Spectral Clustering Algorithm Based on Attribute Weight of Information Entropy

Simulated annealing spectral clustering algorithm for image segmentation

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.

Text document clustering using Spectral Clustering algorithm with Particle Swarm Optimization

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.

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.

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.

We present an image set classification algorithm based on unsupervised clustering of labeled training and unlabeled test data where labels are only used in the stopping criterion. The probability distribution of each class over the set of clusters is used to define a true set based similarity measure. To this end, we propose an iterative sparse spectral clustering algorithm. In each iteration, a proximity matrix is efficiently recomputed to better represent the local subspace structure. Initial clusters capture the global data structure and finer clusters at the later stages capture the subtle class differences not visible at the global scale. Image sets are compactly represented with multiple Grassmannian manifolds which are subsequently embedded in Euclidean space with the proposed spectral clustering algorithm. We also propose an efficient eigenvector solver which not only reduces the computational cost of spectral clustering by many folds but also improves the clustering quality and final classification results. Experiments on five standard datasets and comparison with seven existing techniques show the efficacy of our algorithm.

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.

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.

The protein fragment libraries play an important role in a wide variety of structural biology applications. In this work, we present the use of a spectral clustering algorithm to analyze the fixed-length protein backbone fragment sets derived from the continuously growing Protein Data Bank (PDB) to construct libraries of protein fragments. Incorporating the rank-revealing randomized singular value decomposition algorithm into spectral clustering to fast approximate the dominant eigenvectors of the fragment affinity matrix enables the clustering algorithm to handle large-scale fragment sample sets. Compared to the popularly used protein fragment libraries developed by Kolodny et al., the fragments in our new libraries exhibit better representability across diverse protein structures in PDB. Moreover, using much larger fragment sample sets, libraries of longer fragments with length up to 20 residues are also generated. Our fragment libraries can be found at http://hpcr.cs.odu.edu/frag/.

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.

This paper presents a novel use of spectral clustering algorithms to support cases where the entries in the affinity matrix are costly to compute. The method is incremental - the spectral clustering algorithm is applied to the affinity matrix after each row/column is added - which makes it possible to inspect the clusters as new data points are added. The method is well suited to the problem of appearance-based, on-line topological mapping for mobile robots. In this problem domain, we show that we can reduce environment-dependent parameters of the clustering algorithm to just a single, intuitive parameter. Experimental results in large outdoor and indoor environments show that we can close loops correctly by computing only a fraction of the entries in the affinity matrix. The accompanying video clip shows how an example map is produced by the algorithm.

In this paper, we propose a hybrid method for text binarization of historical documents. Proposed method incorporates the advantages of Otsu and spectral clustering algorithm. In text binarization problem, there are noise and faint text challenges. To overcome the noise problem, a preprocessing step is applied to the colored document. After that, the resulted image is binarized using Otsu, producing a global binary image. As a final step, the spectral clustering algorithm is locally applied to the original image, with the aid of the global binary image, in order to retrieve faint text. The proposed design of spectral clustering provides a significant reduction of the similarity matrix computing time and size use, without affecting the quality of clustering. This method is suitable for colored document images. The efficiency of this method is illustrated by experiments using DIBCO images.