Topic

# Constrained clustering

About: Constrained clustering is a research topic. Over the lifetime, 5335 publications have been published within this topic receiving 213270 citations.

##### Papers published on a yearly basis

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TL;DR: An overview of pattern clustering methods from a statistical pattern recognition perspective is presented, with a goal of providing useful advice and references to fundamental concepts accessible to the broad community of clustering practitioners.

Abstract: 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.

14,054 citations

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03 Jan 2001TL;DR: A simple spectral clustering algorithm that can be implemented using a few lines of Matlab is presented, and tools from matrix perturbation theory are used to analyze the algorithm, and give conditions under which it can be expected to do well.

Abstract: Despite many empirical successes of spectral clustering methods— algorithms that cluster points using eigenvectors of matrices derived from the data—there are several unresolved issues. First. there are a wide variety of algorithms that use the eigenvectors in slightly different ways. Second, many of these algorithms have no proof that they will actually compute a reasonable clustering. In this paper, we present a simple spectral clustering algorithm that can be implemented using a few lines of Matlab. Using tools from matrix perturbation theory, we analyze the algorithm, and give conditions under which it can be expected to do well. We also show surprisingly good experimental results on a number of challenging clustering problems.

9,043 citations

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TL;DR: This work presents a simple and efficient implementation of Lloyd's k-means clustering algorithm, which it calls the filtering algorithm, and establishes the practical efficiency of the algorithm's running time.

Abstract: In k-means clustering, we are given a set of n data points in d-dimensional space R/sup d/ and an integer k and the problem is to determine a set of k points in Rd, called centers, so as to minimize the mean squared distance from each data point to its nearest center. A popular heuristic for k-means clustering is Lloyd's (1982) algorithm. We present a simple and efficient implementation of Lloyd's k-means clustering algorithm, which we call the filtering algorithm. This algorithm is easy to implement, requiring a kd-tree as the only major data structure. We establish the practical efficiency of the filtering algorithm in two ways. First, we present a data-sensitive analysis of the algorithm's running time, which shows that the algorithm runs faster as the separation between clusters increases. Second, we present a number of empirical studies both on synthetically generated data and on real data sets from applications in color quantization, data compression, and image segmentation.

5,288 citations

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01 Jun 1999TL;DR: A new algorithm is introduced for the purpose of cluster analysis which does not produce a clustering of a data set explicitly; but instead creates an augmented ordering of the database representing its density-based clustering structure.

Abstract: Cluster analysis is a primary method for database mining. It is either used as a stand-alone tool to get insight into the distribution of a data set, e.g. to focus further analysis and data processing, or as a preprocessing step for other algorithms operating on the detected clusters. Almost all of the well-known clustering algorithms require input parameters which are hard to determine but have a significant influence on the clustering result. Furthermore, for many real-data sets there does not even exist a global parameter setting for which the result of the clustering algorithm describes the intrinsic clustering structure accurately. We introduce a new algorithm for the purpose of cluster analysis which does not produce a clustering of a data set explicitly; but instead creates an augmented ordering of the database representing its density-based clustering structure. This cluster-ordering contains information which is equivalent to the density-based clusterings corresponding to a broad range of parameter settings. It is a versatile basis for both automatic and interactive cluster analysis. We show how to automatically and efficiently extract not only 'traditional' clustering information (e.g. representative points, arbitrary shaped clusters), but also the intrinsic clustering structure. For medium sized data sets, the cluster-ordering can be represented graphically and for very large data sets, we introduce an appropriate visualization technique. Both are suitable for interactive exploration of the intrinsic clustering structure offering additional insights into the distribution and correlation of the data.

4,020 citations

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28 Jun 2001

TL;DR: This paper demonstrates how the popular k-means clustering algorithm can be protably modied to make use of information about the problem domain that is available in addition to the data instances themselves.

Abstract: Clustering is traditionally viewed as an unsupervised method for data analysis. However, in some cases information about the problem domain is available in addition to the data instances themselves. In this paper, we demonstrate how the popular k-means clustering algorithm can be protably modied to make use of this information. In experiments with articial constraints on six data sets, we observe improvements in clustering accuracy. We also apply this method to the real-world problem of automatically detecting road lanes from GPS data and observe dramatic increases in performance.

2,641 citations