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In high dimensional settings, sparse structures are crucial for efficiency, both in term of memory, computation and performance. It is customary to consider $\ell_1$ penalty to enforce sparsity in such scenarios. Sparsity enforcing methods,…
A trend in compressed sensing (CS) is to exploit structure for improved reconstruction performance. In the basic CS model, exploiting the clustering structure among nonzero elements in the solution vector has drawn much attention, and many…
Typical dimension reduction techniques for nonoverlapping sparse optimization involve screening or sieving strategies based on a dual certificate derived from the first-order optimality condition, approximating the gradients or exploiting…
Subspace clustering refers to the problem of segmenting high dimensional data drawn from a union of subspaces into the respective subspaces. In some applications, partial side-information to indicate "must-link" or "cannot-link" in…
This paper considers the problem of clustering a collection of unlabeled data points assumed to lie near a union of lower-dimensional planes. As is common in computer vision or unsupervised learning applications, we do not know in advance…
This paper presents Orthogonal Subspace Clustering (OSC), an innovative method for high-dimensional data clustering. We first establish a theoretical theorem proving that high-dimensional data can be decomposed into orthogonal subspaces in…
We propose a novel algorithm for efficiently computing a sparse directed adjacency matrix from a group of time series following a causal graph process. Our solution is scalable for both dense and sparse graphs and automatically selects the…
Recent breakthrough results in compressed sensing (CS) have established that many high dimensional objects can be accurately recovered from a relatively small number of non- adaptive linear projection observations, provided that the objects…
Subspace clustering discovers the clusters embedded in multiple, overlapping subspaces of high dimensional data. Many significant subspace clustering algorithms exist, each having different characteristics caused by the use of different…
In this paper, we propose a new framework for segmenting feature-based moving objects under affine subspace model. Since the feature trajectories in practice are high-dimensional and contain a lot of noise, we firstly apply the sparse PCA…
Calculation of near-neighbor interactions among high dimensional, irregularly distributed data points is a fundamental task to many graph-based or kernel-based machine learning algorithms and applications. Such calculations, involving…
In several application domains, high-dimensional observations are collected and then analysed in search for naturally occurring data clusters which might provide further insights about the nature of the problem. In this paper we describe a…
We introduce the Neural Collaborative Subspace Clustering, a neural model that discovers clusters of data points drawn from a union of low-dimensional subspaces. In contrast to previous attempts, our model runs without the aid of spectral…
The problem of estimating parameters of a deterministic jump or piecewise linear model is considered. A subspace technique referred to as spectral clustering on subspace (SCS) algorithm is proposed to estimate a set of linear model…
Spectral-type subspace clustering algorithms have shown excellent performance in many subspace clustering applications. The existing spectral-type subspace clustering algorithms either focus on designing constraints for the reconstruction…
This paper focuses on the sparse subspace clustering problem, and develops an online algorithmic solution to cluster data points on-the-fly, without revisiting the whole dataset. The strategy involves an online solution of a sparse…
The network Lasso is a recently proposed convex optimization method for machine learning from massive network structured datasets, i.e., big data over networks. It is a variant of the well-known least absolute shrinkage and selection…
Clustering images according to their acquisition devices is a well-known problem in multimedia forensics, which is typically faced by means of camera Sensor Pattern Noise (SPN). Such an issue is challenging since SPN is a noise-like signal,…
This paper aims at developing a clustering approach with spectral images directly from the compressive measurements of coded aperture snapshot spectral imager (CASSI). Assuming that compressed measurements often lie approximately in low…
Compressive sensing (CS) exploits sparsity to recover sparse or compressible signals from dimensionality reducing, non-adaptive sensing mechanisms. Sparsity is also used to enhance interpretability in machine learning and statistics…