A Spectral Clustering Image Segmentation Algorithm Based on Nyström Approximation

Simulated annealing spectral clustering algorithm for image segmentation

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.

Clustering is often considered as an unsupervised data analysis method, but making full use of the prior information in the process of clustering will significantly improve the performance of the clustering algorithm. Spectral clustering algorithm can well use the prior pairwise constraint information to cluster and has become a new hot spot of machine learning research in recent years. In this paper, we propose an effective clustering algorithm, called a semi-supervised spectral clustering algorithm based on pairwise constraints, in which the similarity matrix of data points is adjusted and optimized by pairwise constraints. The experiments on real-world data sets demonstrate the effectiveness of this algorithm.

Fuzzy spectral clustering with robust spatial information for 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.

An unsupervised learning algorithm, named soft spectral clustering ensemble (SSCE), is proposed in this paper. Until now many proposed ensemble algorithms cannot be used on image data, even images of a mere 256 × 256 pixels are too expensive in computational cost and storage. The proposed method is suitable for performing image segmentation and can, to some degree, solve some open problems of spectral clustering (SC). In this paper, a random scaling parameter and Nystrom approximation are applied to generate the individual spectral clusters for ensemble learning. We slightly modify the standard SC algorithm to aquire a soft partition and then map it via a centralized logcontrast transform to relax the constraint of probability data, the sum of which is one. All mapped data are concatenated to form the new features for each instance. Principal component analysis (PCA) is used to reduce the dimension of the new features. The final aggregated result can be achieved by clustering dimension-reduced data. Experimental results, on UCI data and different image types, show that the proposed algorithm is more efficient compared with some existing consensus functions.

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.

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.

Recently, spectral clustering has become one of the most popular modern clustering algorithms which are mainly applied to image segmentation. In this paper, we propose a new spectral clustering algorithm and attempt to use it for outlier detection in dataset. Our algorithm takes the number of neighborhoods shared by the objects as the similarity measure to construct a spectral graph. It can help to isolate outliers as well as construct a sparse matrix. We compare the performance of our algorithm with the k-means based clustering algorithm while using them to detect outliers. Experiment results show that the algorithm can obtain stable clusters and is efficient for identifying outliers.

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.

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.

Constrained spectral embedding for K-way data clustering

Introduction: The discovery of tumor subtypes helps to explore tumor pathogenesis, determine the operability of clinical treatment, and improve patient survival. Clustering analysis is increasingly applied to multi-genomic data. However, due to the diversity and complexity of multi-omics data, developing a complete clustering algorithm for tumor molecular typing is still challenging. Methods: In this study, we present an adaptive density-aware spectral clustering method based on a variational autoencoder (ADSVAE). ADSVAE first learns the underlying spatial information of each omics data using a variational autoencoder (VAE) based on the Wasserstein distance metric. Secondly, a similarity matrix is built for each gene set using an adaptive density-aware kernel. Thirdly, tensor product graphs (TPGs) are used to merge different data sources and reduce noise. Finally, ADSVAE employs a spectral clustering algorithm and utilizes the Gaussian mixture model (GMM) to cluster the final eigenvector matrix to identify cancer subtypes. Results: We tested ADSVAE on 5 TCGA datasets, all with good performance in comparison with several advanced multi-omics clustering algorithms. Compared with the existing multi-group clustering algorithms, the variational autoencoder based on the Wasserstein distance measure in the ADSVAE algorithm can learn the underlying spatial information on each omics data, which has a better effect on learning complex data distribution. The self-tuning density-aware kernel used by the ADSVAE algorithm enhances the similarity between shared near neighbor points, and the process of tensor product plot data integration and diffusion can better reduce the noise and reveal the underlying structure, improving the performance. Conclusion: Due to the inherent pitfalls of computational biology in the study of cancer subtype identification, although some research conclusions have been made in this paper on the related issues, as the research in related fields continues to deepen, the clustering study of cancer subtype identification based on genomic data needs further improvement and refinement.

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.

Image segmentation method based on the existing spectrum clustering algorithm cannot accurately segment sonar image because of the ambiguous object edge, extremely complex noisy background and critical shadow impact of sonar image, and aiming at this problem, this paper proposed an improved spectrum clustering sonar image segmentation method. First of all, to overcome negative impact of the sonar image shadow and achieve selective segmentation of sonar target, morphological top-hat transformation and bottom-hat transformation were used for sonar image preprocessing; Secondly, image segmentation based on spectrum clustering was done after preprocessing and an improved spectral clustering sonar image segmentation system was constructed; Finally, simulation experiment was taken and the results showed that the proposed method is more suitable for sonar image segmentation.