Distributed stochastic principal component analysis using stabilized Barzilai-Borwein step-size for data compression with WSN

The popularity of diverse IoT-based applications and services continuously generating tremendous amount of data has revealed the significance of data compression (DC). Principal component analysis (PCA) is one of the most commonly employed algorithms for DC. However, when dealing with large-scale matrices, the standard PCA takes a very long time and requires a lot of memory. Therefore, this paper presents a novel distributed stochastic PCA algorithm (DSPCA) for hierarchical sensor network based on gradient-based adaptive PCA (GA-PCA), where the standard PCA is reformulated as a single-pass stochastic setting to find the direction of approximate maximal variance. The step-size in each iteration is obtained by incorporating the stabilized Barzilai-Borwein method with the gradient optimization. This enables DSPCA to be processed with low computational complexity while maintaining a high convergence speed. Computer simulation with two types of datasets displays that the proposed scheme consistently outperforms the representative DC schemes in terms of reconstruction accuracy of original data and explained variance.