Decentralized Principal Component Analysis by Integrating Lagrange Programming Neural Networks With Alternating Direction Method of Multipliers

Abstract

Conventional centralized methods use entire data to estimate the projection matrix of dimensionality reduction problem, which are not suitable for the network environment where the sensitive or private data are stored or there is no fusion center. In this paper, we develop a decentralized principal component analysis (DPCA) method to deal with the distributed data without sharing or collecting them together. The main contributions of this paper are as follows: i) The proposed DPCA method only needs the projection vector information communications among neighboring nodes other than the communications of the distributed data; ii) The decentralized projection vector determination problem is replaced by a set of subproblems with consensus constraints and the excellent processing capability of alternating direction method of multipliers (ADMM) is used to obtain the consistent projection vectors; iii) Especially, the integrating Lagrange programming neural networks (LPNN) is introduced to solve the projection vectors determination problem with the complex unitary and orthogonal constraints, and iv) the converge analysis of the proposed optimization problem is provided to ensure that the obtained projection vectors of the distributed method converge to those of the centralized one. Some simulations and experiments are given to show that the proposed algorithm is an alternative decentralized principal component analysis approach, and is suitable for the network environment.

Keywords

• Decentralized principal component analysis (DPCA)
• distributed data
• alternating-direction method of multipliers (ADMM)
• Lagrange programming neural networks (LPNN)