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Fuzzy Partition based Similarity Measure for Spectral Clustering

Yifang Yang, Yuping Wang

2016
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International Journal of Signal Processing, Image Processing and Pattern Recognition
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The efficiency of spectral clustering depends heavily on the similarity measure adopted. A widely used similarity measure is the Gaussian kernel function where Euclidean distance is used. Unfortunately, the result of spectral clustering is very sensitive to the scaling parameter and the Euclidean distance is usually not suitable to the complex distribution data. In this paper, a spectral clustering algorithm based on fuzzy partition similarity measure ( FPSC) is presented to solve the problem
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... solve the problem that result of spectral clustering is very sensitive to scaling parameter. The proposed algorithm is steady extremely and hardly affected by the scaling parameter. Experiments on three benchmark datasets, two synthetic texture images are made, and the results demonstrate the effectiveness of the proposed algorithm. the distance to a nearby neighbor, is still a Euclidean distance factor and cannot make any contribution to clustering better than using the scale parameter of Gaussian kernel function [20] . Fischer, B. et. al., [21] proposed the path-based similarity, this similarity reflects the idea that no matter how far the physical distance between two points, they should be considered as in one cluster if they are connected by a set of successive points in dense regions. This is intuitively reasonable. However, it is not robust enough against noise and outliers [22]. Feng Zhao et. al., [23] proposed fuzzy similarity measure by utilizing the partition matrix obtained by fuzzy c-means clustering algorithm. Secondly, when the scale n of the data set is relatively large, the overall time complexity and space complexity of standard spectral clustering can reach O(n 3) and O(n 2 ) respectively [9], which is difficult to store and decompose a large similarity matrix, especially for one image. Fowlkes et. al., [4] presented the Nyström approximation technique to alleviate the computational burden of spectral clustering algorithms. [30] generated sparse similarity matrix using the t-nearest-neighbor method to avoid the dense similarity matrix storing problem. There are several papers reported the kernel fuzzy-clustering algorithm has better performance than the standard FCM. Authors in [24] reported good performance of kernel fuzzy-clustering algorithm on a 2-dimensional non-linearly separable synthetic dataset and compared the obtained results with those produced by the standard FCM; the classification rate for kernel FCM is much higher than standard FCM. The kernel based clustering algorithms can cluster specific nonspherical clusters such as the ring cluster, and quite well outperform FCM for the same number of clusters [25] . In this paper, a novel kernel fuzzy similarity measure is proposed and a new spectral clustering algorithm based on this measure is used in image segmentation. To alleviate the computational complexity, time and space complexity of the algorithm and avoid the dense similarity matrix storing problem, the t-nearest-neighbor method is applied to the algorithm. The rest of this paper is organized as follows. In Section 2, we present a short overview about techniques of NJW, A new kernel fuzzy similarity measure which is used to construct the similarity matrix and the proposed FPSC method for image segmentation are described in details in Section 3. Experimental results analysis, discussion and parameter setting are described in Section 4. Finally, conclusions are given in Section 5. Spectral Clustering Algorithm and the NJW Method Spectral clustering methods widely adopt graph-based approaches for data clustering. Given a dataset 1 2

doi:10.14257/ijsip.2016.9.10.39
fatcat:emooekgaabfuta77tvwk4ydenq