Finding useful patterns in large datasets has attracted considerable interest recently, and one of the most widely st,udied problems in this area is the identification of clusters, or deusel y populated regions, in a multi-dir nensional clataset. Prior work does not adequately address the problem of large datasets and minimization of 1/0 costs. This paper presents a data clustering method named Bfll (;”H (Balanced Iterative Reducing and Clustering using Hierarchies), and demonstrates that it is especially suitable for very large databases. BIRCH incrementally and clynamicall y clusters incoming multi-dimensional metric data points to try to produce the best quality clustering with the available resources (i. e., available memory and time constraints). BIRCH can typically find a goocl clustering with a single scan of the data, and improve the quality further with a few aclditioual scans. BIRCH is also the first clustering algorithm proposerl in the database area to handle “noise) ’ (data points that are not part of the underlying pattern) effectively. We evaluate BIRCH’S time/space efficiency, data input order sensitivity, and clustering quality through several experiments. We also present a performance comparisons of BIR (;’H versus CLARA NS, a clustering method proposed recently for large datasets, and S11OW that BIRCH is consistently 1

Accrue Software, Inc. Clustering is a division of data into groups of similar objects. Representing the data by fewer clusters necessarily loses certain fine details, but achieves simplification. It models data by its clusters. Data modeling puts clustering in a historical perspective rooted in mathematics, statistics, and numerical analysis. From a machine learning perspective clusters correspond to hidden patterns, the search for clusters is unsupervised learning, and the resulting system represents a data concept. From a practical perspective clustering plays an outstanding role in data mining applications such as scientific data exploration, information retrieval and text mining, spatial database applications, Web analysis, CRM, marketing, medical diagnostics, computational biology, and many others. Clustering is the subject of active research in several fields such as statistics, pattern recognition, and machine learning. This survey focuses on clustering in data mining. Data mining adds to clustering the complications of very large datasets with very many attributes of different types. This imposes unique

Clustering techniques are used in database mining for finding interesting patterns in high dimensional data. These are useful in various applications of knowledge discovery in databases. Some challenges in clustering for large data sets in terms of scalability, data distribution, understanding end-results, and sensitivity to input order, have received attention in the recent past. Recent approaches attempt to find clusters embedded in subspaces of high dimensional data. In this paper we propose the use of adaptive grids for efficient and scalable computation of clusters in subspaces for large data sets and large number of dimensions. The bottom-up algorithm for subspace clustering computes the dense units in all dimensions and combines these to generate the dense units in higher dimensions. Computation is heavily dependent on the choice of the partitioning parameter chosen to partition each dimension into intervals (bins) to be tested for density. The number of bins determine...

. This paper presents the Collective Hierarchical Clustering (CHC) algorithm for analyzing distributed, heterogeneous data. This algorithm first generates local cluster models and then combines them to generate the global cluster model of the data. The proposed algorithm runs in O(jSjn 2 ) time, with a O(jSjn) space requirement and O(n) communication requirement, where n is the number of elements in the data set and jSj is the number of data sites. This approach shows significant improvement over naive methods with O(n 2 ) communication costs in the case that the entire distance matrix is transmitted and O(nm) communication costs to centralize the data, where m is the total number of features. A specific implementation based on the single link clustering and results comparing its performance with that of a centralized clustering algorithm are presented. An analysis of the algorithm complexity, in terms of overall computation time and communication requirements, is pres...

This paper considers distributed clustering of high dimensional heterogeneous data using a distributed Principal Component Analysis (PCA) technique called the Collective PCA. It presents the Collective PCA technique that can be used independent of the clustering application. It shows a way to integrate the Collective PCA with a given o-the-shelf clustering algorithm in order to develop a distributed clustering technique. It also presents experimental results using dierent test data sets including an application for web mining.

The problem of record linkage focuses on determining whether two object descriptions refer to the same underlying entity. Addressing this problem effectively has many practical applications, e.g., elimination of duplicate records in databases and citation matching for scholarly articles. In this paper, we consider a new domain where the record linkage problem is manifested: Internet comparison shopping. We address the resulting linkage setting that requires learning a similarity function between record pairs from streaming data. The learned similarity function is subsequently used in clustering to determine which records are co-referent and should be linked. We present an online machine learning method for addressing this problem, where a composite similarity function based on a linear combination of basis functions is learned incrementally. We illustrate the efficacy of this approach on several real-world datasets from an Internet comparison shopping site, and show that our method is able to effectively learn various distance functions for product data with differing characteristics. We also provide experimental results that show the importance of considering multiple performance measures in record linkage evaluation. 1

This paper describes the design and implementation on MIMD parallel machines of P-AutoClass, a parallel version of the AutoClass system based upon the Bayesian method for determining optimal classes in large datasets. The P-AutoClass implementation divides the clustering task among the processors of a multicomputer so that they work on their own partition and exchange their intermediate results. The system architecture, its implementation and experimental performance results on different processor numbers and dataset sizes are presented and discussed. In particular, efficiency and scalability of P-AutoClass versus the sequential AutoClass system are evaluated and compared. 1

Ant-based clustering and sorting is a nature-inspired heuristic for general clustering tasks. It has been applied variously, from problems arising in commerce, to circuit design, to text-mining, all with some promise. However, although early results were broadly encouraging, there has been very limited analytical evaluation of the algorithm. Toward this end, we first propose a scheme that enables unbiased interpretation of the clustering solutions obtained, and then use this to conduct a full evaluation of the algorithm. Our analysis uses three sets each of real and artificial data, and four distinct analytical measures. These results are compared with those obtained using established clustering techniques and we find evidence that ant-based clustering is a robust and viable alternative.

This paper shows that the pose clustering method of object recognition can be decomposed into small subproblems without loss of accuracy. Randomization can then be used to limit the number of subproblems that need to be examined to achieve accurate recognition. These techniques are used to decrease the computational complexity of pose clustering. The clustering step is formulated as an efficient tree search of the pose space. This method requires little memory since not many poses are clustered at a time. Analysis shows that pose clustering is not inherently more sensitive to noise than other methods of generating hypotheses. Finally, experiments on real and synthetic data are presented. 1 Introduction Model-based object recognition systems determine which objects appear in images using a catalog of object models and estimate their positions and orientations (poses) relative to the camera. This paper examines methods of improving the efficiency of the pose clustering method of object ...

Clustering is a data mining problem which finds dense regions in a sparse multi-dimensional data set. The attribute values and ranges of these regions characterize the clusters. Clustering algorithms need to scale with the data base size and also with the large dimensionality of the data set. Further, these algorithms need to explore the embedded clusters in a sub-space of a high dimensional space. However, the time complexity of the algorithm to explore clusters in subspaces is exponential in the dimension-ality of the data and is thus extremely compute intensive. Thus, paral-lelization is the choice for discovering clusters for large data sets. In this paper we present a scalable parallel subspace clustering algorithm which has both data and task parallelism embedded in it. We also formulate the technique of adaptive grids and present a truly un-supervised clustering al-gorithm requiring no user inputs. Our implementation shows near linear speedups with negligible communication overheads. The use of adaptive grids results in two orders of magnitude improvement in the computation time of our serial algorithm over current methods with much better quality of clustering. Performance results on both real and synthetic data sets with very large number of dimensions on a 16 node IBM SP2 demonstrate our algorithm to be a practical and scalable clustering technique. 1.