Related papers: Optimal Laplacian regularization for sparse spectr…
We consider a minimization problem whose objective function is the sum of a fidelity term, not necessarily convex, and a regularization term defined by a positive regularization parameter $\lambda$ multiple of the $\ell_0$ norm composed…
From neuroscience and genomics to systems biology and ecology, researchers rely on clustering similarity data to uncover modular structure. Yet widely used clustering methods, such as hierarchical clustering, k-means, and WGCNA, lack…
As a powerful statistical image modeling technique, sparse representation has been successfully used in various image restoration applications. The success of sparse representation owes to the development of l1-norm optimization techniques,…
Joint network topology inference represents a canonical problem of jointly learning multiple graph Laplacian matrices from heterogeneous graph signals. In such a problem, a widely employed assumption is that of a simple common component…
Synchronization is an important and prevalent phenomenon in natural and engineered systems. In many dynamical networks, the coupling is balanced or adjusted in order to admit global synchronization, a condition called Laplacian coupling.…
Sparse model selection is ubiquitous from linear regression to graphical models where regularization paths, as a family of estimators upon the regularization parameter varying, are computed when the regularization parameter is unknown or…
Laplacian Eigenvectors of the graph constructed from a data set are used in many spectral manifold learning algorithms such as diffusion maps and spectral clustering. Given a graph constructed from a random sample of a $d$-dimensional…
Complex networks can model a range of different systems, from the human brain to social connections. Some of those networks have a large number of nodes and links, making it impractical to analyze them directly. One strategy to simplify…
Spectral clustering is one of the most popular clustering methods. However, the high computational cost due to the involved eigen-decomposition procedure can immediately hinder its applications in large-scale tasks. In this paper we use…
As an indicator of the stability of spectral clustering of an undirected weighted graph into $k$ clusters, the $k$th spectral gap of the graph Laplacian is often considered. The $k$th spectral gap is characterized in this paper as an…
Community detection refers to finding densely connected groups of nodes in graphs. In important applications, such as cluster analysis and network modelling, the graph is sparse but outliers and heavy-tailed noise may obscure its structure.…
Jacobian and Hessian regularization aim to reduce the magnitude of the first and second-order partial derivatives with respect to neural network inputs, and they are predominantly used to ensure the adversarial robustness of image…
Sparse hyperspectral unmixing from large spectral libraries has been considered to circumvent limitations of endmember extraction algorithms in many applications. This strategy often leads to ill-posed inverse problems, which can benefit…
Complex time-varying networks are prominent models for a wide variety of spatiotemporal phenomena. The functioning of networks depends crucially on their connectivity, yet reliable techniques for learning communities in time-evolving…
In this paper, we consider optimal low-rank regularized inverse matrix approximations and their applications to inverse problems. We give an explicit solution to a generalized rank-constrained regularized inverse approximation problem,…
We propose a novel SPARsity and Clustering (SPARC) regularizer, which is a modified version of the previous octagonal shrinkage and clustering algorithm for regression (OSCAR), where, the proposed regularizer consists of a $K$-sparse…
Many regression and classification procedures fit a parameterized function $f(x;w)$ of predictor variables $x$ to data $\{x_{i},y_{i}\}_1^N$ based on some loss criterion $L(y,f)$. Often, regularization is applied to improve accuracy by…
The sparse representation classifier (SRC) is shown to work well for image recognition problems that satisfy a subspace assumption. In this paper we propose a new implementation of SRC via screening, establish its equivalence to the…
In this paper, we consider a ${\rm U}(1)$-connection graph, that is, a graph where each oriented edge is endowed with a unit modulus complex number that is conjugated under orientation flip. A natural replacement for the combinatorial…
Randomized matrix sparsification has proven to be a fruitful technique for producing faster algorithms in applications ranging from graph partitioning to semidefinite programming. In the decade or so of research into this technique, the…