Clustering by Mining Density Distributions and Splitting Manifold Structure

Spectral clustering has been successfully used in the field of pattern recognition and image processing. The efficiency of spectral clustering, however, depends heavily on the similarity measure adopted. A widely used similarity measure is the Gaussian kernel function where Euclidean distance is used. Unfortunately, the Gaussian kernel function is parameter sensitive and the Euclidean distance is usually not suitable to the complex distribution data. In this paper, a novel similarity measure called kernel fuzzy similarity measure is proposed first, Then this novel measure is integrated into spectral clustering to get a new clustering method: kernel fuzzy similarity based spectral clustering (KFSC). To alleviate the computational complexity of KFSC on image segmentation, Nystr\(\ddot{o}\)m method is used in KFSC. At last, the experiments on three synthetic texture images are made, and the results demonstrate the effectiveness of the proposed algorithm.

Simulated annealing spectral clustering algorithm for image segmentation

Spectral clustering and DBSCAN are two famous clustering methods, the former reduces data dimensionality by spectrum of similarity matrix, and then utilizes kmeans to cluster data in low dimensional space. While DBSCAN performs clustering by finding different density regions that depart from each other, which makes it seems quite different from spectral clustering, and there is little literal discusses the relationship between them. In this paper, we revisit DBSCAN from Similarity Graph and Graph Cut point of views, uncover the underlying relationship between DBSCAN and spectral clustering, which proves that DBSCAN can be explained and rewritten under the framework of spectral clustering. Furthermore, eigenvectors are often approximately resolved, and k-means is usually used in the final stage, often converges in local optimization. Hence, we rewrite spectral clustering by using nearest neighbor query instead of k-means to obtain exact result. Experimental results address that the revised spectral clustering method can obtain the same result as DBSCAN on core point set. Therefore, we come to the conclusion that DBSCAN is semi-spectral clustering. The work of this paper theoretically illustrates that spectral clustering is as good as DBSCAN, and both algorithms can be replaced with each other to avoid their own disadvantages.

In this paper, a spectral clustering method based on relation-invariable persistent formation (RIPF) is proposed, which can character the similarity graph succinctly. RIPF is an optimal formation, which can remain the formation by using least edges in the comminution graph. After generating the RIPF, the algorithm builds a network graph weighted according to distance between neighborhoods, and then applies spectral clustering. Three methods to construct similarity graphs in standard spectral clustering are ε -neighborhood graph, k- nearest neighbor graph, or fully connected graph. However, ε -neighborhood graph or k -nearest neighbor graph is sensitive to the parameters ε or k, and fully connected similarity graph of which is redundant. The similarity graph is constructed by generating RIPF, which can model the concise local neighborhood relationships by using the least edges in similarity graph. In this paper, a new algorithm is proposed to weaken the parameter dependence while maintaining the solution quality. Experimental results show that out algorithm performs as well as or even better than the state-of-the-art standard spectral methods.

The matrix factorization recommender system based on manifold regularization, taking into account the similarity of local neighbors and manifold structure, can improve the quality of a recommendation system. However, the similarity between samples may not be accurate due to the sparsity of the data or the incompleteness of the tag information. Therefore, we propose a new model called SI-GMF (Similarity-learning-based Improved Graph Regularized matrix Factorization) by embedding the new similarity measure strategy in GMF (Graph Regularized matrix Factorization) framework, and induce three new matrix factorization algorithms (SI-GMF_1, SI-GMF_2, SI-GMF_3) based on three initial similarities by employing three different similarity measures. The solutions to the newly developed algorithms can be effectively obtained by SGD method. The experimental results show that the newly designed algorithms significantly improve the accuracy of a recommender system.

A fast spectral clustering technique using MST based proximity graph for diversified datasets

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.

A new method to build the adaptive k-nearest neighbors similarity graph matrix for spectral clustering

Unsupervised feature selection via discrete spectral clustering and feature weights

Remote homology detection among proteins utilizing only the unlabelled sequences is a central problem in comparative genomics. The existing cluster kernel methods based on neighborhoods and profiles and the Markov clustering algorithms are currently the most popular methods for protein family recognition. The deviation from random walks with inflation or dependency on hard threshold in similarity measure in those methods requires an enhancement for homology detection among multi-domain proteins. We propose to combine spectral clustering with neighborhood kernels in Markov similarity for enhancing sensitivity in detecting homology independent of “recent” paralogs. The spectral clustering approach with new combined local alignment kernels more effectively exploits the unsupervised protein sequences globally reducing inter-cluster walks. When combined with the corrections based on modified symmetry based proximity norm deemphasizing outliers, the technique proposed in this article outperforms other state-of-the-art cluster kernels among all twelve implemented kernels. The comparison with the state-of-the-art string and mismatch kernels also show the superior performance scores provided by the proposed kernels. Similar performance improvement also is found over an existing large dataset. Therefore the proposed spectral clustering framework over combined local alignment kernels with modified symmetry based correction achieves superior performance for unsupervised remote homolog detection even in multi-domain and promiscuous domain proteins from Genolevures database families with better biological relevance. Source code available upon request. Contact: sarkar@labri.fr.

Clustering of independent component (IC) topographies of Electroencephalograms (EEG) is an effective way to find brain-generated IC processes associated with a population of interest, particularly for those cases where event-related potential features are not available. This paper proposes a novel algorithm for the clustering of these IC topographies and compares its results with the most currently used clustering algorithms. In this study, 32-electrode EEG signals were recorded at a sampling rate of 500 Hz for 48 participants. EEG signals were pre-processed and IC topographies computed using the AMICA algorithm. The algorithm implements a hybrid approach where genetic algorithms are used to compute more accurate versions of the centroids and the final clusters after a pre-clustering phase based on spectral clustering. The algorithm automatically selects the optimum number of clusters by using a fitness function that involves local-density along with compactness and separation criteria. Specific internal validation metrics adapted to the use of the absolute correlation coefficient as the similarity measure are defined for the benchmarking process. Assessed results across different ICA decompositions and groups of subjects show that the proposed clustering algorithm significantly outperforms the (baseline) clustering algorithms provided by the software EEGLAB, including CORRMAP.

Improving Analytics in Urban Water Management: A Spectral Clustering-based Approach for Leakage Localization

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.

Adaptive subspace clustering techniques, such as LDA Kmeans (henceforth LDAKM), try to perform clustering on a compact discriminative subspace. However, the subspace extracted by LDAKM may be inferior when encountering noise, so it is with the clustering results. In this paper, we generalize the LDAKM algorithm, and propose the Local Manifold Preserving LDAKM (henceforth LMP–LDAKM) approach, which considers both local manifold structure and discriminative information. A Laplacian similarity matrix is introduced in the subspace extraction subprocess for preserving local manifold information while retaining discrimination of latent clusters, and it is also utilized for the weighted Kmeans clustering subprocess in the subspace to eliminate the influence of distant noise data. Experimental results on both benchmark and artificial datasets indicate the effectiveness and noise-robustness of our method.

The paper propose a new non-linear dimensionality reduction algorithm based on locally linear embedding called supervised locally linear embedding in tensor space (SLLE/T), in which the local manifold structure within same class are preserved and the separability between different classes is enforced by maximizing distance of each point with its neighbors. To keep structure of data, we introduce tensor representation and reduce SLLE/T into the optimization problem based on HOSVD which is desirable to solve the out of sample problem. We also prove SLLE/T can be united in the graph embedding framework. The comparison experiments on face recognition indicate that SLLE/T outperform most popular dimensionality reduction algorithms both vectorization and tensor version.