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While orthogonalization exists in current dimensionality reduction methods in spectral clustering on undirected graphs, it does not scale in parallel computing environments. We propose four orthogonalization-free methods for spectral…

Spectral clustering is a leading clustering method. Two of its major shortcomings are the disjoint optimization process and the limited representation capacity. To address these issues, we propose a deep spectral clustering model (named…

Cluster algorithms are increasingly popular in biomedical research due to their compelling ability to identify discrete subgroups in data, and their increasing accessibility in mainstream software. While guidelines exist for algorithm…

Spectral clustering is known as a powerful technique in unsupervised data analysis. The vast majority of approaches to spectral clustering are driven by a single modality, leaving the rich information in multi-modal representations…

Spectral Clustering (SC) is a widely used data clustering method which first learns a low-dimensional embedding $U$ of data by computing the eigenvectors of the normalized Laplacian matrix, and then performs k-means on $U^\top$ to get the…

The k-means clustering algorithm is a popular algorithm that partitions data into k clusters. There are many improvements to accelerate the standard algorithm. Most current research employs upper and lower bounds on point-to-cluster…

In this paper, the new algorithm based on clustered multitask network is proposed to solve spectral unmixing problem in hyperspectral imagery. In the proposed algorithm, the clustered network is employed. Each pixel in the hyperspectral…

We propose and study a novel graph clustering method for data with an intrinsic network structure. Similar to spectral clustering, we exploit an intrinsic network structure of data to construct Euclidean feature vectors. These feature…

We focus on spectral clustering of unlabeled graphs and review some results on clustering methods which achieve weak or strong consistent identification in data generated by such models. We also present a new algorithm which appears to…

Subspace clustering aims to group data points into multiple clusters of which each corresponds to one subspace. Most existing subspace clustering approaches assume that input data lie on linear subspaces. In practice, however, this…

It has always been a great challenge for clustering algorithms to automatically determine the cluster numbers according to the distribution of datasets. Several approaches have been proposed to address this issue, including the recent…

Recent work on deep clustering has found new promising methods also for constrained clustering problems. Their typically pairwise constraints often can be used to guide the partitioning of the data. Many problems however, feature…

Graph clustering involves the task of dividing nodes into clusters, so that the edge density is higher within clusters as opposed to across clusters. A natural, classic and popular statistical setting for evaluating solutions to this…

In the last few years, large improvements in image clustering have been driven by the recent advances in deep learning. However, due to the architectural complexity of deep neural networks, there is no mathematical theory that explains the…

In many statistical linear inverse problems, one needs to recover classes of similar curves from their noisy images under an operator that does not have a bounded inverse. Problems of this kind appear in many areas of application.…

The problem of estimating the number of clusters (say k) is one of the major challenges for the partitional clustering. This paper proposes an algorithm named k-SCC to estimate the optimal k in categorical data clustering. For the…

Clustering is a fundamental task in unsupervised learning. Previous research has focused on learning-augmented $k$-means in Euclidean metrics, limiting its applicability to complex data representations. In this paper, we generalize…

Graph clustering is a basic technique in machine learning, and has widespread applications in different domains. While spectral techniques have been successfully applied for clustering undirected graphs, the performance of spectral…

Our problem of interest is to cluster vertices of a graph by identifying underlying community structure. Among various vertex clustering approaches, spectral clustering is one of the most popular methods because it is easy to implement…

A natural way to characterize the cluster structure of a dataset is by finding regions containing a high density of data. This can be done in a nonparametric way with a kernel density estimate, whose modes and hence clusters can be found…