Related papers: Random Projections of Sparse Adjacency Matrices

In this letter, we propose an algorithm for learning a sparse weighted graph by estimating its adjacency matrix under the assumption that the observed signals vary smoothly over the nodes of the graph. The proposed algorithm is based on the…

The use of complex networks as a modern approach to understanding the world and its dynamics is well-established in literature. The adjacency matrix, which provides a one-to-one representation of a complex network, can also yield several…

We revisit the probabilistic construction of sparse random matrices where each column has a fixed number of nonzeros whose row indices are drawn uniformly at random. These matrices have a one-to-one correspondence with the adjacency…

Random projection, a dimensionality reduction technique, has been found useful in recent years for reducing the size of optimization problems. In this paper, we explore the use of sparse sub-gaussian random projections to approximate…

We provide a simple proof of the Johnson-Lindenstrauss lemma for sub-Gaussian variables. We extend the analysis to identify how sparse projections can be, and what the cost of sparsity is on the target dimension.The Johnson-Lindenstrauss…

Random projections or sketching are widely used in many algorithmic and learning contexts. Here we study the performance of iterative Hessian sketch for least-squares problems. By leveraging and extending recent results from random matrix…

We propose and investigate a unifying class of sparse random graph models, based on a hidden coloring of edge-vertex incidences, extending an existing approach, Random graphs with a given degree distribution, in a way that admits a…

Most existing motion planning algorithms assume that a map (of some quality) is fully determined prior to generating a motion plan. In many emerging applications of robotics, e.g., fast-moving agile aerial robots with constrained embedded…

We propose a novel statistical model for sparse networks with overlapping community structure. The model is based on representing the graph as an exchangeable point process, and naturally generalizes existing probabilistic models with…

This paper, broadly speaking, covers the use of randomness in two main areas: low-rank approximation and kernel methods. Low-rank approximation is very important in numerical linear algebra. Many applications depend on matrix decomposition…

Graph embedding is gaining its popularity for link prediction in complex networks and achieving excellent performance. However, limited work has been done in sparse networks that represent most of real networks. In this paper, we propose a…

Graph-based representations underlie a wide range of scientific problems. Graph connectivity is typically represented as a sparse matrix in the Compressed Sparse Row format. Large-scale graphs rely on distributed storage, allocating…

It is proposed that the propagation of light in disordered photonic lattices can be harnessed as a random projection that preserves distances between a set of projected vectors. This mapping is enabled by the complex evolution matrix of a…

Sketch-and-project is a framework which unifies many known iterative methods for solving linear systems and their variants, as well as further extensions to non-linear optimization problems. It includes popular methods such as randomized…

Existing techniques for motion imitation often suffer a certain level of latency due to their computational overhead or a large set of correspondence samples to search. To achieve real-time imitation with small latency, we present a…

Generative graph models struggle to scale due to the need to predict the existence or type of edges between all node pairs. To address the resulting quadratic complexity, existing scalable models often impose restrictive assumptions such as…

Statistical analysis of large and sparse graphs is a challenging problem in data science due to the high dimensionality and nonlinearity of the problem. This paper presents a fast and scalable algorithm for partitioning such graphs into…

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…

We consider the problem of efficient randomized dimensionality reduction with norm-preservation guarantees. Specifically we prove data-dependent Johnson-Lindenstrauss-type geometry preservation guarantees for Ho's random subspace method:…

Random projection algorithm is an iterative gradient method with random projections. Such an algorithm is of interest for constrained optimization when the constraint set is not known in advance or the projection operation on the whole…