Spatial data mining is the discovery of interesting relationships and characteristics that may exist implicitly in spatial databases. In this paper, we explore whether clustering methods have a role to play in spatial data mining. To this end, we develop a new clustering method called CLARANS which is based on randomized search. We also de- velop two spatial data mining algorithms that use CLARANS. Our analysis and experiments show that with the assistance of CLARANS, these two algorithms are very effective and can lead to discoveries that are difficult to find with current spatial data mining algorithms.

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

We propose a method (the \Gap statistic") for estimating the number of clusters (groups) in a set of data. The technique uses the output of any clustering algorithm (e.g. k-means or hierarchical), comparing the change in within cluster dispersion to that expected under an appropriate reference null distribution. Some theory is developed for the proposal and a simulation study that shows that the Gap statistic usually outperforms other methods that have been proposed in the literature. We also briey explore application of the same technique to the problem for estimating the number of linear principal components. 1 Introduction Cluster analysis is an important tool for \unsupervised" learning| the problem of nding groups in data without the help of a response variable. A major challenge in cluster analysis is estimation of the optimal number of \clusters". Figure 1 (top right) shows a typical plot of an error measure W k (the within cluster dispersion dened below) for a clustering pr...

Prolonged network lifetime, scalability, and load balancing are important requirements for many ad-hoc sensor network applications. Clustering sensor nodes is an effective technique for achieving these goals. In this work, we propose a new energy-efficient approach for clustering nodes in adhoc sensor networks. Based on this approach, we present a protocol, HEED (Hybrid Energy-Efficient Distributed clustering), that periodically selects cluster heads according to a hybrid of their residual energy and a secondary parameter, such as node proximity to its neighbors or node degree. HEED does not make any assumptions about the distribution or density of nodes, or about node capabilities, e.g., location-awareness. The clustering process terminates in O(1) iterations, and does not depend on the network topology or size. The protocol incurs low overhead in terms of processing cycles and messages exchanged. It also achieves fairly uniform cluster head distribution across the network. A careful selection of the secondary clustering parameter can balance load among cluster heads. Our simulation results demonstrate that HEED outperforms weight-based clustering protocols in terms of several cluster characteristics. We also apply our approach to a simple application to demonstrate its effectiveness in prolonging the network lifetime and supporting data aggregation.

Cluster analysis aims at identifying groups of similar objects and, therefore helps to discover distribution of patterns and interesting correlations in large data sets. It has been subject of wide research since it arises in many application domains in engineering, business and social sciences. Especially, in the last years the availability of huge transactional and experimental data sets and the arising requirements for data mining created needs for clustering algorithms that scale and can be applied in diverse domains.

We present a novel clustering method using the approach of support vector machines. Data points are mapped by means of a Gaussian kernel to a high dimensional feature space, where we search for the minimal enclosing sphere. This sphere, when mapped back to data space, can separate into several components, each enclosing a separate cluster of points. We present a simple algorithm for identifying these clusters. The width of the Gaussian kernel controls the scale at which the data is probed while the soft margin constant helps coping with outliers and overlapping clusters. The structure of a dataset is explored by varying the two parameters, maintaining a minimal number of support vectors to assure smooth cluster boundaries. We demonstrate the performance of our algorithm on several datasets.

The burgeoning field of genomics, and in particular microarray experiments, have revived interest in both discriminant and cluster analysis, by raising new methodological and computational challenges. The present paper discusses applications of resampling methods to problems in cluster analysis. A resampling method, known as bagging in discriminant analysis, is applied to increase clustering accuracy and to assess the confidence of cluster assignments for individual observations. A novel prediction-based resampling method is also proposed to estimate the number of clusters, if any, in a dataset. The performance of the proposed and existing methods are compared using simulated data and gene expression data from four recently published cancer microarray studies.

The k-means algorithm is well known for its efficiency in clustering large data sets. However, working only on numeric values prohibits it from being used to cluster real world data containing categorical values. In this paper we present two algorithms which extend the k-means algorithm to categorical domains and domains with mixed numeric and categorical values. The k-modes algorithm uses a simple matching dissimilarity measure to deal with categorical objects, replaces the means of clusters with modes, and uses a frequency-based method to update modes in the clustering process to minimise the clustering cost function. With these extensions the k-modes algorithm enables the clustering of categorical data in a fashion similar to k-means. The k-prototypes algorithm, through the definition of a combined dissimilarity measure, further integrates the k-means and k-modes algorithms to allow for clustering objects described by mixed numeric and categorical attributes. We use the well known soybean disease and credit approval data sets to demonstrate the clustering performance of the two algorithms. Our experiments on two real world data sets with half a million objects each show that the two algorithms are efficient when clustering large data sets, which is critical to data mining applications.

The self-organizing map (SOM) is an excellent tool in exploratory phase of data mining. It projects input space on prototypes of a low-dimensional regular grid that can be effectively utilized to visualize and explore properties of the data. When the number of SOM units is large, to facilitate quantitative analysis of the map and the data, similar units need to be grouped, i.e., clustered. In this paper, different approaches to clustering of the SOM are considered. In particular, the use of hierarchical agglomerative clustering and partitive clustering using-means are investigated. The two-stage procedure---first using SOM to produce the prototypes that are then clustered in the second stage---is found to perform well when compared with direct clustering of the data and to reduce the computation time.

Several recent machine learning publications demonstrate the utility of using feature selection algorithms in supervised learning tasks. Among these, scqucnlial feature s1ion algorithms are receiving attention. The most frequently studied variants of these algorithms are forward and backward sequential selection. Many studies on supervised learning with sequential feature selection report applications of these algorithms, but do not consider variants of them that might be more appropriate for some performance tasks. This paper reports positive empirical results on such variants, and argues for their serious consideration in similar learning tasks.