Related papers: Revisiting Co-Occurring Directions: Sharper Analys…
We introduce co-occurring directions sketching, a deterministic algorithm for approximate matrix product (AMM), in the streaming model. We show that co-occuring directions achieves a better error bound for AMM than other randomized and…
Approximate matrix multiplication with limited space has received ever-increasing attention due to the emergence of large-scale applications. Recently, based on a popular matrix sketching algorithm -- frequent directions, previous work has…
Matrix multiplication is a core operation in numerous applications, yet its exact computation becomes prohibitively expensive as data scales, especially in streaming environments where timeliness is critical. In many real-world scenarios,…
We explore the problem of approximate matrix multiplication (AMM) within the sliding window model, where algorithms utilize limited space to perform large-scale matrix multiplication in a streaming manner. This model has garnered increasing…
This paper describes Sparse Frequent Directions, a variant of Frequent Directions for sketching sparse matrices. It resembles the original algorithm in many ways: both receive the rows of an input matrix $A^{n \times d}$ one by one in the…
Convolutional sparse coding improves on the standard sparse approximation by incorporating a global shift-invariant model. The most efficient convolutional sparse coding methods are based on the alternating direction method of multipliers…
Convolutional sparse coding (CSC) improves sparse coding by learning a shift-invariant dictionary from the data. However, existing CSC algorithms operate in the batch mode and are expensive, in terms of both space and time, on large…
A streaming algorithm to compute the spectral proper orthogonal decomposition (SPOD) of stationary random processes is presented. As new data becomes available, an incremental update of the truncated eigenbasis of the estimated…
We consider the problem of selecting non-zero entries of a matrix $A$ in order to produce a sparse sketch of it, $B$, that minimizes $\|A-B\|_2$. For large $m \times n$ matrices, such that $n \gg m$ (for example, representing $n$…
Matrix multiplication is a fundamental building block for large scale computations arising in various applications, including machine learning. There has been significant recent interest in using coding to speed up distributed matrix…
From a dual perspective of the sparse representation model, Nam et al. proposed the cosparse analysis model. In this paper, we aim to investigate the convergence of the alternating direction method of multipliers (ADMM) for the cosparse…
We adapt a well known streaming algorithm for approximating item frequencies to the matrix sketching setting. The algorithm receives the rows of a large matrix $A \in \R^{n \times m}$ one after the other in a streaming fashion. It maintains…
We describe a new algorithm called Frequent Directions for deterministic matrix sketching in the row-updates model. The algorithm is presented an arbitrary input matrix $A \in R^{n \times d}$ one row at a time. It performed $O(d \times…
In a large-scale and distributed matrix multiplication problem $C=A^{\intercal}B$, where $C\in\mathbb{R}^{r\times t}$, the coded computation plays an important role to effectively deal with "stragglers" (distributed computations that may…
We propose an efficient ADMM method with guarantees for high-dimensional problems. We provide explicit bounds for the sparse optimization problem and the noisy matrix decomposition problem. For sparse optimization, we establish that the…
We consider the least-squares approximation of a matrix C in the set of doubly stochastic matrices with the same sparsity pattern as C. Our approach is based on applying the well-known Alternating Direction Method of Multipliers (ADMM) to a…
We present a new algorithm for finding a near optimal low-rank approximation of a matrix $A$ in $O(nnz(A))$ time. Our method is based on a recursive sampling scheme for computing a representative subset of $A$'s columns, which is then used…
Sparse coding aims to model data vectors as sparse linear combinations of basis elements, but a majority of related studies are restricted to continuous data without spatial or temporal structure. A new model-based sparse coding (MSC)…
Maximum coverage and minimum set cover problems --collectively called coverage problems-- have been studied extensively in streaming models. However, previous research not only achieve sub-optimal approximation factors and space…
Sparse coding has shown its power as an effective data representation method. However, up to now, all the sparse coding approaches are limited within the single domain learning problem. In this paper, we extend the sparse coding to cross…