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Algorithms for clustering data
01 Jan 1988-
About: The article was published on 1988-01-01 and is currently open access. It has received 8586 citations till now. The article focuses on the topics: Cluster analysis & Correlation clustering.
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TL;DR: An efficient segmentation algorithm is developed based on a predicate for measuring the evidence for a boundary between two regions using a graph-based representation of the image and it is shown that although this algorithm makes greedy decisions it produces segmentations that satisfy global properties.
Abstract: This paper addresses the problem of segmenting an image into regions. We define a predicate for measuring the evidence for a boundary between two regions using a graph-based representation of the image. We then develop an efficient segmentation algorithm based on this predicate, and show that although this algorithm makes greedy decisions it produces segmentations that satisfy global properties. We apply the algorithm to image segmentation using two different kinds of local neighborhoods in constructing the graph, and illustrate the results with both real and synthetic images. The algorithm runs in time nearly linear in the number of graph edges and is also fast in practice. An important characteristic of the method is its ability to preserve detail in low-variability image regions while ignoring detail in high-variability regions.
5,791 citations
TL;DR: Clustering algorithms for data sets appearing in statistics, computer science, and machine learning are surveyed, and their applications in some benchmark data sets, the traveling salesman problem, and bioinformatics, a new field attracting intensive efforts are illustrated.
Abstract: Data analysis plays an indispensable role for understanding various phenomena. Cluster analysis, primitive exploration with little or no prior knowledge, consists of research developed across a wide variety of communities. The diversity, on one hand, equips us with many tools. On the other hand, the profusion of options causes confusion. We survey clustering algorithms for data sets appearing in statistics, computer science, and machine learning, and illustrate their applications in some benchmark data sets, the traveling salesman problem, and bioinformatics, a new field attracting intensive efforts. Several tightly related topics, proximity measure, and cluster validation, are also discussed.
5,744 citations
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
University of Vermont1, University of Minnesota2, University of Texas at Austin3, Hong Kong University of Science and Technology4, Osaka University5, University of Queensland6, Griffith University7, University of Illinois at Chicago8, IBM9, Nanjing University10, Imperial College London11, University of Salford12
TL;DR: This paper presents the top 10 data mining algorithms identified by the IEEE International Conference on Data Mining (ICDM) in December 2006: C4.5, k-Means, SVM, Apriori, EM, PageRank, AdaBoost, kNN, Naive Bayes, and CART.
Abstract: This paper presents the top 10 data mining algorithms identified by the IEEE International Conference on Data Mining (ICDM) in December 2006: C4.5, k-Means, SVM, Apriori, EM, PageRank, AdaBoost, kNN, Naive Bayes, and CART. These top 10 algorithms are among the most influential data mining algorithms in the research community. With each algorithm, we provide a description of the algorithm, discuss the impact of the algorithm, and review current and further research on the algorithm. These 10 algorithms cover classification, clustering, statistical learning, association analysis, and link mining, which are all among the most important topics in data mining research and development.
4,944 citations
TL;DR: An overview of this emerging field is provided, clarifying how data mining and knowledge discovery in databases are related both to each other and to related fields, such as machine learning, statistics, and databases.
Abstract: ■ Data mining and knowledge discovery in databases have been attracting a significant amount of research, industry, and media attention of late. What is all the excitement about? This article provides an overview of this emerging field, clarifying how data mining and knowledge discovery in databases are related both to each other and to related fields, such as machine learning, statistics, and databases. The article mentions particular real-world applications, specific data-mining techniques, challenges involved in real-world applications of knowledge discovery, and current and future research directions in the field.
4,782 citations
References
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TL;DR: In this paper, the basic problem of interconnecting a given set of terminals with a shortest possible network of direct links is considered, and a set of simple and practical procedures are given for solving this problem both graphically and computationally.
Abstract: The basic problem considered is that of interconnecting a given set of terminals with a shortest possible network of direct links Simple and practical procedures are given for solving this problem both graphically and computationally It develops that these procedures also provide solutions for a much broader class of problems, containing other examples of practical interest
4,395 citations
TL;DR: A Monte Carlo evaluation of 30 procedures for determining the number of clusters was conducted on artificial data sets which contained either 2, 3, 4, or 5 distinct nonoverlapping clusters to provide a variety of clustering solutions.
Abstract: A Monte Carlo evaluation of 30 procedures for determining the number of clusters was conducted on artificial data sets which contained either 2, 3, 4, or 5 distinct nonoverlapping clusters. To provide a variety of clustering solutions, the data sets were analyzed by four hierarchical clustering methods. External criterion measures indicated excellent recovery of the true cluster structure by the methods at the correct hierarchy level. Thus, the clustering present in the data was quite strong. The simulation results for the stopping rules revealed a wide range in their ability to determine the correct number of clusters in the data. Several procedures worked fairly well, whereas others performed rather poorly. Thus, the latter group of rules would appear to have little validity, particularly for data sets containing distinct clusters. Applied researchers are urged to select one or more of the better criteria. However, users are cautioned that the performance of some of the criteria may be data dependent.
3,551 citations
TL;DR: Sibson gives an O(n 2) algorithm for single-linkage clustering, and proves that this algorithm achieves the theoretically optimal lower time bound for obtaining a single- linkage dendrogram.
Abstract: Main point Sibson gives an O(n 2) algorithm for single-linkage clustering, and proves that this algorithm achieves the theoretically optimal lower time bound for obtaining a single-linkage dendrogram. This improves upon the naive O(n 3) implementation of single linkage clustering. A single linkage dendrogram is a tree, where each level of the tree corresponds to a different threshold dissimilarity measure h. The nodes of a dataset are grouped into \" equivalence classes \" c(h) at each level of the dendrogram, where two classes C i and C j are merged if there is a pair of \" OTU's \" (vertices) v i ∈ C i and v j ∈ C j such that the dissimilarity measure between v i and v j is less than h, or D(v i , v j) < h. For example, consider a set of 10 vertices v 1 ,. .. , v 10 for which the dissimilarity matrix D is given below, with D ij equal to the dissimilarity between v i and v j. Suppose we take four cutoff dissimilarity measures h 1 , h 2 , h 3 , h 4 and produce the dendrogram according to these thresholds. An example illustrating how the 10 vertices are grouped into equivalence classes at each level is shown in Figure 1. Since no dissimilarity is at or below 1, each vertex or \" OTU \" is its own equivalence class at the level corresponding to h 1 = 1. At the next level, however, we see that some classes have been merged together because several dissimilarity measures are below h 2 = 2. We can see that c(h 2) consists of 6 equivalence classes, c(h 3) has 3 equivalence classes, and c(h 4 = 4) aggregates all the vertices into one equivalence class. In single linkage clustering, the number of levels in the tree is determined by the nearest-neighbor criterion – at each level, at least one new merge is made between two clusters, and the merge is made for clusters C i and C j if the minimal distance between vertices v i ∈ C i and v j ∈ C j is the smallest such distance across all the clusters. In other words, the nearest neighbors between clusters C j and C i are found, and if these neighbors are closer than all the other nearest-neighbor pairs, then C i and C …
1,208 citations