Traditional Spectral Clustering Algorithms Research Articles

Spectral Clustering Community Detection Algorithm Based on Point-Wise Mutual Information Graph Kernel.

To address the problem that traditional spectral clustering algorithms cannot obtain the complete structural information of networks, this paper proposes a spectral clustering community detection algorithm, PMIK-SC, based on the point-wise mutual information (PMI) graph kernel. The kernel is constructed according to the point-wise mutual information between nodes, which is then used as a proximity matrix to reconstruct the network and obtain the symmetric normalized Laplacian matrix. Finally, the network is partitioned by the eigendecomposition and eigenvector clustering of the Laplacian matrix. In addition, to determine the number of clusters during spectral clustering, this paper proposes a fast algorithm, BI-CNE, for estimating the number of communities. For a specific network, the algorithm first reconstructs the original network and then runs Monte Carlo sampling to estimate the number of communities by Bayesian inference. Experimental results show that the detection speed and accuracy of the algorithm are superior to other existing algorithms for estimating the number of communities. On this basis, the spectral clustering community detection algorithm PMIK-SC also has high accuracy and stability compared with other community detection algorithms and spectral clustering algorithms.

Spectral Clustering With Adaptive Neighbors for Deep Learning.

Spectral clustering is a well-known clustering algorithm for unsupervised learning, and its improved algorithms have been successfully adapted for many real-world applications. However, traditional spectral clustering algorithms are still facing many challenges to the task of unsupervised learning for large-scale datasets because of the complexity and cost of affinity matrix construction and the eigen-decomposition of the Laplacian matrix. From this perspective, we are looking forward to finding a more efficient and effective way by adaptive neighbor assignments for affinity matrix construction to address the above limitation of spectral clustering. It tries to learn an affinity matrix from the view of global data distribution. Meanwhile, we propose a deep learning framework with fully connected layers to learn a mapping function for the purpose of replacing the traditional eigen-decomposition of the Laplacian matrix. Extensive experimental results have illustrated the competitiveness of the proposed algorithm. It is significantly superior to the existing clustering algorithms in the experiments of both toy datasets and real-world datasets.

Fast spectral clustering with self-adapted bipartite graph learning

Spectral Clustering (SC) is a widespread used clustering algorithm in data mining, image processing, etc. It is a graph-based algorithm capable of handling arbitrarily distributed data. However, the distances of all samples in the high-dimensional space tend to be equal, so the similarity matrix of SC may not be reasonable in high-dimensional data. In addition, the similarity matrix and clustering results in SC are performed in two steps. To solve these problems, a novel joint clustering method called fast spectral clustering with self-adapted bipartite graph learning (FSBGL), is proposed. It is capable of obtaining low-dimensional representations from high dimensional data, thus decreasing the complexity and increase the efficiency of the algorithm. In contrast to traditional spectral clustering algorithms that obtain clustering results in a two-step process, FSBGL obtains clustering results directly from the concatenated components of the optimized similarity matrix while learning the optimized bipartite graph. This eliminates the effect of performing these two steps separately in SC. In effect, a more discriminative low-dimensional representation may be derived from the adaptively learned bipartite graph, while the better low-dimensional representation can continue to be used to learn the structure of the graph. The learning of the bipartite graph alternates with the iteration of the low-dimensional representation, which allows the algorithm to obtain more accurate clustering results. Furthermore, by means of a low-dimensional representation on the basis of fast spectral embedding, the algorithm has better performance on some large-scale datasets. The results of the experiment indicate that the FSBGL is better than other comparative methods in various data sets.

A Method for Detection of Corn Kernel Mildew Based on Co-Clustering Algorithm with Hyperspectral Image Technology.

Hyperspectral imaging can simultaneously acquire spectral and spatial information of the samples and is, therefore, widely applied in the non-destructive detection of grain quality. Supervised learning is the mainstream method of hyperspectral imaging for pixel-level detection of mildew in corn kernels, which requires a large number of training samples to establish the prediction or classification models. This paper presents an unsupervised redundant co-clustering algorithm (FCM-SC) based on multi-center fuzzy c-means (FCM) clustering and spectral clustering (SC), which can effectively detect non-uniformly distributed mildew in corn kernels. This algorithm first carries out fuzzy c-means clustering of sample features, extracts redundant cluster centers, merges the cluster centers by spectral clustering, and finally finds the category of corresponding cluster centers for each sample. It effectively solves the problems of the poor ability of the traditional fuzzy c-means clustering algorithm to classify the data with complex structure distribution and the complex calculation of the traditional spectral clustering algorithm. The experimental results demonstrated that the proposed algorithm could describe the complex structure of mildew distribution in corn kernels and exhibits higher stability, better anti-interference ability, generalization ability, and accuracy than the supervised classification model.

Feature selection based on non-negative spectral feature learning and adaptive rank constraint

Unsupervised feature selection plays a significant role in data classification and clustering. General regression models cannot directly exploit the information on the feature space and fail to accurately describe the local geometric structure of data during feature selection. To address these problems, this paper proposes the feature selection algorithm, which is based on non-negative spectral feature learning and adaptive rank constraint (NNSAFS). First, the algorithm utilizes the residual term in sparse regression to ensure that the learned low-dimensional subspaces have greater fault tolerance and introduces a feature graph on the sparse transformation matrix to reveal the manifold information on the feature space. This sparse transformation matrix is the projection matrix because the introduction of feature graphs on this matrix can connect manifold learning to feature selection. In addition, traditional spectral clustering algorithms usually construct fixed similarity graphs for clustering analysis. The NNSAFS algorithm imposes a rank constraint on the clustering indicator matrix, which is equivalent to the graph regularization that can recover accurate local structure information. Moreover, the similarity matrix in the regularization term is constructed by using the maximum entropy theory, which can increase the adaptability of manifold learning. Finally, the algorithm imposes the l1-norm constraint on the projection matrix, which makes the selected features more conducive to clustering performance. The clustering performance of the NNSAFS algorithm is evaluated against seven other unsupervised feature selection algorithms on nine benchmark datasets. The experimental results show that the features selected by the proposed algorithm are more discriminative and outperform other algorithms in the clustering task.11The code of the proposed algorithm has been uploaded and available at the following link: https://github.com/Vita427/NNSAFS.git.

A fuzzy spectral clustering algorithm for hyperspectral image classification

Spectral clustering is an unsupervised clustering algorithm, and is widely used in the field of pattern recognition and computer vision due to its good clustering performance. However, the traditional spectral clustering algorithm is not suitable for large-scale data classification, such as hyperspectral remote sensing image, because of its high computational complexity, and it is difficult to characterize the inherent uncertainty of the hyperspectral remote sensing image. This paper uses fuzzy anchors to process hyperspectral image classification and proposes a novel spectral clustering algorithm based on fuzzy similarity measure. The proposed algorithm utilizes the fuzzy similarity measure to obtain the similarity between the data points and the anchors, and then gets the similarity matrix. Finally, spectral clustering is performed on the similarity matrix to compute the classification results. The experimental results on the hyperspectral remote sensing image data sets have demonstrated the effectiveness of the proposed algorithm, and the introduction of fuzzy similarity measure gives rise to a more robust similarity matrix. Compared with existing methods, the proposed algorithm has a better classification result on the hyperspectral remote sensing image, and the kappa coefficient obtained by the proposed algorithm is 2% higher than the traditional algorithms.

Improved spectral clustering approach — A new tool for unsupervised seismic facies analysis of variable window length

The traditional constant time window-based waveform classification method is a robust tool for seismic facies analysis. However, when the interval thickness is seismically variable, the fixed time window is not able to contain the complete geologic information of interest. Therefore, the constant time window-based waveform classification method is inapplicable to conduct seismic facies analysis. To expand the application scope of seismic waveform classification in the strata with varying thickness, we have proposed a novel scheme for unsupervised seismic facies analysis of variable window length. The input of the top and bottom horizons can guarantee the comprehensive geologic information of the target interval. Throughout the whole workflow, we use the dynamic time warping (DTW) distance to measure the similarities between seismic waveforms of different lengths. First, we improve the traditional spectral clustering algorithm by replacing the Euclidean distance with the DTW distance. Therefore, it can be applicable in the interval of variable thickness. Second, to solve the problem of large computation when applying the improved spectral clustering approach, we adopt the method of seismic data thinning based on the technology of the superpixel. We combine these two algorithms and perform the integrated workflow of improved spectral clustering. The experiments on synthetic data show that the proposed workflow outperforms the traditional fixed time window-based clustering algorithm in recognizing the boundaries of different lithologies and lithologic associations with varying thickness. The practical application shows great promise for reservoir characterization of interval with varying thickness. The plane map of waveform classification provides convincing reference to delineate reservoir distribution of the data set.

Aesthetic Differences Between Chinese and Western Cultures Based on Big Data Analysis

With the development of the times, the gradual integration of Chinese and foreign civilizations and the continuous expansion of people’s living circles, the aesthetic consciousness of the interior space design of Chinese and Western residential buildings is also changing. The purpose of this article is to analyze the aesthetic differences between Chinese and Western cultures based on big data, analyze the clustering algorithms for aesthetic differences between Chinese and Western cultures, and conclude that different clustering algorithms have their own blind spots and misunderstandings for different data calculation processes. Aiming at the spatial distribution characteristics of aesthetic difference data between Chinese and Western cultures, an improved spectral clustering algorithm is proposed to better solve the problem of clustering and mining of aesthetic difference data between Chinese and Western cultures. The experimental results show that the fast clustering algorithm suitable for the aesthetic difference data sets of Chinese and Western cultures, the improved algorithm reduces the time of the traditional spectral clustering algorithm by 2%.

Phase transition in spectral clustering based on resistance matrix

Community detection is a significant strategy to reveal the structure and function of real-world networks, especially in the era of social big data. Compared with the traditional spectral clustering algorithm for community detection, the spectral clustering algorithm based on resistance matrix reduces the computational complexity. In this work, we first show the presence of a phase transition for community detection strategy based on resistance matrix and show the critical condition in the accuracy of community detection. In detail, when the resistance distance r3 between subnetworks Ci(i=1,2) approaches r∗=n1r1+n2r2n, the detectability of community detection mutates suddenly, where ri(i=1,2) is the mean resistance distance of Ci. Finally, the actual critical value is verified by simulation experiments.

A Wavelet Analysis-Based Big Data Spectral Clustering Algorithm for Electric Internet of Things

As traditional spectral clustering algorithm is not ideal in big data scenarios, this paper proposes a wavelet analysis-based big data spectral clustering algorithm for Electric Internet of Things. Firstly, using wavelet analysis to measure the dissimilarity of the network communication data, and then the similarity relationship between EIoT data is established to obtain the similarity matrix. Finally the spectral clustering algorithm is used to cluster the data based on similarity matrix obtained above. The experimental results show that the accuracy and purity of the proposed spectral clustering algorithm based on wavelet analysis are respectively 36.2 percent and 19.6 percent higher than traditional algorithms, indicating that the proposed spectral clustering algorithm based on wavelet analysis is effective for EIoT data clustering.

Spectral Clustering Algorithm Based on Improved Gaussian Kernel Function and Beetle Antennae Search with Damping Factor.

There are two problems in the traditional spectral clustering algorithm. Firstly, when it uses Gaussian kernel function to construct the similarity matrix, different scale parameters in Gaussian kernel function will lead to different results of the algorithm. Secondly, K-means algorithm is often used in the clustering stage of the spectral clustering algorithm. It needs to initialize the cluster center randomly, which will result in the instability of the results. In this paper, an improved spectral clustering algorithm is proposed to solve these two problems. In constructing a similarity matrix, we proposed an improved Gaussian kernel function, which is based on the distance information of some nearest neighbors and can adaptively select scale parameters. In the clustering stage, beetle antennae search algorithm with damping factor is proposed to complete the clustering to overcome the problem of instability of the clustering results. In the experiment, we use four artificial data sets and seven UCI data sets to verify the performance of our algorithm. In addition, four images in BSDS500 image data sets are segmented in this paper, and the results show that our algorithm is better than other comparison algorithms in image segmentation.

Just noticeable difference color space consistency spectral clustering based on firefly algorithm for image segmentation

When applied into image segmentation, the traditional spectral clustering algorithm may suffer from parameters influence, inconvenient storage, and high computational complexity. In order to solve these problems, a just noticeable difference color space consistency spectral clustering method based on firefly algorithm is proposed to segment color images. Firstly, some representative color pixels are obtained by using just noticeable difference thresholding measure. Then, a similarity measure with the properties of color space connectivity and discreteness measure is proposed to construct the similarity between any two representative pixels. Finally, using the proposed similarity measure, representative color pixels are grouped according to the graph partition criterion. In order to overcome the influence of threshold parameter in just noticeable difference measure, the supervised information and firefly algorithm are introduced in the proposed method. According to the result of representative pixels, all pixels in the image are partitioned into different groups and the final segmentation result is obtained. Experimental results on Berkeley segmentation images show that this method has better segmentation performance and is superior to the existing clustering methods.

Spectral Embedding Norm: Looking Deep into the Spectrum of the Graph Laplacian.

The extraction of clusters from a dataset which includes multiple clusters and a significant background component is a non-trivial task of practical importance. In image analysis this manifests for example in anomaly detection and target detection. The traditional spectral clustering algorithm, which relies on the leading K eigenvectors to detect K clusters, fails in such cases. In this paper we propose the spectral embedding norm which sums the squared values of the first I normalized eigenvectors, where I can be significantly larger than K. We prove that this quantity can be used to separate clusters from the background in unbalanced settings, including extreme cases such as outlier detection. The performance of the algorithm is not sensitive to the choice of I, and we demonstrate its application on synthetic and real-world remote sensing and neuroimaging datasets.

MultiSpectralNet: Spectral Clustering Using Deep Neural Network for Multi-View Data

Multi-view data provide more comprehensive information than single views by providing different feature sets of the same object. Learning its data structure through spectral clustering has always been the mainstream of research. However, due to the limitation of its core graph theory, traditional spectral graph-based multi-view clustering algorithms are inapplicable for analyzing large-scale data sets. In this paper, we propose MultiSpectralNet (MvSN), a deep learning approach to spectral multi-view clustering, provides mapping multi-view data points to their fusion eigenvectors and can obtain a more accurate data structure by correcting the misleading information in the single views to a certain extent by feedback in the network training process. In addition, our model can cluster large multi-view data sets and provide cluster prediction for out-of-sample extension. We test ACC and normalized mutual information (NMI) of our method in clustering several artificial and real-world data sets, and the experimental results show that our method outperforms conventional compared state-of-the-art works.

An Improvement of Spectral Clustering via Message Passing and Density Sensitive Similarity

Spectral clustering transforms the data clustering problem into a graph-partitioning problem and classifies data points by finding the optimal sub-graphs. Traditional spectral clustering algorithms use Gaussian kernel function to construct the similarity matrix, so they are sensitive to the selection of scale parameter. In addition, they need to randomly determine the initial cluster centers at the clustering stage and the clustering performance is not stable. Therefore, this paper presents an algorithm on the basis of message passing, which makes use of a density adaptive similarity measure, describing the relations between data points and obtaining high-quality cluster centers through message passing mechanism in AP clustering. The performance of clustering is optimized by this method. The experiments show that the proposed algorithm can effectively deal with the clustering problem of multi-scale datasets. Moreover, its clustering performance is very stable, and the clustering quality is better than traditional spectral clustering algorithm and k-means algorithm.

Image segmentation algorithm based on superpixel clustering

The main task of image segmentation is to partition an image into disjoint sets of pixels called clusters. Spectral clustering algorithm has been developed rapidly in recent years and it has been widely used in image segmentation. The traditional spectral clustering algorithm requires huge amount of computation to process colour images with high resolution. While one possible solution is reducing image resolution, but it will lead to the loss of image information and reduce segmentation performance. To overcome the problem of traditional spectral clustering, an image segmentation algorithm based on superpixel clustering is proposed. Firstly, the algorithm uses the superpixel preprocessing technique to quickly divide the image into a certain number of superpixel regions with specific information. Then, the similarity matrix is used to provide the input information to the spectral clustering algorithm to cluster the superpixel regions and get the final image segmentation results. The experiment results show that the proposed algorithm can effectively improve the performance in image segmentation compared with the traditional spectral clustering algorithm, and finally the substantial improvement has been obtained in respect of computational complexity, processing time and the overall segmentation effect.

Resource Scheduling Based on Improved Spectral Clustering Algorithm in Edge Computing

With the development of Internet of Things (IoT), the massive data generated by it forms big data, and the complexity of dealing with big data brings challenges to resource scheduling in edge computing. In order to solve the problem of resource scheduling and improve the satisfaction of users in edge computing environment, we propose a user-oriented improved spectral clustering scheduling algorithm (ISCM) in this paper. Based on the improved k-means algorithm, the ISCM algorithm solves the problem that the clustering result is sensitive to the initial value and realizes the reclustering, which makes the obtained clustering results more stable. Finally, the edge computing resource scheduling scheme is obtained based on the clustering results. The experimental results show that the resource scheduling scheme based on improved spectral clustering algorithm is superior to traditional spectral clustering algorithm in edge computing environment.

Unified Spectral Clustering With Optimal Graph

Spectral clustering has found extensive use in many areas. Most traditional spectral clustering algorithms work in three separate steps: similarity graph construction; continuous labels learning; discretizing the learned labels by k-means clustering. Such common practice has two potential flaws, which may lead to severe information loss and performance degradation. First, predefined similarity graph might not be optimal for subsequent clustering. It is well-accepted that similarity graph highly affects the clustering results. To this end, we propose to automatically learn similarity information from data and simultaneously consider the constraint that the similarity matrix has exact c connected components if there are c clusters. Second, the discrete solution may deviate from the spectral solution since k-means method is well-known as sensitive to the initialization of cluster centers. In this work, we transform the candidate solution into a new one that better approximates the discrete one. Finally, those three subtasks are integrated into a unified framework, with each subtask iteratively boosted by using the results of the others towards an overall optimal solution. It is known that the performance of a kernel method is largely determined by the choice of kernels. To tackle this practical problem of how to select the most suitable kernel for a particular data set, we further extend our model to incorporate multiple kernel learning ability. Extensive experiments demonstrate the superiority of our proposed method as compared to existing clustering approaches.

Optimization and Application of Clustering Algorithm in Community Discovery

In order to make up for the defect that the traditional spectral clustering algorithm cannot determine the number of clusters and the time-consuming calculation, this paper studies and improves the spectral clustering algorithm. In complex community networks, the spectral clustering algorithm based on modularity optimization is chosen to find the number of communities. In addition, four types of user attribute information are integrated, and a more reasonable user similarity model is constructed. At the same time, the original non-parallelized spectral clustering algorithm is optimized, and its improved scheme is suitable for the application of distributed computing. Many Hadoop optimization strategies are proposed for virtual community discovery scenarios in large-scale communities. Finally, the experimental results show that the efficiency of the parallelized spectral clustering algorithm is greatly improved, which can be applied to the virtual community discovery in large-scale social networks.

Constrains optimal propagation-based modified semi-supervised spectral clustering for large-scale data

We focus on the problem of high computational complexity in the clustering process of traditional spectral clustering algorithm that cannot satisfy the requirement of current large-scale data clustering applications. In this article, we establish a constrained optimal propagation based semi-supervised large-scale data clustering model. In this model, micro similarity matrix is constructed by using prior dotted pair constraint information at first. On this basis, the Gabow algorithm is exploited to extract each strongly connected component from the micro similarity matrix that is represented by its connected graph. Then, a new constrained optimisation propagation algorithm for each strongly connected component is proposed to calculate the similarity of the whole dataset. Finally, we employ the singular value decomposition and the accelerated k-means algorithm to obtain the clustering results of large-scale data. Experiments on multiple standard testing datasets show that compared with other previous research results in this field, the proposed clustering model has higher clustering accuracy and lower computation complexity, and is more suitable for large-scale data clustering applications.