Streaming Principal Component Analysis From Incomplete Data

TL;DR

This paper introduces SNIPE, a streaming algorithm for subspace estimation from incomplete data, which converges globally and performs efficiently on large datasets with missing entries.

Contribution

The paper presents SNIPE, a novel streaming subspace estimation algorithm that handles incomplete data efficiently and guarantees convergence to a stationary point.

Findings

SNIPE converges globally to a stationary point.

SNIPE exhibits locally linear convergence with high probability.

SNIPE achieves state-of-the-art performance in numerical simulations.

Abstract

Linear subspace models are pervasive in computational sciences and particularly used for large datasets which are often incomplete due to privacy issues or sampling constraints. Therefore, a critical problem is developing an efficient algorithm for detecting low-dimensional linear structure from incomplete data efficiently, in terms of both computational complexity and storage. In this paper we propose a streaming subspace estimation algorithm called Subspace Navigation via Interpolation from Partial Entries (SNIPE) that efficiently processes blocks of incomplete data to estimate the underlying subspace model. In every iteration, SNIPE finds the subspace that best fits the new data block but remains close to the previous estimate. We show that SNIPE is a streaming solver for the underlying nonconvex matrix completion problem, that it converges globally to a stationary point of this program regardless of initialization, and that the convergence is locally linear with high probability. We also find that SNIPE shows state-of-the-art performance in our numerical simulations.