Non-unique cluster numbers determination methods based on stability in spectral clustering

Simulated annealing spectral clustering algorithm for image segmentation

Network analysis-based module detection has significant implications in many fields. In cellular/ molecular biology, module detection based on analyses of metabolic/regulatory networks will not only help us understand more about the function and evolution of cellular machinery of an organism, but will also provide tractable contextual information for potential drug targets and facilitate improvements in drug designs. We here present our preliminary study on the module detection for bacteria based on the spectral clustering of the protein-protein functional association networks. We first examined how the parameter of the spectral clustering algorithm (i.e., the number of clusters) affects our module detection results, and demonstrated that when the number of clusters was set too small or too large the resulting module collection deteriorate in terms of gene coverage and intra-module association. We then compared our predicted modules against the randomly generated modules, and demonstrated that our modules (i) have a higher ratio of the intra-module to inter-module gene-gene functional association scores and (ii) can better capture the modularization information inherent in the experimentally verified modules. Finally we compared the module collections of seven bacterial organisms, and observed that modules related to membrane transport and cell motility are among those that are conserved among multiple organisms. Because it is desirable from both scientific and technical points of view to study functional modules at various resolution levels, we believe that the spectral clustering algorithm, with the flexibility rendered by different parameter settings, provides an appropriate solution in terms of capturing the modularization properties of networks and computational affordability.

A robust adaptive clustering analysis method for automatic identification of clusters

For the spectral clustering algorithm in the large-scale samples, there are bottlenecks in the storage space and computing time, and the paper analyzes the current common solutions, namely based on the sparse t-nearest neighbor spectral clustering. In order to improve the accuracy of the spectral clustering algorithms, the Euclidean distance based on the attribute weight of information entropy is proposed to calculate the similarity between the samples. First, calculate the weight of each attribute of the sample and then calculate the similarity between the samples. The degree matrix is applied to the spectral clustering of sparse t-nearest neighbors in the last number of numbers. The experimental results show that the clustering accuracy of the method on some data sets is higher than that of the original spectral clustering algorithm.

The spectral clustering algorithm's space complexity is O(n <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> ), while time complexity is O(n <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> ). When dealing with large amounts of data, the memory will overflow and run-time is too long. For the general problem of spectral clustering, if the clustering data of sub-problem between the original problem has the same probability distribution, it can be applied to divide and conquer strategy for the problem of spectral clustering, by the spectral clustering results of sub-problems to get the spectral clustering results of original problem. To spectral clustering image segmentation as a research object, we will discuss the divide and conquer strategy for spectral clustering in this paper. Experiments show that the application of divide and conquer method for spectral clustering image segmentation, we can get a perfect performance in image segmentation.

SummaryCluster ensemble combines multiple base clustering results in a suitable way to improve the accuracy of the clustering result. In the conventional cluster ensemble frameworks, pairwise constraints and constraint projections have not been used together, and spectral clustering algorithm is rarely adopted to serve as the consensus function. In this paper, we design a constraint projections for semi‐supervised spectral clustering ensemble (CPSSSCE) model. It takes advantages of spectral clustering algorithm and executes semi‐supervised learning twice. Compared to traditional cluster ensemble approaches, CPSSSCE is characterized by several properties. First, the original data are transformed to lower‐dimensional representations by constraint projection before base clustering. Second, a similarity matrix is constructed using the base clustering results and modified using pairwise constraints. Third, the spectral clustering algorithm is applied to process the similarity matrix to obtain a consensus cluster result. Extensive experiments on standard University of California Irvine Machine Learning Repository (UCI) and Microsoft datasets demonstrated that the CPSSSCE is superior to other cluster ensemble algorithms including a semi‐supervised spectral clustering ensemble.

Spectral graph clustering methods have been a hot topic in the field of image segmentation. However, because the computational demands are needed for Spectral graph clustering methods, it has been severely limited to apply them into large data sets, such as high resolution image. It would be too expensive or even impractical for spectral decomposition to provide the optimal approximation in dealing with large or high-dimensional datasets. A novel approach aiming at reducing the computational requirements is proposed in this paper. Our approach focuses on Nystrom method for the solution of eigen-function problems. This approach enables us to use a small number of samples to infer the overall clustering solution. Based on the proposed Nystrom sampling method, this paper presents a spectral clustering algorithm for massive data analysis, and the experiments show the method is both feasible and effective.

Towards Using Graph Analytics for Tracking Covid-19.

Spectral clustering has exhibited a superior performance in analyzing the cluster structure of network. However, the exponentially computational complexity limits its application in analyzing large-scale social networks. To tackle this problem, many low-rank matrix approximating algorithms are proposed, of which the NystrÖm method is an approach with proved lower approximate errors. Currently, most existing sampling techniques for NystrÖm method are designed on affinity matrices, which are time-consuming to compute by some similarity metrics. Moreover, the social networks are often built on link relations, in which there is no information to construct an affinity matrix for the approximate computing of NystrÖm method for spectral clustering except for the degrees of nodes. This paper proposes a spectral clustering algorithm for large-scale social networks via a pre-coarsening sampling based NystrÖm method. By virtue of a novel triangle-based coarsening policy, the proposed algorithm first shrinks the social network into a smaller weighted network, and then does an efficient sampling for NystrÖm method to approximate the eigen-decomposition of matrix of spectral clustering. Experimental results on real large-scale social networks demonstrate that the proposed algorithm outperforms the state-of-the-art spectral clustering algorithms, which are realized by the existing sampling techniques based NystrÖm methods.

Spectral clustering has become a typical and efficient clustering method used in a variety of applications. The critical step of spectral clustering is the similarity measurement, which largely determines the performance of the spectral clustering method. In this paper, we propose a novel spectral clustering algorithm based on the local similarity measure of shared neighbors. This similarity measurement exploits the local density information between data points based on the weight of the shared neighbors in a directed k $$ k $$ -nearest neighbor graph with only one parameter k $$ k $$ , that is, the number of nearest neighbors. Numerical experiments on synthetic and real-world datasets demonstrate that our proposed algorithm outperforms other existing spectral clustering algorithms in terms of the clustering performance measured via the normalized mutual information, clustering accuracy, and F $$ F $$ -measure. As an example, the proposed method can provide an improvement of 15.82% in the clustering performance for the Soybean dataset.

Fuzzy spectral clustering with robust spatial information for image segmentation

The similarity between words is used for word clustering. In spectral clustering algorithms, the information contained in the eigenvectors of an affinity matrix is used to detect the similarity. Compared with traditional clustering methods, spectral clustering performs much better for clustering the words especially in multidimensional vector spaces. the spectral clustering is implemented by Visual C++ and Matlab in the paper, which is applied to cluster small scale segmented Chinese corpus and large scale non-segmented Chinese corpus. good experimental results are observed and result analysis are given for spectral clustering.

Text document clustering using Spectral Clustering algorithm with Particle Swarm Optimization

Previous chapter Next chapter Full AccessProceedings Proceedings of the 2007 SIAM International Conference on Data Mining (SDM)Incremental Spectral Clustering With Application to Monitoring of Evolving Blog CommunitiesHuazhong Ning, Wei Xu, Yun Chi, Yihong Gong, and Thomas HuangHuazhong Ning, Wei Xu, Yun Chi, Yihong Gong, and Thomas Huangpp.261 - 272Chapter DOI:https://doi.org/10.1137/1.9781611972771.24PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAboutAbstract In recent years, spectral clustering method has gained attentions because of its superior performance compared to other traditional clustering algorithms such as K-means algorithm. The existing spectral clustering algorithms are all off-line algorithms, i.e., they can not incrementally update the clustering result given a small change of the data set. However, the capability of incrementally updating is essential to some applications such as real time monitoring of the evolving communities of websphere or blogsphere. Unlike traditional stream data, these applications require incremental algorithms to handle not only insertion/deletion of data points but also similarity changes between existing items. This paper extends the standard spectral clustering to such evolving data by introducing the incidence vector/matrix to represent two kinds of dynamics in the same framework and by incrementally updating the eigenvalue system. Our incremental algorithm, initialized by a standard spectral clustering, continuously and efficiently updates the eigenvalue system and generates instant cluster labels, as the data set is evolving. The algorithm is applied to a blog data set. Compared with recomputation of the solution by standard spectral clustering, it achieves similar accuracy but with much lower computational cost. Close inspection into the blog content shows that the incremental approach can discover not only the stable blog communities but also the evolution of the individual multi-topic blogs. Previous chapter Next chapter RelatedDetails Published:2007ISBN:978-0-89871-630-6eISBN:978-1-61197-277-1 https://doi.org/10.1137/1.9781611972771Book Series Name:ProceedingsBook Code:PR127Book Pages:xiv + 648Key words:Incremental clustering, Spectral Clustering, Incidence Vector/Matrix, Web-blogs

Feature subset selection and/or dimensionality reduction is an essential preprocess before performing any data mining task, especially when there are too many features in the problem space. In this paper, a clustering-based feature subset selection (CFSS) algorithm is proposed for discriminating more relevant features. In each level of agglomeration, it uses similarity measure among features to merge two most similar clusters of features. By gathering similar features into clusters and then introducing representative features of each cluster, it tries to remove some redundant features. To identify the representative features, a criterion based on mutual information is proposed. Since CFSS works in a filter manner in specifying the representatives, it is noticeably fast. As an advantage of hierarchical clustering, it does not need to determine the number of clusters in advance. In CFSS, the clustering process is repeated until all features are distributed in some clusters. However, to diffuse the features in a reasonable number of clusters, a recently proposed approach is used to obtain a suitable level for cutting the clustering tree. To assess the performance of CFSS, we have applied it on some valid UCI datasets and compared with some popular feature selection methods. The experimental results reveal the efficiency and fastness of our proposed method.