On The Complexity of Sparse Label Propagation

TL;DR

This paper analyzes the computational complexity of sparse label propagation, a convex optimization method for network data, providing bounds on iteration counts and demonstrating sharpness for chain-structured datasets.

Contribution

It characterizes the iteration complexity of sparse label propagation and establishes bounds that are tight for chain-structured datasets.

Findings

Derived an upper bound on iteration count for accuracy

Proved the bound is sharp for chain-structured datasets

Enhanced understanding of sparse label propagation's computational efficiency

Abstract

This paper investigates the computational complexity of sparse label propagation which has been proposed recently for processing network structured data. Sparse label propagation amounts to a convex optimization problem and might be considered as an extension of basis pursuit from sparse vectors to network structured datasets. Using a standard first-order oracle model, we characterize the number of iterations for sparse label propagation to achieve a prescribed accuracy. In particular, we derive an upper bound on the number of iterations required to achieve a certain accuracy and show that this upper bound is sharp for datasets having a chain structure (e.g., time series).