Fuzzy Clustering Model for Fuzzy Data with Outliers

This paper proposes a fuzzy clustering model for fuzzy data with outliers. The model is based on Wasserstein distance between interval valued data, which is generalized to fuzzy data. In addition, Keller’s approach is used to identify outliers and reduce their influences. The authors also define a transformation to change the distance to the Euclidean distance. With the help of this approach, the problem of fuzzy clustering of fuzzy data is reduced to fuzzy clustering of crisp data. In order to show the performance of the proposed clustering algorithm, two simulation experiments are discussed.

A fuzzy case based reasoning approach to value engineering

This paper is intended to assist the experts during the creativity phase of value engineering through utilizing the past experiences and avoid them in a specific domain from repeating the same experience. To this purpose, a general fuzzy case based reasoning (CBR) system is developed. Our system benefits from a fuzzy clustering model for fuzzy data to facilitate case retrieval and reduce the time complexity. The inherent analogical nature of a case-based reasoning (CBR) model and its integration with fuzzy theory would facilitate access to more precise and systematically classified information during a VE workshop. In order to test the performance of the proposed system, it is applied to suburban highway design data extracted from National Cooperative Highway Research Program (NCHRP) Report 282.

A regularized k-means and multiphase scale segmentation

We propose a data clustering model reduced from variational approach. This new clustering model, a regularized k-means, is an extension from the classical k-means model. It uses the sum-of-squares error for assessing fidelity, and the number of data in each cluster is used as a regularizer. The model automatically gives a reasonable number of clusters by a choice of a parameter. We explore various properties of this classification model and present different numerical results.This model is motivated by an application to scale segmentation. A typical Mumford-Shah-based image segmentation is driven by the intensity of objects in a given image, and we consider image segmentation using additional scale information in this paper. Using the scale of objects, one can further classify objects in a given image from using only the intensity value. The scale of an object is not a local value, therefore the procedure for scale segmentation needs to be separated into two steps: multiphase segmentation and scale clustering. The first step requires a reliable multiphase segmentation where we applied unsupervised model, and apply a regularized k-means for a fast automatic data clustering for the second step. Various numerical results are presented to validate the model.

Fuzzy evolutionary optimization modeling and its applications to unsupervised categorization and extractive summarization

Modern information retrieval (IR) systems consist of many challenging components, e.g. clustering, summarization, etc. Nowadays, without browsing the whole volume of datasets, IR systems present users with clusters of documents they are interested in, and summarize each document briefly which facilitates the task of finding the desired documents. This paper proposes a fuzzy evolutionary optimization modeling (FEOM) and its applications to unsupervised categorization and extractive summarization. In view of the nature of biological evolution, we take advantage of several fuzzy control parameters to adaptively regulate the behaviors of the evolutionary optimization, which can effectively prevent premature convergence to a local optimal solution. As a portable, modular and extensively executable model, FEOM is firstly implemented for clustering text documents. The searching capability of FEOM is exploited to explore appropriate partitions of documents such that the similarity metric of the resulting clusters is optimized. In order to further investigate its effectiveness as a generic data clustering model, FEOM is then applied to sentence clustering based extractive document summarization. It selects the most important sentence from each cluster to represent the overall meaning of document. We demonstrate the improved performance by a series of experiments using standard test sets, e.g. Reuter document collection, 20-newsgroup corpus, DUC01 and DUC02, as evaluated by some commonly used metrics, i.e. F-measure and ROUGE. The experimental results show that FEOM achieves performance as good as or better than state of arts of clustering and summarizing systems.

*omeSOM: a software for clustering and visualization of transcriptional and metabolite data mined from interspecific crosses of crop plants

BackgroundModern biology uses experimental systems that involve the exploration of phenotypic variation as a result of the recombination of several genomes. Such systems are useful to investigate the functional evolution of metabolic networks. One such approach is the analysis of transcript and metabolite profiles. These kinds of studies generate a large amount of data, which require dedicated computational tools for their analysis.ResultsThis paper presents a novel software named *omeSOM (transcript/metabol-ome Self Organizing Map) that implements a neural model for biological data clustering and visualization. It allows the discovery of relationships between changes in transcripts and metabolites of crop plants harboring introgressed exotic alleles and furthermore, its use can be extended to other type of omics data. The software is focused on the easy identification of groups including different molecular entities, independently of the number of clusters formed. The *omeSOM software provides easy-to-visualize interfaces for the identification of coordinated variations in the co-expressed genes and co-accumulated metabolites. Additionally, this information is linked to the most widely used gene annotation and metabolic pathway databases.Conclusions*omeSOM is a software designed to give support to the data mining task of metabolic and transcriptional datasets derived from different databases. It provides a user-friendly interface and offers several visualization features, easy to understand by non-expert users. Therefore, *omeSOM provides support for data mining tasks and it is applicable to basic research as well as applied breeding programs. The software and a sample dataset are available free of charge at http://sourcesinc.sourceforge.net/omesom/.

A More Relaxed Model for Graph-Based Data Clustering: s-Plex Cluster Editing

We introduce the s-Plex Cluster Editing problem as a generalization of the well-studied Cluster Editing problem; both are NP-hard and both are motivated by graph-based data clustering. Instead of transforming a given graph by a minimum number of edge modifications into a disjoint union of cliques (this is Cluster Editing), the task in the case of s-Plex Cluster Editing is to transform a graph into a cluster graph consisting of a disjoint union of so-called s-plexes. Herein, an s-plex is a vertex set S inducing a subgraph in which every vertex has degree at least $|S|-s$. Cliques are 1-plexes. The advantage of s-plexes for $s\geq2$ is that they allow us to model a more relaxed cluster notion (s-plexes instead of cliques), better reflecting inaccuracies of the input data. We develop a provably effective preprocessing based on data reduction (yielding a so-called problem kernel), a forbidden subgraph characterization of s-plex cluster graphs, and a depth-bounded search tree which is used to find optimal edge modification sets. Altogether, this yields efficient algorithms in case of moderate numbers of edge modifications; this is often a reasonable assumption under a maximum parsimony model for data clustering.

Optimal stepwise experimental design for pairwise functional interaction studies.

Pairwise experimental perturbation is increasingly used to probe gene and protein function because these studies offer powerful insight into the activity and regulation of biological systems. Symmetric two-dimensional datasets, such as pairwise genetic interactions are amenable to an optimally designed measurement procedure because of the equivalence of cases and conditions where fewer experimental measurements may be required to extract the underlying structure. We show that optimal experimental design can provide improvements in efficiency when collecting data in an iterative manner. We develop a method built on a statistical clustering model for symmetric data and the Fisher information uncertainty estimates, and we also provide simple heuristic approaches that have comparable performance. Using yeast epistatic miniarrays as an example, we show that correct assignment of the major subnetworks could be achieved with <50% of the measurements in the complete dataset. Optimization is likely to become critical as pairwise functional studies extend to more complex mammalian systems where all by all experiments are currently intractable.

A hierarchical ant based clustering algorithm and its use in three real-world applications

In this paper is presented a new model for data clustering, which is inspired from the self-assembly behavior of real ants. Real ants can build complex structures by connecting themselves to each others. It is shown is this paper that this behavior can be used to build a hierarchical tree-structured partitioning of the data according to the similarities between those data. Several algorithms have been detailed using this model (called AntTree): deterministic or stochastic algorithms that may use or not global or local thresholds. Those algorithms have been evaluated using artificial and real databases. Our algorithms obtain competitive results when compared to the Kmeans, to ANTCLASS, and to Ascending Hierarchical Clustering. AntTree has been applied to three real world applications: the analysis of human healthy skin, the on-line mining of web sites usage, and the automatic construction of portal sites.

Stochastic process semantics for dynamical grammars

We define a class of probabilistic models in terms of an operator algebra of stochastic processes, and a representation for this class in terms of stochastic parameterized grammars. A syntactic specification of a grammar is formally mapped to semantics given in terms of a ring of operators, so that composition of grammars corresponds to operator addition or multiplication. The operators are generators for the time-evolution of stochastic processes. The dynamical evolution occurs in continuous time but is related to a corresponding discrete-time dynamics. An expansion of the exponential of such time-evolution operators can be used to derive a variety of simulation algorithms. Within this modeling framework one can express data clustering models, logic programs, ordinary and stochastic differential equations, branching processes, graph grammars, and stochastic chemical reaction kinetics. The mathematical formulation connects these apparently distant fields to one another and to mathematical methods from quantum field theory and operator algebra. Such broad expressiveness makes the framework particularly suitable for applications in machine learning and multiscale scientific modeling.

Robust analysis of MRS brain tumour data using [formula omitted]-GTM

This paper proposes a principled, self-organized, framework to manage two sources of uncertainty that are inherent in intelligent systems for medical decision support, namely outliers and missing data. The framework is applied to magnetic resonance spectra (MRS), which are indicators of the grade of malignancy in brain tumours. A model for multivariate data clustering and visualization, the generative topographic mapping (GTM), is re-formulated as a mixture of Student's t-distributions making it more robust to outliers while supporting the imputation of missing values. An important new development is the extension of the model to provide automatic feature relevance determination. Its effectiveness on the MRS data is demonstrated empirically.

Discriminative clustering

A distributional clustering model for continuous data is reviewed and new methods for optimizing and regularizing it are introduced and compared. Based on samples of discrete-valued auxiliary data associated to samples of the continuous primary data, the continuous data space is partitioned into Voronoi regions that are maximally homogeneous in terms of the discrete data. Then only variation in the primary data associated to variation in the discrete data affects the clustering; the discrete data “supervises” the clustering. Because the whole continuous space is partitioned, new samples can be easily clustered by the continuous part of the data alone. In experiments, the approach is shown to produce more homogeneous clusters than alternative methods. Two regularization methods are demonstrated to further improve the results: an entropy-type penalty for unequal cluster sizes, and the inclusion of a model for the marginal density of the primary data. The latter is also interpretable as special kind of joint distribution modeling with tunable emphasis for discrimination and the marginal density.

A weighted fuzzy c-means clustering model for fuzzy data

A fuzzy clustering model for fuzzy data is proposed. The model is based on a ‘weighted’ dissimilarity measure for comparing pairs of fuzzy data, composed by two distances, the so-called center (mode) distance and spread distance. The peculiarity of the proposed fuzzy clustering model is the objective estimation, incorporated in the clustering procedure, of suitable weights concerning the distance measures of the center and the spreads of the fuzzy data. In this way, the model objectively tunes the influence of the two components of the fuzzy data (center and spreads) for computing the mode and spread centroids in the fuzzy partitioning process. In order to show the performance of the proposed clustering algorithm, a simulation study and two illustrative applications are discussed.

An implementation for the ATLAS conditions data management based on relational DBMSs

Developing the trigger and the data acquisition (TDAQ) for A Toroidal LHC ApparatuS (ATLAS) detector at LHC poses new challenges including the requirement to monitor, calibrate and align the detector while the on line selection is running simultaneously over thousands of processors. These include slowly evolving data such as detector alignment, calibration, and robustness, as well as data from the detector control system that cannot be stored with the event data, but must be directly accessible from each event. Motivated by the ATLAS data challenges and the recent evolution of Open Source database systems such as MySQL and Postgres, we have developed an implementation of the ATLAS Conditions database system based on the MySQL Relational DBMS. Together with Postgres, MySQL is well known for performance and simplicity and an increasing number of supported features. Several issues were investigated: how to develop a programmable API that could be used everywhere through the ATLAS online and offline computing systems; what are the optimal ways to map the conditions data model into a relational model; what is the data clustering model that is best suited to address the ATLAS data volume scalability problems. Some general issues of conditions databases are also studied, including: the schema; facilities for tagging and versioning; problems involved in managing the tiny detector control data as well as the complex; interrelated detector configuration objects. The extensive tests that were performed to monitor the development of the system are also described.

A General Fuzzy Clustering Model based on Asymmetric Aggregation Operators

We have discussed a generalized fuzzy clustering model for similarity data. In this clustering model, fuzzy aggregation operators are used to define the degree of simultaneous belongingness of a pair of objects to a cluster. In this paper, asymmetric aggregation operators are proposed to classify objects based on asymmetric similarities. Using the asymmetric aggregation operators, we get clusters which represent the asymmetric structure between objects. Moreover, the validity of this model is shown both by investigating the features of the model and through numerical applications.

Dynamic clustering for time incremental data

The aim of this article is to propose a model for on-line data clustering when a new subset of data accumulates after an interval of time. The new data may be absorbed in the old clusters or form new clusters or appear as stray data. The absorbed data may cause the clusters to grow so that two grown clusters may merge to form a single cluster. On the other hand, a large number of absorbed data may change the density profile of a cluster so that it should be split into two or more clusters. Procedures to compute these situations are proposed.