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16
A Clustering Algorithm based on Graph Connectivity
 Information Processing Letters
, 1999
"... We have developed a novel algorithm for cluster analysis that is based on graph theoretic techniques. ..."
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Cited by 99 (3 self)
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We have developed a novel algorithm for cluster analysis that is based on graph theoretic techniques.
A Generic Grouping Algorithm and its Quantitative Analysis
 IEEE Transactions on Pattern Analysis and Machine Intelligence
, 1998
"... This paper presents a generic method for perceptual grouping, and an analysis of its expected grouping quality. The grouping method is fairly general: it may be used for the grouping of various types of data features, and to incorporate different grouping cues, operating over feature sets of diff ..."
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Cited by 56 (4 self)
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This paper presents a generic method for perceptual grouping, and an analysis of its expected grouping quality. The grouping method is fairly general: it may be used for the grouping of various types of data features, and to incorporate different grouping cues, operating over feature sets of different sizes. The proposed method is divided into two parts: Constructing a graph representation of the available perceptual grouping evidence, and then finding the "best" partition of the graph into groups. The first stage includes a cue enhancement procedure, which integrates the information available from multifeature cues into very reliable bifeature cues. Both stages are implemented using known statistical tools such as Wald's SPRT algorithm and the Maximum Likelihood criterion. The accompanying theoretical analysis of this grouping criterion quantifies intuitive expectations and predicts that the expected grouping quality increases with cue reliability. It also shows that investing more computational effort in the grouping algorithm leads to better grouping results. This analysis, which quantifies the grouping power of the Maximum Likelihood criterion, is independent of the grouping domain. To our best knowledge, such an analysis of a grouping process is given here for the first time. Three grouping algorithms, in three different domains, are synthesized as instances of the generic method, They demonstrate the applicability and generality of this grouping method. Keywords : Perceptual Grouping, Grouping Analysis, Graph Clustering, Maximum Likelihood, Wald's SPRT, Performance Prediction, Generic Grouping Algorithm. 1
Computational Methods for the Identification of Differential and Coordinated Gene Expression
 Human Molecular Genetics
, 1999
"... this article, I review the theoretical and computational approaches used to: (i) identify genes differentially expressed (across cell types, developmental stages, pathological conditions, etc.); (ii) identify genes expressed in a coordinated manner across a set of conditions; and (iii) delineate clu ..."
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Cited by 45 (0 self)
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this article, I review the theoretical and computational approaches used to: (i) identify genes differentially expressed (across cell types, developmental stages, pathological conditions, etc.); (ii) identify genes expressed in a coordinated manner across a set of conditions; and (iii) delineate clusters of genes sharing coherent expression features, eventually defining global biological pathways
CLUE: Clusterbased Retrieval of Images by Unsupervised Learning
 IEEE Transactions on Image Processing
, 2003
"... In a typical contentbased image retrieval (CBIR) system, query results are a set of images sorted by feature similarities with respect to the query. However, images with high feature similarities to the query may be very di#erent from the query in terms of semantics. This discrepancy between lowle ..."
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Cited by 45 (2 self)
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In a typical contentbased image retrieval (CBIR) system, query results are a set of images sorted by feature similarities with respect to the query. However, images with high feature similarities to the query may be very di#erent from the query in terms of semantics. This discrepancy between lowlevel features and highlevel concepts is known as the semantic gap. This paper introduces a novel image retrieval scheme, CLUsterbased rEtrieval of images by unsupervised learning (CLUE), which attempts to tackle the semantic gap problem based on a hypothesis that images of the same semantics are similar in a way, images of di#erent semantics are di#erent in their own ways. CLUE attempts to capture semantic concepts by learning the way that images of the same semantics are similar and retrieving image clusters instead of a set of ordered images. Clustering in CLUE is dynamic. In particular, clusters formed depend on which images are retrieved in response to the query. Therefore, the clusters give the algorithm as well as the users semantic relevant clues as to where to navigate. CLUE is a general approach that can be combined with any realvalued symmetric similarity measure (metric or nonmetric). Thus it may be embedded in many current CBIR systems. An experimental image retrieval system using CLUE has been implemented. The performance of the system is evaluated on a database of about 60, 000 images from COREL. Empirical results demonstrate improved performance compared with a typical CBIR system using the same image similarity measure. In addition, preliminary results on images returned by Google's Image Search reveal the potential of applying CLUE to real world image data and integrating CLUE as a part of the interface for keywordbased image retrieval systems.
An Algorithm for Clustering cDNAs for Gene Expression Analysis
 In RECOMB99: Proceedings of the Third Annual International Conference on Computational Molecular Biology
, 1999
"... We have developed a novel algorithm for cluster analysis that is based on graph theoretic techniques. A similarity graph is defined and clusters in that graph correspond to highly connected subgraphs. A polynomial algorithm to compute them efficiently is presented. Our algorithm produces a clusterin ..."
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Cited by 45 (4 self)
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We have developed a novel algorithm for cluster analysis that is based on graph theoretic techniques. A similarity graph is defined and clusters in that graph correspond to highly connected subgraphs. A polynomial algorithm to compute them efficiently is presented. Our algorithm produces a clustering with some provably good properties. The application that motivated this study was gene expression analysis, where a collection of cDNAs must be clustered based on their oligonucleotide fingerprints. The algorithm has been tested intensively on simulated libraries and was shown to outperform extant methods. It demonstrated robustness to high noise levels. In a blind test on real cDNA fingerprint data the algorithm obtained very good results. Utilizing the results of the algorithm would have saved over 70% of the cDNA sequencing cost on that data set. 1 Introduction Cluster analysis seeks grouping of data elements into subsets, so that elements in the same subset are in some sense more cl...
Fixed Points Approach to Clustering
, 1993
"... Assume that a dissimilarity measure between elements and subsets of the set being clustered is given. We define the transformation of the set of subsets under which each subset is transformed into the set of all elements whose dissimilarity to its is not greater than a given threshold. Then the c ..."
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Cited by 12 (2 self)
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Assume that a dissimilarity measure between elements and subsets of the set being clustered is given. We define the transformation of the set of subsets under which each subset is transformed into the set of all elements whose dissimilarity to its is not greater than a given threshold. Then the cluster is defined as fixed point of this transformation. Three wellknown clustering strategies are considered from this point of view: hierarchical clustering, graphtheoretic methods, and conceptual clustering. For hierarchical clustering generalizations are obtained that allow for overlapping clusters and/or clusters not forming a cover. Three properties of dissimilarity are introduced which guarantee the existence of fixed points for each threshold. We develop the relation to the theory of quasiconcave set functions, to help give an additional interpretation of clusters.
Investigation of Measures for Grouping by Graph Partitioning
 In Computer Vision and Pattern RecognitionCVPR2001
, 2001
"... Grouping by graph partitioning is an effective engine for perceptual organization. This graph partitioning process, mainly motivated by computational efficiency considerations, is usually implemented as recursive bipartitioning, where at each step the graph is broken into two parts based on a parti ..."
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Cited by 7 (1 self)
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Grouping by graph partitioning is an effective engine for perceptual organization. This graph partitioning process, mainly motivated by computational efficiency considerations, is usually implemented as recursive bipartitioning, where at each step the graph is broken into two parts based on a partitioning measure. We study four such measures, namely, the minimum cut [11], average cut [6], ShiMalik normalized cut [7], and a variation of the ShiMalik normalized cut. Using probabilistic analysis we show that the minimization of the average cut and the normalized cut measure, using recursive bipartitioning will, on an average, result in the correct segmentation. The minimum cut and the variation of the normalized cut will, on an average, not result in the correct segmentation and we can precisely express the conditions. Based on a rigorous empirical evaluation, we also show that, in practice, the quality of the groups generated using minimum, average or normalized cuts are statistically equivalent for object recognition, i.e. the best, the mean, and the variation of the qualities are statistically equivalent. We also find that for certain image classes, such as aerial and scenes with manmade objects in manmade surroundings, the performance of grouping by partitioning is the worst, irrespective of the cut measure. 1.
An indepth study of graph partitioning measures for perceptual organization
 IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE
, 2003
"... In recent years, one of the effective engines for perceptual organization of lowlevel image features is based on the partitioning of a graph representation that captures Gestalt inspired local structures, such as similarity, proximity, continuity, parallelism, and perpendicularity, over the lowle ..."
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Cited by 6 (0 self)
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In recent years, one of the effective engines for perceptual organization of lowlevel image features is based on the partitioning of a graph representation that captures Gestalt inspired local structures, such as similarity, proximity, continuity, parallelism, and perpendicularity, over the lowlevel image features. Mainly motivated by computational efficiency considerations, this graph partitioning process is usually implemented as a recursive bipartitioning process, where, at each step, the graph is broken into two parts based on a partitioning measure. We concentrate on three such measures, namely, the minimum [41], average [28], and normalized [32] cuts. The minimum cut partition seeks to minimize the total link weights cut. The average cut measure is proportional to the total link weight cut, normalized by the sizes of the partitions. The normalized cut measure is normalized by the product of the total connectivity (valencies) of the nodes in each partition. We provide theoretical and empirical insight into the nature of the three partitioning measures in terms of the underlying image statistics. In particular, we consider for what kinds of image statistics would optimizing a measure, irrespective of the particular algorithm used, result in correct partitioning. Are the quality of the groups significantly different for each cut measure? Are there classes of images for which grouping by partitioning does not work well? Another question of interest is if the recursive bipartitioning strategy can separate out groups corresponding toK objects from each other. In the analysis, we draw from probability theory and the rich body of work on stochastic ordering of random variables. Our major conclusion is that optimization of none of the three measures is guaranteed to result in the correct partitioning ofK objects, in the strict stochastic order sense, for all image statistics. Qualitatively speaking, under very restrictive conditions, when the average interobject feature affinity is very weak
Clustering and Group Selection of Multiple Criteria Alternatives with Application to Spacebased Networks
 IEEE Trans. on Systems, Man, and Cybernetics Part B: Cybernetics
, 2002
"... In many real world problems the range of consequences of different alternatives are considerably different. Also, sometimes, selection of a group of alternatives (instead of only one best alternative) is necessary. Traditional decision making approaches treat the set of alternatives with the same me ..."
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Cited by 3 (0 self)
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In many real world problems the range of consequences of different alternatives are considerably different. Also, sometimes, selection of a group of alternatives (instead of only one best alternative) is necessary. Traditional decision making approaches treat the set of alternatives with the same method of analysis and selection. In this paper, we propose clustering alternatives into different groups so that different methods of analysis, selection, and implementation for each group can be applied. As an example, consider the selection of a group of functions (or tasks) to be processed by a group of processors. The set of tasks can be grouped according to their similar criteria, and hence each cluster of tasks to be processed by a processor.