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Spectral Clustering (SC) is an important method in areas such as data mining, image processing, computer science and so on. It attracts more and more attention owing to its effectiveness in unsupervised learning. However, SC has poor performance in the high-dimensional data. Traditional SC methods conduct the spectral embedding of the affinity matrix among data at the first beginning, and then obtain clustering results by the K -means clustering. The also have drawbacks int two processing steps: the clustering results are sensitive to the affinity matrix which may be inaccurate and the post-processing K -means may also be limited by its initialization problem. In the paper, a new approach which joints spectral embedding and clustering with structured graph optimization (called JSEGO) is proposed. In the new model, the low-dimensional representation of data can first be obtained by the spectral embedding method, which can handle with the high-dimensional data better. Then, the optimization similarity matrix would be obtained with such the embedded data. Furthermore, the learning structure graph gives feedback to the similarity matrix to generate better spectral embedded data. As a result, better similarity matrix and clustering result can be obtained by the iterations simultaneously, which are often conducted in two separate steps in the spectral clustering. As a result, the drawbacks introduced by the two processing introduces can be solved. At last, we use an alternative optimization method in the new model and conduct the theoretical analysis by comparing this proposed method with K -means clustering. Experiments based on synthetic data and actual benchmark data prove the advantage of this new approach. [ABSTRACT FROM AUTHOR]

• Semi-supervised hashing-based affinity matrix computation method is proposed for DSC. • Unsupervised extension of the HAM-DSC is proposed for unsupervised clustering cases. • HAM-DSC yields the better experimental clustering performance with lowest time cost. Dominant set clustering has been widely used to solve a variety of problems such as image segmentation, video analysis, and image retrieval. However, the key problem of it is the need of a given affinity matrix to provide similarity for every pair of data points. The affinity matrix is either user-given or computed using a pairwise computation, which is impractical for big data situations. Therefore, this work proposes a semi-supervised hashing-based affinity matrix computation method (HAM) for dominant set clustering (HAM-DSC) for cases of semi-supervised clustering where labels are available to a portion of data. The HAM computes affinity matrix efficiently based on Hamming distance between learned hash codes, which preserve semantic similarities effectively. To deal with unsupervised clustering problems, an unsupervised extension of the HAM-DSC is also given in this work. Experimental results on 7 real-world datasets show that the HAM-DSC yields an overall better performance together with lower time costs compared to dominant set clustering using other affinity matrix computation methods. [ABSTRACT FROM AUTHOR]

We propose a symmetric low-rank representation (SLRR) method for subspace clustering, which assumes that a data set is approximately drawn from the union of multiple subspaces. The proposed technique can reveal the membership of multiple subspaces through the self-expressiveness property of the data. In particular, the SLRR method considers a collaborative representation combined with low-rank matrix recovery techniques as a low-rank representation to learn a symmetric low-rank representation, which preserves the subspace structures of high-dimensional data. In contrast to performing iterative singular value decomposition in some existing low-rank representation based algorithms, the symmetric low-rank representation in the SLRR method can be calculated as a closed form solution by solving the symmetric low-rank optimization problem. By making use of the angular information of the principal directions of the symmetric low-rank representation, an affinity graph matrix is constructed for spectral clustering. Extensive experimental results show that it outperforms state-of-the-art subspace clustering algorithms. [ABSTRACT FROM AUTHOR]

In the first part of this paper, we present a method to build affinity matrices for spectral clustering from a density estimator relying on K-means with subbagging procedure. The approach is anchored in the theoretical works of Wong (1980, 1982a, b) [13–15] on the asymptotic properties of K-means as a density estimation method. The subbagging procedure is introduced to improve the density estimate accuracy. The behavior of the proposed method is analyzed on diverse data sets and two new mechanisms are suggested to improve clustering results on non-convex data. In the second part of the paper, we establish a link between the presented method and the evidence accumulation clustering (EAC) approach by showing that a normalized version of the density-based similarity matrix is approximately equal to a normalized version of the co-association matrix. The co-association matrix provides the co-occurrence probability of data pairs assigned to a same cluster over multiple K-means clustering partitions. Experimental results on artificial and real data demonstrate the effectiveness of the method and provide empirical support for the established link. [ABSTRACT FROM AUTHOR]

Abstract: Ng–Jordan–Weiss (NJW) spectral clustering method partitions data using the largest K eigenvectors of the normalized affinity matrix derived from a dataset, but when the dataset is of complex structure, the affinity matrix constructed by traditional Gaussian function could not reflect the real similarity among data points, then the decision of clustering number and selection of K largest eigenvectors are not always effective. Constructing a good affinity matrix is very important to spectral clustering. A new affinity matrix generation method is proposed by using neighbor relation propagation principle and a neighbor relation propagation algorithm is also given. The affinity matrix generated can increase the similarity of point pairs that should be in same cluster and can well detect the structure of data. An improved multi-way spectral clustering algorithm is proposed then. We have performed experiments on dataset of complex structure, adopting Tian Xia and his partner''s method for a baseline. The experiment result shows that our affinity matrix well reflects the real similarity among data points and selecting the largest K Eigenvectors gives the correct partition. We have also made comparison with NJW method on some common datasets, the results show that our method is more robust. [Copyright &y& Elsevier]