Related papers: Sketching for Kronecker Product Regression and P-s…
We present parallel algorithms and data structures for three fundamental operations in Numerical Linear Algebra: (i) Gaussian and CountSketch random projections and their combination, (ii) computation of the Gram matrix and (iii)…
Low-rank tensor decomposition generalizes low-rank matrix approximation and is a powerful technique for discovering low-dimensional structure in high-dimensional data. In this paper, we study Tucker decompositions and use tools from…
Large machine learning models achieve unprecedented performance on various tasks and have evolved as the go-to technique. However, deploying these compute and memory hungry models on resource constraint environments poses new challenges. In…
Sketch is an important media for human to communicate ideas, which reflects the superiority of human intelligence. Studies on sketch can be roughly summarized into recognition and generation. Existing models on image recognition failed to…
Matrices arising in scientific applications frequently admit linear low-rank approximations due to smoothness in the physical and/or temporal domain of the problem. In large-scale problems, computing an optimal low-rank approximation can be…
Tensor Kronecker products, the natural generalization of the matrix Kronecker product, are independently emerging in multiple research communities. Like their matrix counterpart, the tensor generalization gives structure for implicit…
CountSketch is a popular dimensionality reduction technique that maps vectors to a lower dimension using randomized linear measurements. The sketch supports recovering $\ell_2$-heavy hitters of a vector (entries with $v[i]^2 \geq…
In this work, we propose a method for speeding up linear regression distributively, while ensuring security. We leverage randomized sketching techniques, and improve straggler resilience in asynchronous systems. Specifically, we apply a…
Many real-world matrix datasets arrive as high-throughput vector streams, making it impractical to store or process them in their entirety. To enable real-time analytics under limited computational, memory, and communication resources,…
Subspace clustering is a useful technique for many computer vision applications in which the intrinsic dimension of high-dimensional data is often smaller than the ambient dimension. Spectral clustering, as one of the main approaches to…
We study the problem of residual error estimation for matrix and vector norms using a linear sketch. Such estimates can be used, for example, to quickly assess how useful a more expensive low-rank approximation computation will be. The…
Recent advancement of the WWW, IOT, social network, e-commerce, etc. have generated a large volume of data. These datasets are mostly represented by high dimensional and sparse datasets. Many fundamental subroutines of common data analytic…
A litany of theoretical and numerical results have established the sketch-and-precondition paradigm as a powerful approach to solving large linear regression problems in standard computing environments. Perhaps surprisingly, much less work…
Tensor, a multi-dimensional data structure, has been exploited recently in the machine learning community. Traditional machine learning approaches are vector- or matrix-based, and cannot handle tensorial data directly. In this paper, we…
Thanks to its great potential in reducing both computational cost and memory requirements, combining sketching and Krylov subspace techniques has attracted a lot of attention in the recent literature on projection methods for linear…
In this paper, we introduce a method for multivariate function approximation using function evaluations, Chebyshev polynomials, and tensor-based compression techniques via the Tucker format. We develop novel randomized techniques to…
The Grassmannian manifold G(k, n) serves as a fundamental tool in signal processing, computer vision, and machine learning, where problems often involve classifying, clustering, or comparing subspaces. In this work, we propose a…
This paper describes a new algorithm for computing a low-Tucker-rank approximation of a tensor. The method applies a randomized linear map to the tensor to obtain a sketch that captures the important directions within each mode, as well as…
This article considers "compressive learning," an approach to large-scale machine learning where datasets are massively compressed before learning (e.g., clustering, classification, or regression) is performed. In particular, a "sketch" is…
Sketch-an-Anchor is a novel method to train state-of-the-art Zero-shot Sketch-based Image Retrieval (ZSSBIR) models in under an epoch. Most studies break down the problem of ZSSBIR into two parts: domain alignment between images and…