AeroSketch: Near-Optimal Time Matrix Sketch Framework for Persistent, Sliding Window, and Distributed Streams

TL;DR

AeroSketch is a new matrix sketching framework that significantly improves update efficiency and maintains optimal resource costs for real-time streaming data analysis.

Contribution

AeroSketch introduces a near-optimal, efficient matrix sketching method leveraging RandNLA, reducing update time complexity from cubic to quadratic while preserving approximation quality.

Findings

Outperforms state-of-the-art methods in update throughput

Reduces update time complexity from cubic to quadratic

Maintains optimal space and communication costs

Abstract

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, matrix sketching techniques have been developed over recent decades to provide compact approximations of such streaming data. Some algorithms have achieved optimal space and communication complexity. However, these approaches often require frequent time-consuming matrix factorization operations. In particular, under tight approximation error bounds, each matrix factorization computation incurs cubic time complexity, thereby limiting their update efficiency. In this paper, we introduce AeroSketch, a novel matrix sketching framework that leverages recent advances in randomized numerical linear algebra (RandNLA). AeroSketch achieves optimal communication and space costs while delivering near-optimal update time complexity (within logarithmic factors) across persistent, sliding window, and distributed streaming scenarios. Extensive experiments on both synthetic and real-world datasets demonstrate that AeroSketch consistently outperforms state-of-the-art methods in update throughput. In particular, under tight approximation error constraints, AeroSketch reduces the cubic time complexity to the quadratic level. Meanwhile, it maintains comparable approximation quality while retaining optimal communication and space costs.