On defining affinity graph for spectral clustering through ranking on manifolds

Cao, Juan; Zhang, Yongdong; Li, Jintao

doi:10.1016/j.neucom.2009.03.012

Cited by 27 publications

(11 citation statements)

References 5 publications

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“…To evaluate the effectiveness of the max-flow-based similarity measure, which we will hereafter refer to as FLOW, we conduct experiments on synthetic and real datasets including a comparison with other state-of-the-art similarity measures for the affinity graph, including the locally scaled Gaussian kernel function (TUNING) [12], the path-based similarity (PATH) [14], the ranking on manifolds (ROM) [10], and the amplified commute kernel (ACK) [20]. The affinity graphs constructed by different measures are used in the spectral clustering algorithm [11] to evaluate the effectiveness.…”

Section: Methodsmentioning

confidence: 99%

“…As for TUNING, the only hyper-parameter M is set to 7, as suggested in [12]. As in the literature [10], [11], [13], [14], the number of clusters is an input of the spectral clustering algorithm.…”

Section: Methodsmentioning

confidence: 99%

“…It has been shown that the affinity matrix is crucial to the performance of spectral clustering [10]- [16]. Most spectral clustering methods adopted the Gaussian kernel function as a similarity measure to construct the affinity matrix [5], [11]- [13], where only the parameters are different.…”

Section: Introductionmentioning

confidence: 99%

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A Max-Flow-Based Similarity Measure for Spectral Clustering

Cao¹

2013

ETRI J

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In most spectral clustering approaches, the Gaussian kernel-based similarity measure is used to construct the affinity matrix. However, such a similarity measure does not work well on a dataset with a nonlinear and elongated structure. In this paper, we present a new similarity measure to deal with the nonlinearity issue. The maximum flow between data points is computed as the new similarity, which can satisfy the requirement for similarity in the clustering method. Additionally, the new similarity carries the global and local relations between data. We apply it to spectral clustering and compare the proposed similarity measure with other state-of-the-art methods on both synthetic and real-world data. The experiment results show the superiority of the new similarity: 1) The max-flow-based similarity measure can significantly improve the performance of spectral clustering; 2) It is robust and not sensitive to the parameters.Keywords: Spectral clustering, maximum flow, affinity graph, similarity measure. Manuscript received July 31, 2012; revised Oct. 7, 2012; accepted Oct. 22, 2012. This work was supported by the National Natural Science Foundation of China through the program 61173083, by the Ministry of Science and Technology, China, through the 973 Program 2011CB302200 and by the Economic & Information Commission of Guangdong province through the Program GDIID2008IS007.Jiangzhong Cao (phone: +86 135 6008 2826, cjz510@gdut.edu.cn) is with the School of Information Science and Technology, Sun Yat-sen University, Guangzhou, China, and also with the School of Information Engineering, Guangdong University of Technology, Guangzhou, China.Pei Chen (chenpei@mail.sysu.edu.cn) and Yun Zheng (zhengyun84@gmail.com) are with the School of Information Science and Technology, Sun Yat-sen University, Guangzhou, China.Qingyun Dai (daiqy@gdut.edu.cn) is with the School of Information Engineering, Guangdong University of Technology, Guangzhou, China.http://dx.doi.org/10.4218/etrij.13.0112.0520 I. IntroductionSpectral clustering has attracted a significant amount of attention [1]-[4] due to its impressive performance on some challenging clustering datasets, with successful applications in computer vision [5], [6], VLSI design [7], and speech processing [8], [9]. It has been shown that the affinity matrix is crucial to the performance of spectral clustering [10]- [16]. Most spectral clustering methods adopted the Gaussian kernel function as a similarity measure to construct the affinity matrix [5], [11]-[13], where only the parameters are different. In [11], a fixed scaling parameter controls how fast the similarity falls off with the distance between points. In [12], a self-tuning parameter was used to adapt to the multiscale dataset. In [13], the Gaussian kernel function was scaled according to the local density between data points so that the similarity between two points is higher if there are more common points in their ε-neighborhood.Though the Gaussian kernel-based similarity measure can describe the information of the loc...

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Section: Methodsmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

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A Max-Flow-Based Similarity Measure for Spectral Clustering

Cao¹

2013

ETRI J

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“…[18]. However both the solutions fail to reveal the properties of real world data sets [16]. Another open issue of key importance in spectral clustering is that of choosing a proper number of groups.…”

Section: Introductionmentioning

confidence: 99%

Spectral Clustering Based on k-Nearest Neighbor Graph

Lucińska

Wierzchoń

2012

Lecture Notes in Computer Science

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Abstract. Finding clusters in data is a challenging task when the clusters differ widely in shapes, sizes, and densities. We present a novel spectral algorithm Speclus with a similarity measure based on modified mutual nearest neighbor graph. The resulting affinity matrix reflex the true structure of data. Its eigenvectors, that do not change their sign, are used for clustering data. The algorithm requires only one parameter -a number of nearest neighbors, which can be quite easily established. Its performance on both artificial and real data sets is competitive to other solutions.

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“…Recently, spectral clustering has become one of the most popular clustering algorithms and has been widely applied to image segmentation [4]. Spectral clustering method mainly consists of two stages [5,6]: (1) select a similarity measure function to build the affinity matrix (weighted and undirected graph) from the input data set and (2) cluster the data points through finding an optimal partition of the affinity graph. Similarity measurement is crucial to the performance of spectral clustering method [6,7].…”

Section: Introductionmentioning

confidence: 99%

A quaternion-based spectral clustering method for color image segmentation

Jin

Liu

et al. 2011

SPIE Proceedings

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Spectral clustering method has been widely used in image segmentation. A key issue in spectral clustering is how to build the affinity matrix. When it is applied to color image segmentation, most of the existing methods either use Euclidean metric to define the affinity matrix, or first converting color-images into gray-level images and then use the gray-level images to construct the affinity matrix (component-wise method). However, it is known that Euclidean distances can not represent the color differences well and the component-wise method does not consider the correlation between color channels. In this paper, we propose a new method to produce the affinity matrix, in which the color images are first represented in quaternion form and then the similarities between color pixels are measured by quaternion rotation (QR) mechanism. The experimental results show the superiority of the new method.

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On defining affinity graph for spectral clustering through ranking on manifolds

Cited by 27 publications

References 5 publications

A Max-Flow-Based Similarity Measure for Spectral Clustering

A Max-Flow-Based Similarity Measure for Spectral Clustering

Spectral Clustering Based on k-Nearest Neighbor Graph

A quaternion-based spectral clustering method for color image segmentation

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