Fast Decentralized Linear Functions via Successive Graph Shift Operators

TL;DR

This paper introduces a decentralized framework for implementing a broad class of linear transformations on graph signals using successive graph shift operators, enabling fast and efficient computations in networked systems.

Contribution

It develops a novel decentralized method leveraging successive graph shift operators to compute diverse linear transformations efficiently, overcoming limitations of prior approaches.

Findings

Enables fast computation of linear transformations in decentralized networks.

Supports a wide class of linear transformations beyond special cases.

Reduces the number of iterations needed for implementation.

Abstract

We study decentralized designing of the graph shift operators to implement linear transformations between graph signals. Since this operator captures the local structure of the graph, the proposed method of this paper gives rise to decentralized linear network operators. Unfortunately, existing decentralized approaches either consider some special instances of linear transformations or confine themselves to some known graph shift operators reduced family of the designing linear transformations task. To remedy these limitations, this paper develops a framework for computing a wide class of linear transformations in a decentralized fashion by relying on the notion of graph shift operator. To this end, a set of successive graph shift operators is implemented to compute linear transformations in a small number of iterations (as fast as possible).