Clustering is the unsupervised classification of patterns (observations, data items, or feature vectors) into groups (clusters). The clustering problem has been addressed in many contexts and by researchers in many disciplines; this reflects its broad appeal and usefulness as one of the steps in exploratory data analysis. However, clustering is a difficult problem combinatorially, and differences in assumptions and contexts in different communities has made the transfer of useful generic concepts and methodologies slow to occur. This paper presents an overview of pattern clustering methods from a statistical pattern recognition perspective, with a goal of providing useful advice and references to fundamental concepts accessible to the broad community of clustering practitioners. We present a taxonomy of clustering techniques, and identify cross-cutting themes and recent advances. We also describe some important applications of clustering algorithms such as image segmentation, object recognition, and information retrieval.

Motivated by applications such as document and image classification in information retrieval, we consider the problem of clustering dynamic point sets in a metric space. We propose a model called incremental clustering which is based on a careful analysis of the requirements of the information retrieval application, and which should also be useful in other applications. The goal is to efficiently maintain clusters of small diameter as new points are inserted. We analyze several natural greedy algorithms and demonstrate that they perform poorly. We propose new deterministic and randomized incremental clustering algorithms which have a provably good performance. We complement our positive results with lower bounds on the performance of incremental algorithms. Finally, we consider the dual clustering problem where the clusters are of fixed diameter, and the goal is to minimize the number of clusters. 1 Introduction We consider the following problem: as a sequence of points from a metric...

We present and analyze the off-line star algorithm for clustering static information systems and the on-line star algorithm for clustering dynamic information systems. These algorithms organize a document collection into a number of clusters that is naturally induced by the collection via a computationally efficient cover by dense subgraphs. We further show a lower bound on the quality of the clusters produced by these algorithms as well as demonstrate that these algorithms are efficient (running times roughly linear in the size of the problem). Finally, we provide data from a number of experiments.

Current best-match ranking (BMR) systems perform well but cannot handle word mismatch between a query and a document. The best known alternative ranking method, hierarchical clustering-based ranking (HCR), seems to be more robust than BMR with respect to this problem, but it is hampered by theoretical and practical limitations. We present an approach to document ranking that explicitly addresses the word mismatch problem by exploiting interdocument similarity information in a novel way. Document ranking is seen as a querydocument transformation driven by a conceptual representation of the whole document collection, into which the query is merged. Our approach is based on the theory of concept (or Galois) lattices, which, we argue, provides a powerful, well-founded, and computationallytractable framework to model the space in which documents and query are represented and to compute such a transformation. We compared information retrieval using concept lattice-based ranking (CLR) to BMR and HCR. The results showed that HCR was outperformed by CLR as well as by BMR, and suggested that, of the two best methods, BMR achieved better performance than CLR on the whole document set while CLR compared more favorably when only the first retrieved documents were used for evaluation. We also evaluated the three methods' specific ability to rank documents that did not match the query, in which case the superiority of CLR over BMR and HCR (and that of HCR over BMR) was apparent.

Visualization systems traditionally focus on graphical representation of information. They tend not to provide integrated analytical services that could aid users in tackling complex knowledge discovery tasks. Users’ exploration in such environments is usually impeded due to several problems: 1) valuable information is hard to discover when too much data is visualized on the screen; 2) Users have to manage and organize their discoveries off line, because no systematic discovery management mechanism exists; 3) their discoveries based on visual exploration alone may lack accuracy; 4) and they have no convenient access to the important knowledge learned by other users. To tackle these problems, it has been recognized that analytical tools must be introduced into visualization systems. In this paper, we present a novel analysis-guided exploration system, called the Nugget Management System (NMS). It leverages the collaborative effort of human comprehensibility and machine computations to facilitate users ’ visual exploration processes. Specifically, NMS first extracts the valuable information (nuggets) hidden in datasets based on the interests of users. Given that similar nuggets may be re-discovered by different users, NMS consolidates the nugget candidate set by clustering based on their semantic similarity. To solve the problem of inaccurate discoveries, localized data mining techniques are applied to refine the nuggets to best represent the captured patterns in datasets. Lastly, the resulting well-organized nugget pool is used to guide users ’ exploration. To evaluate the effectiveness of NMS, we integrated NMS into XmdvTool, a freeware multivariate visualization system. User studies were performed to compare the users ’ efficiency and accuracy in finishing tasks on real datasets, with and without the help of NMS. Our user studies confirmed the effectiveness of NMS.

We propose a unique cluster-based retrieval (CBR) strategy using a new cluster-skipping inverted file for improving query processing efficiency. The new inverted file incorporates cluster membership and centroid information along with the usual document information into a single structure. In our incremental-CBR strategy, during query evaluation both best(-matching) clusters and best(-matching) documents of such clusters are computed together with a single posting list access per query term. As we switch from term to term, best clusters are recomputed and can dynamically change. During query-document matching, only relevant portions of the posting lists corresponding to the best clusters are considered and the rest is skipped. The proposed approach is essentially tailored for environments where inverted files are compressed, and provides substantial efficiency improvements while yielding comparable or sometimes better effectiveness figures. Our experiments with various collections show that, the incremental-CBR strategy using compressed cluster-skipping inverted file significantly improves CPU time efficiency regardless of the query length. The new compressed inverted file imposes an acceptable storage overhead in comparison to a typical inverted file. We also show that our approach scales well with the collection size.

Clustering algorithms typically assume that the available data constitute a random sample from a stationary distribution. As data accumulate over time the underlying process that generates them can change. Thus, the development of algorithms that can extract clustering rules in non-stationary environments is necessary. In this paper, we present an extension of the k-windows algorithm that can track the evolution of cluster models in dynamically changing databases, without a significant computational overhead. Experiments show that the k-windows algorithm can effectively and efficiently identify the changes on the pattern structure. Ó 2005 Elsevier B.V. All rights reserved.

We present an algorithm for clustering nominal data that is based on a metric on the set of partitions of a finite set of objects; this metric is defined starting from a lower valuation of the lattice of partitions. The proposed algorithm seeks to determine a clustering partition such that the total distance between this partition and the partitions determined by the attributes of the objects has a local minimum. The resulting clustering is quite stable relative to the ordering of the objects.

Clustering techniques were originally conceived by Aristotle and Theophrastos in the fourth century B.C. and in the 18th century by Linnaeus [6], but it was not until 1939 when one of the first comprehensive foundations of these methods was published [9]. Clustering is a fundamental process in the knowledge acquisition domain. It refers to the partitioning of a sets of objects in groups (clusters) such that objects within the same group are more similar to each other than objects in different groups. Even the simplest clustering problems are known to be NP-Hard [1]. For instance the Euclidean k-center problem in the plane is NP-Hard [7]. In general, the clustering problem can be defined as: Given a set S of n points in a d–dimensional metric space (R d, ρ) and an integer k � n, compute a partition Σ of S into k subsets S1,..., Sk, such that Σ has the smallest possible size. Each Si is called a cluster and k is called the number of clusters. We define the size of a cluster Si to be the maximum distance (under the ρ-metric) between a fixed point ci called center of the cluster and a point of Si. The size of a partition is defined as the maximum size of a cluster in the partition.

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