It is crucial to evaluate the quality of clustering results in cluster analysis. Although many cluster validity indices (CVIs) have been proposed in the literature, they have some limitations when dealing with non-spherical datasets. One reason is that the measure of cluster separation does not consider the impact of outliers and neighborhood clusters. In this paper, a new robust distance measure, one into which density is incorporated, is designed to solve the problem, and an internal validity index based on this separation measure is then proposed. This index can cope with both the spherical and non-spherical structure of clusters. The experimental results indicate that the proposed index outperforms some classical CVIs. The MATLAB code and experimental data are available at https://github.com/hulianyu/CVDD
Spectral clustering is one of the most popular clustering methods. However, how to balance the efficiency and effectiveness of the large-scale spectral clustering with limited computing resources has not been properly solved for a long time. In this paper, we propose a divide-and-conquer based large-scale spectral clustering method to strike a good balance between efficiency and effectiveness. In the proposed method, a divide-and-conquer based landmark selection algorithm and a novel approximate similarity matrix approach are designed to construct a sparse similarity matrix within low computational complexities. Then clustering results can be computed quickly through a bipartite graph partition process. The proposed method achieves a lower computational complexity than most existing large-scale spectral clustering methods. Experimental results on ten large-scale datasets have demonstrated the efficiency and effectiveness of the proposed method. The MATLAB code of the proposed method and experimental datasets are available at https://github.com/Li-Hongmin/MyPaperWithCode.
Ensemble clustering has attracted much attention in machine learning and data mining for the high performance in the task of clustering. Spectral clustering is one of the most popular clustering methods and has superior performance compared with the traditional clustering methods. Existing ensemble clustering methods usually directly use the clustering results of the base clustering algorithms for ensemble learning, which cannot make good use of the intrinsic data structures explored by the graph Laplacians in spectral clustering, thus cannot obtain the desired clustering result. In this paper, we propose a new ensemble learning method for spectral clustering-based clustering algorithms. Instead of directly using the clustering results obtained from each base spectral clustering algorithm, the proposed method learns a robust presentation of graph Laplacian by ensemble learning from the spectral embedding of each base spectral clustering algorithm. Finally, the proposed method applies k-means on the spectral embedding obtain from the learned graph Laplacian to get clusters. Experimental results on both synthetic and real-world datasets show that the proposed method outperforms other existing ensemble clustering methods.
This paper focuses on scalability and robustness of spectral clustering for extremely large-scale datasets with limited resources. Two novel algorithms are proposed, namely, ultra-scalable spectral clustering (U-SPEC) and ultra-scalable ensemble clustering (U-SENC). In U-SPEC, a hybrid representative selection strategy and a fast approximation method for K-nearest representatives are proposed for the construction of a sparse affinity sub-matrix. By interpreting the sparse sub-matrix as a bipartite graph, the transfer cut is then utilized to efficiently partition the graph and obtain the clustering result. In U-SENC, multiple U-SPEC clusterers are further integrated into an ensemble clustering framework to enhance the robustness of U-SPEC while maintaining high efficiency. Based on the ensemble generation via multiple U-SEPC's, a new bipartite graph is constructed between objects and base clusters and then efficiently partitioned to achieve the consensus clustering result. It is noteworthy that both U-SPEC and U-SENC have nearly linear time and space complexity, and are capable of robustly and efficiently partitioning ten-million-level nonlinearly-separable datasets on a PC with 64GB memory. Experiments on various large-scale datasets have demonstrated the scalability and robustness of our algorithms. The MATLAB code and experimental data are available at https://www.researchgate.net/publication/330760669.
Learning graphs from data automatically has shown encouraging performance on clustering and semisupervised learning tasks. However, real data are often corrupted, which may cause the learned graph to be inexact or unreliable. In this paper, we propose a novel robust graph learning scheme to learn reliable graphs from real-world noisy data by adaptively removing noise and errors in the raw data. We show that our proposed model can also be viewed as a robust version of manifold regularized robust PCA, where the quality of the graph plays a critical role. The proposed model is able to boost the performance of data clustering, semisupervised classification, and data recovery significantly, primarily due to two key factors: 1) enhanced low-rank recovery by exploiting the graph smoothness assumption, 2) improved graph construction by exploiting clean data recovered by robust PCA. Thus, it boosts the clustering, semi-supervised classification, and data recovery performance overall. Extensive experiments on image/document clustering, object recognition, image shadow removal, and video background subtraction reveal that our model outperforms the previous state-of-the-art methods.
Spectral clustering is one of the most effective clustering approaches that capture hidden cluster structures in the data. However, it does not scale well to large-scale problems due to its quadratic complexity in constructing similarity graphs and computing subsequent eigendecomposition. Although a number of methods have been proposed to accelerate spectral clustering, most of them compromise considerable information loss in the original data for reducing computational bottlenecks. In this paper, we present a novel scalable spectral clustering method using Random Binning features (RB) to simultaneously accelerate both similarity graph construction and the eigendecomposition. Specifically, we implicitly approximate the graph similarity (kernel) matrix by the inner product of a large sparse feature matrix generated by RB. Then we introduce a state-of-the-art SVD solver to effectively compute eigenvectors of this large matrix for spectral clustering. Using these two building blocks, we reduce the computational cost from quadratic to linear in the number of data points while achieving similar accuracy. Our theoretical analysis shows that spectral clustering via RB converges faster to the exact spectral clustering than the standard Random Feature approximation. Extensive experiments on 8 benchmarks show that the proposed method either outperforms or matches the state-of-the-art methods in both accuracy and runtime. Moreover, our method exhibits linear scalability in both the number of data samples and the number of RB features.