Related papers: Random Projections of Sparse Adjacency Matrices

Random projections are random linear maps, sampled from appropriate distributions, that approx- imately preserve certain geometrical invariants so that the approximation improves as the dimension of the space grows. The well-known…

As a typical dimensionality reduction technique, random projection can be simply implemented with linear projection, while maintaining the pairwise distances of high-dimensional data with high probability. Considering this technique is…

Random projection is often used to project higher-dimensional vectors onto a lower-dimensional space, while approximately preserving their pairwise distances. It has emerged as a powerful tool in various data processing tasks and has…

We introduce sparse random projection, an important dimension-reduction tool from machine learning, for the estimation of discrete-choice models with high-dimensional choice sets. Initially, high-dimensional data are compressed into a…

Random Projection is a foundational research topic that connects a bunch of machine learning algorithms under a similar mathematical basis. It is used to reduce the dimensionality of the dataset by projecting the data points efficiently to…

Random Projections have been widely used to generate embeddings for various graph learning tasks due to their computational efficiency. The majority of applications have been justified through the Johnson-Lindenstrauss Lemma. In this paper,…

Embeddings provide compact representations of signals in order to perform efficient inference in a wide variety of tasks. In particular, random projections are common tools to construct Euclidean distance-preserving embeddings, while…

We investigate graph representation learning approaches that enable models to generalize across graphs: given a model trained using the representations from one graph, our goal is to apply inference using those same model parameters when…

There has been recently a lot of research on sparse variants of random projections, faster adaptations of the state-of-the-art dimensionality reduction technique originally due to Johsnon and Lindenstrauss. Although the construction is very…

There is an increasing body of work exploring the integration of random projection into algorithms for numerical linear algebra. The primary motivation is to reduce the overall computational cost of processing large datasets. A suitably…

In this note we illustrate how common matrix approximation methods, such as random projection and random sampling, yield projection-cost-preserving sketches, as introduced in [FSS13, CEM+15]. A projection-cost-preserving sketch is a matrix…

The representation of graphs is commonly based on the adjacency matrix concept. This formulation is the foundation of most algebraic and computational approaches to graph processing. The advent of deep learning language models offers a wide…

We revisit the asymptotic analysis of probabilistic construction of adjacency matrices of expander graphs proposed in [4]. With better bounds we derived a new reduced sample complexity for the number of nonzeros per column of these…

Projecting a vector onto a simplex is a well-studied problem that arises in a wide range of optimization problems. Numerous algorithms have been proposed for determining the projection; however, the primary focus of the literature has been…

We propose a novel sparse sliced inverse regression method based on random projections in a large $p$ small $n$ setting. Embedded in a generalized eigenvalue framework, the proposed approach finally reduces to parallel execution of…

Random projections reduce the dimension of a set of vectors while preserving structural information, such as distances between vectors in the set. This paper proposes a novel use of row-product random matrices in random projection, where we…

Transforms using random matrices have been found to have many applications. We are concerned with the projection of a signal onto Gaussian-distributed random orthogonal bases. We also would like to easily invert the process through…

Visualizing very large matrices involves many formidable problems. Various popular solutions to these problems involve sampling, clustering, projection, or feature selection to reduce the size and complexity of the original task. An…

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 with replacement. These matrices have a one-to-one correspondence with the…

In recent years, a variety of randomized constructions of sketching matrices have been devised, that have been used in fast algorithms for numerical linear algebra problems, such as least squares regression, low-rank approximation, and the…