Related papers: Simple and Deterministic Matrix Sketching

We study the problem of extracting a small subset of representative items from a large data stream. In many data mining and machine learning applications such as social network analysis and recommender systems, this problem can be…

Probabilistic ideas and tools have recently begun to permeate into several fields where they had traditionally not played a major role, including fields such as numerical linear algebra and optimization. One of the key ways in which these…

We consider the problem of finding a minimum cut of a weighted graph presented as a single-pass stream. While graph sparsification in streams has been intensively studied, the specific application of finding minimum cuts in streams is less…

Truss decomposition is a method used to analyze large sparse graphs in order to identify successively better connected subgraphs. Since in many domains the underlying graph changes over time, its associated truss decomposition needs to be…

Modern data stream applications demand memory-efficient solutions for accurately tracking frequent items, such as heavy hitters and heavy changers, under strict resource constraints. Traditional sketches face inherent accuracy-memory…

Histograms, i.e., piece-wise constant approximations, are a popular tool used to represent data distributions. Traditionally, the difference between the histogram and the underlying distribution (i.e., the approximation error) is measured…

Frequency estimation in streaming data often relies on sketches like Count-Min (CM) to provide approximate answers with sublinear space. However, CM sketches introduce additive errors that disproportionately impact low-frequency elements,…

Consider the problem of maintaining source sink reachability($st$-Reachability), single source reachability(SSR) and strongly connected component(SCC) in an edge decremental directed graph. In particular, we design a randomized algorithm…

Random data sketching (or projection) is now a classical technique enabling, for instance, approximate numerical linear algebra and machine learning algorithms with reduced computational complexity and memory. In this context, the…

We develop fixed-point algorithms for the approximation of structured matrices with rank penalties. In particular we use these fixed-point algorithms for making approximations by sums of exponentials, or frequency estimation. For the basic…

We consider sketching algorithms which first compress data by multiplication with a random sketch matrix, and then apply the sketch to quickly solve an optimization problem, e.g., low-rank approximation and regression. In the learning-based…

Count-sketch is a popular matrix sketching algorithm that can produce a sketch of an input data matrix X in O(nnz(X))time where nnz(X) denotes the number of non-zero entries in X. The sketched matrix will be much smaller than X while…

Randomized algorithms, such as randomized sketching or stochastic optimization, are a promising approach to ease the computational burden in analyzing large datasets. However, randomized algorithms also produce non-deterministic outputs,…

We consider dynamic algorithms for maintaining Single-Source Reachability (SSR) and approximate Single-Source Shortest Paths (SSSP) on $n$-node $m$-edge directed graphs under edge deletions (decremental algorithms). The previous fastest…

We consider distributed optimization methods for problems where forming the Hessian is computationally challenging and communication is a significant bottleneck. We leverage randomized sketches for reducing the problem dimensions as well as…

Many real-world networks such as Twitter and YouTube are given as fully dynamic graph streams represented as sequences of edge insertions and deletions. (e.g., users can subscribe and unsubscribe to channels on YouTube). Existing similarity…

We consider streaming algorithms for approximating a product of input probabilities up to multiplicative error of $1-\epsilon$. It is shown that every randomized streaming algorithm for this problem needs space $\Omega(\log n + \log b -…

In the research field of big data, one of important issues is how to recover the sequentially changing sets of true features when the data sets arrive sequentially. The paper presents a general framework for online updating variable…

We propose a randomized algorithm with quadratic convergence rate for convex optimization problems with a self-concordant, composite, strongly convex objective function. Our method is based on performing an approximate Newton step using a…

Matrices have become essential data representations for many large-scale problems in data analytics, and hence matrix sketching is a critical task. Although much research has focused on improving the error/size tradeoff under various…