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The sparsity of natural signals and images in a transform domain or dictionary has been extensively exploited in several applications such as compression, denoising and inverse problems. More recently, data-driven adaptation of synthesis…
Subspace clustering is the problem of partitioning unlabeled data points into a number of clusters so that data points within one cluster lie approximately on a low-dimensional linear subspace. In many practical scenarios, the…
Subspace clustering refers to the task of finding a multi-subspace representation that best fits a collection of points taken from a high-dimensional space. This paper introduces an algorithm inspired by sparse subspace clustering (SSC) [In…
Subspace clustering is the unsupervised grouping of points lying near a union of low-dimensional linear subspaces. Algorithms based directly on geometric properties of such data tend to either provide poor empirical performance, lack…
Graph clustering is a crucial task in network analysis with widespread applications, focusing on partitioning nodes into distinct groups with stronger intra-group connections than inter-group ones. Recently, contrastive learning has…
Despite its nonconvex nature, $\ell_0$ sparse approximation is desirable in many theoretical and application cases. We study the $\ell_0$ sparse approximation problem with the tool of deep learning, by proposing Deep $\ell_0$ Encoders. Two…
Auto-Encoder (AE)-based deep subspace clustering (DSC) methods have achieved impressive performance due to the powerful representation extracted using deep neural networks while prioritizing categorical separability. However,…
In this paper, we present a deep extension of Sparse Subspace Clustering, termed Deep Sparse Subspace Clustering (DSSC). Regularized by the unit sphere distribution assumption for the learned deep features, DSSC can infer a new data…
A data filtering method for cluster analysis is proposed, based on minimizing a least squares function with a weighted $\ell_0$-norm penalty. To overcome the discontinuity of the objective function, smooth non-convex functions are employed…
Sparse estimation methods are aimed at using or obtaining parsimonious representations of data or models. While naturally cast as a combinatorial optimization problem, variable or feature selection admits a convex relaxation through the…
Sparse subspace clustering (SSC) is a state-of-the-art method for segmenting a set of data points drawn from a union of subspaces into their respective subspaces. It is now well understood that SSC produces subspace-preserving data affinity…
Accurate land cover segmentation of spectral images is challenging and has drawn widespread attention in remote sensing due to its inherent complexity. Although significant efforts have been made for developing a variety of methods, most of…
Graph clustering is an unsupervised machine learning method that partitions the nodes in a graph into different groups. Despite achieving significant progress in exploiting both attributed and structured data information, graph clustering…
Spectral clustering (SC) and graph-based semi-supervised learning (SSL) algorithms are sensitive to how graphs are constructed from data. In particular if the data has proximal and unbalanced clusters these algorithms can lead to poor…
Spectral-based subspace clustering methods have proved successful in many challenging applications such as gene sequencing, image recognition, and motion segmentation. In this work, we first propose a novel spectral-based subspace…
In this letter, we propose a novel semi-supervised subspace clustering method, which is able to simultaneously augment the initial supervisory information and construct a discriminative affinity matrix. By representing the limited amount of…
This paper considers the problem of clustering a partially observed unweighted graph---i.e., one where for some node pairs we know there is an edge between them, for some others we know there is no edge, and for the remaining we do not know…
Under the framework of spectral clustering, the key of subspace clustering is building a similarity graph which describes the neighborhood relations among data points. Some recent works build the graph using sparse, low-rank, and…
We present a new approach for solving (minimum disagreement) correlation clustering that results in sublinear algorithms with highly efficient time and space complexity for this problem. In particular, we obtain the following algorithms for…
Although many successful ensemble clustering approaches have been developed in recent years, there are still two limitations to most of the existing approaches. First, they mostly overlook the issue of uncertain links, which may mislead the…