A min-max cut algorithm for graph partitioning and data clustering

Ding, Chris; He, Xiaofeng; Zha, Hongyuan; Gu, Ming; Simon, Horst D.

doi:10.1109/icdm.2001.989507

Cited by 635 publications

(487 citation statements)

References 16 publications

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“…It seems that norm-(k-)cut is quite established as an ideal criterion here, but there are different, such as min-max cut [3]. But also SDP has been used in connection with spectral clustering and kernels: [11] propose a SDP relaxation for norm-k-cut clustering based on a similarity matrix, while [6] and [7] use SDP for completion and learning of kernel matrices, respectively.…”

Section: Relations To Other Work and Conclusionmentioning

confidence: 99%

Clustering Pairwise Distances with Missing Data: Maximum Cuts Versus Normalized Cuts

Poland

Zeugmann

2006

Lecture Notes in Computer Science

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Abstract. Clustering algorithms based on a matrix of pairwise similarities (kernel matrix) for the data are widely known and used, a particularly popular class being spectral clustering algorithms. In contrast, algorithms working with the pairwise distance matrix have been studied rarely for clustering. This is surprising, as in many applications, distances are directly given, and computing similarities involves another step that is error-prone, since the kernel has to be chosen appropriately, albeit computationally cheap. This paper proposes a clustering algorithm based on the SDP relaxation of the max-k-cut of the graph of pairwise distances, based on the work of Frieze and Jerrum. We compare the algorithm with Yu and Shi's algorithm based on spectral relaxation of a norm-k-cut. Moreover, we propose a simple heuristic for dealing with missing data, i.e., the case where some of the pairwise distances or similarities are not known. We evaluate the algorithms on the task of clustering natural language terms with the Google distance, a semantic distance recently introduced by Cilibrasi and Vitányi, using relative frequency counts from WWW queries and based on the theory of Kolmogorov complexity.

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Section: Relations To Other Work and Conclusionmentioning

confidence: 99%

Clustering Pairwise Distances with Missing Data: Maximum Cuts Versus Normalized Cuts

Poland

Zeugmann

2006

Lecture Notes in Computer Science

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“…In some cases, we would like to obtain a flat partitioning with a given number of block mappings k. For this purpose, we need to extract the optimal block mappings from the dendrogram. In this paper, we use the dynamic programming method proposed in [2,5].…”

Section: Extraction Of the Optimal Block Mappingsmentioning

confidence: 99%

“…In each bisection, it partitions the domain entities into two disjoint block mappings B 1 , B 2 . We adopt the min-max cut (M cut) function [5] as the criterion function. It minimizes the relatedness between the two block mappings meanwhile maximizes the relatedness within each block mapping.…”

Section: The Hierarchical Bisection Algorithmmentioning

confidence: 99%

Block Matching for Ontologies

2006

Lecture Notes in Computer Science

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Abstract. Ontology matching is a crucial task to enable interoperation between Web applications using different but related ontologies. Today, most of the ontology matching techniques are targeted to find 1:1 mappings. However, block mappings are in fact more pervasive. In this paper, we discuss the block matching problem and suggest that both the mapping quality and the partitioning quality should be considered in block matching. We propose a novel partitioning-based approach to address the block matching issue. It considers both linguistic and structural characteristics of domain entities based on virtual documents, and uses a hierarchical bisection algorithm for partitioning. We set up two kinds of metrics to evaluate of the quality of block matching. The experimental results demonstrate that our approach is feasible.

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“…Examples of such cost functions are Normalized Cut [19], MinMax Cut [6], and so on. Note that T L and T U are the two objectives formulated as partition constraints; β is a parameter to control the overall effect of the constraints.…”

Section: Objective Functionmentioning

confidence: 99%

Relaxed Transfer of Different Classes via Spectral Partition

Shi

Wang²,

Yang

et al. 2009

Machine Learning and Knowledge Discovery in Databases

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Abstract. Most existing transfer learning techniques are limited to problems of knowledge transfer across tasks sharing the same set of class labels. In this paper, however, we relax this constraint and propose a spectral-based solution that aims at unveiling the intrinsic structure of the data and generating a partition of the target data, by transferring the eigenspace that well separates the source data. Furthermore, a clusteringbased KL divergence is proposed to automatically adjust how much to transfer. We evaluate the proposed model on text and image datasets where class categories of the source and target data are explicitly different, e.g., 3-classes transfer to 2-classes, and show that the proposed approach improves other baselines by an average of 10% in accuracy. The source code and datasets are available from the authors.

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A min-max cut algorithm for graph partitioning and data clustering

Cited by 635 publications

References 16 publications

Clustering Pairwise Distances with Missing Data: Maximum Cuts Versus Normalized Cuts

Clustering Pairwise Distances with Missing Data: Maximum Cuts Versus Normalized Cuts

Block Matching for Ontologies

Relaxed Transfer of Different Classes via Spectral Partition

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