Divide and conquer strategy for spectral clustering

Simulated annealing spectral clustering algorithm for image segmentation

In the image segmentation, the spectral clustering algorithm are facing the problems, that the similarity matrix and Laplace matrix requires a lot of computing and storage, which limits its expansion in the large-scale image. Aiming at these problems, a semi-supervised spectrum clustering algorithm based on the Nystrom approximation was proposed. In the algorithm, adopting the Nystrom approximation method to estimate the similarity matrix, which effectively reduces the amount of computation and storage of the spectral clustering algorithm. Finally, on the Brodatz texture library, the image segmentation experiments showed the feasibility and effectiveness of the algorithm.

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.

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.

In this work, we propose a new algorithm for spectral color image segmentation based on the use of a kernel matrix. A cost function for spectral kernel clustering is introduced to measure the correlation between clusters. An efficient multiscale method is presented for accelerating spectral color image segmentation. The multiscale strategy uses the lattice geometry of images to construct an image pyramid whose hierarchy provides a framework for rapidly estimating eigenvectors of normalized kernel matrices. To prevent the boundaries from deteriorating, the image size on the top level of the pyramid is generally required to be around 75 x 75, where the eigenvectors of normalized kernel matrices would be approximately solved by the Nyström method. Within this hierarchical structure, the coarse solution is increasingly propagated to finer levels and is refined using subspace iteration. In addition, to make full use of the abundant color information contained in spectral color images, we propose using spectrum extension to incorporate the geometric features of spectra into similarity measures. Experimental results have shown that the proposed method can perform significantly well in spectral color image segmentation as well as speed up the approximation of the eigenvectors of normalized kernel matrices.

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.

Recently, a large amount of work has been devoted to the study of spectral clustering—a simple yet powerful method for finding structure in a data set using spectral properties of an associated pairwise similarity matrix. Most of the existing spectral clustering algorithms estimate only one cluster number or estimate non-unique cluster numbers based on eigengap criterion. However, the number of clusters not always exists one, and eigengap criterion lacks theoretical justification. In this paper, we propose non-unique cluster numbers determination methods based on stability in spectral clustering (NCNDBS). We first utilize the multiway normalized cut spectral clustering algorithm to cluster data set for a candidate cluster number \(k\). Then the ratio value of the multiway normalized cut criterion of the obtained clusters and the sum of the leading eigenvalues (descending sort) of the stochastic transition matrix is chosen as a standard to decide whether the \(k\) is a reasonable cluster number. At last, by varying the scaling parameter in the Gaussian function, we judge whether the reasonable cluster number \(k\) is also a stability one. By three stages, we can determine non-unique cluster numbers of a data set. The Lumpability theorem concluded by Meil\(\breve{a}\) and Xu provides a theoretical base for our methods. NCNDBS can estimate non-unique cluster numbers of the data set successfully by illustrative experiments.

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

Spectral clustering has shown a superior performance in analyzing the cluster structure. However, the exponentially computational complexity limits its application in analyzing large-scale data. To tackle this problem, many low-rank matrix approximating algorithms are proposed, of which the Nystrom method is an approach with proved lower approximate errors. The algorithms commonly combine two powerful techniques in machine learning: spectral clustering algorithms and Nystrom methods commonly used to obtain good quality low rank approximations of large matrices. This paper proposes to analyze a scalable Nystrom-based clustering algorithm with a Minimum Sum of Squared Similarities (MSSS) sampling procedure. We provide theoretical analysis of the performance of the algorithm MSSS and demonstrate its theoretical performance in comparison to the leading spectral clustering methods that use Nystrom sampling.

Spectral clustering algorithms rely on graphs where edges are defined based on the similarity between the vertices (data points). The effectiveness and fairness of spectral clustering depend significantly on how the graph is constructed. While automated graph construction methods, which learn graphs from real-valued vector datasets, have demonstrated strong performance in the quality of clustering, fairness concerns still remain. In this work, we introduce a graph construction method that incorporates a new fairness definition—Edge Disparate Impact—into the edge relationships, aiming to produce a fair graph. This approach modifies the optimization process of automated graph construction to account for fairness, resulting in a more equitable graph. Extensive experiments were conducted to compare our method with the latest graph construction techniques and fair spectral clustering algorithms. The results prove that, by using a fair graph for spectral clustering, fairness is improved in the resulting clusters. We also demonstrate that our method outperforms baseline approaches in both fairness and the quality of clustering.

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.

Constrained spectral embedding for K-way data clustering