A Spectral Clustering Algorithm for Outlier Detection

Simulated annealing spectral clustering algorithm for image segmentation

Fuzzy spectral clustering with robust spatial information for image segmentation

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.

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.

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.

Spectral clustering is one of the most popular modern clustering techniques for conventional data. However, the application of the general spectral clustering method in the geostatistical data framework poses a double challenge. Firstly, applied to geostatistical data, the general spectral clustering method produces clusters that are spatially non-contiguous which is undesirable for many geoscience applications. Secondly, it is limited in its applicability to large-scale problems due to its high computational complexity. This paper presents a spectral clustering method dedicated to large-scale geostatistical datasets in which spatial dependence plays an important role. It extends a previous work to large-scale geostatistical datasets by computing the similarity matrix only at a reduced set of locations over the study domain referred to as anchor locations. It has the advantage of using all data during the computation of the similarity matrix at anchor locations; so there is no sacrifice of data. The spectral clustering algorithm can then be efficiently performed on this similarity matrix at anchor locations rather than all data locations. Given the resulting cluster labels of anchor locations, a weighted k-nearest-neighbour classifier is trained using their geographical coordinates as covariates and their cluster labels as the response. The assignment of clustering membership to the entire data locations is obtained by applying the trained classifier. The effectiveness of the proposed method to discover spatially contiguous and meaningful clusters in large-scale geostatistical datasets is illustrated using the US National Geochemical Survey database.

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.

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.

Text document clustering using Spectral Clustering algorithm with Particle Swarm Optimization

QR image feature extraction effectiveness based on metrics using spectral clustering and grey level Co-Occurrence matrix algorithm

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/.

The widespread adoption of Electric Vehicles (EVs) and their uncoordinated simultaneous charging puts additional stress on the grid due to an increase in peak load. The charging schedule of EVs can be coordinated by an EV Aggregator (EVA) through appropriate price signals. This paper presents an optimal scheduling framework for EV clusters using Time-of-use (TOU) price. Firstly, the EVA aggregates the total demand corresponding to the vehicle's arrival and departure times for optimal power scheduling using clustering algorithms. The accuracy of cluster-based aggregation plays a vital role, hence this study adopts the advanced clustering technique: spectral clustering algorithm, to accurately cluster the EVs. However, the optimal EV scheduling is motivated by dynamic prices like Real-Time Price (RTP) and Time of Use (TOU) but the acceptance rate of RTP is quite less due to its highly volatile nature. Hence, the proposed work focuses on the optimal scheduling of EV clusters based on TOU prices. For this, the historical data of RTPs are considered for TOU price design using hierarchical clustering. For the case study, 500 EVs are aggregated using spectral clustering and compared with the traditional k-means. The aggregation results are analyzed using Principal Component Analysis (PCA) decomposition; highlighting the increased accuracy of aggregation in terms of time. Further, the optimal scheduling of EV clusters is achieved based on the proposed pricing and aggregation strategies.

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.