Spatial Rank-Based Augmentation for Nonparametric Online Monitoring and Adaptive Sampling of Big Data Streams

The age of Internet of Things (IoT) has witnessed the rapid development of modern data acquisition devices and communicating-actuating networks, which enables the generation of big data streams shared across platforms for remote and efficient decision making of many critical systems. The monitoring of big data streams remains a challenging task in various practical applications mainly due to their complexity in interrelationships, large volume, and high velocity, which places prohibitive demands on monitoring methodologies and resources. To tackle the challenges of monitoring unexchangeable and correlated big data streams with only partial observations available under resource constraints, we propose a method by incorporating spatial rank-based statistics with effective data augmentation techniques for the online unobservable data streams that can analytically inform the monitoring and sampling decisions based only on partially observed data streams. By exploiting historical data, the proposed method preserves strong descriptive power of general big data streams under partial observations and can explicitly use the correlation among data streams, and thus allows effective monitoring and equitable sampling over general heterogeneous and correlated big data streams, which is free of simplified assumptions (e.g., exchangeability) compared to existing methods. Theoretical investigations are carried out to evaluate the effectiveness of the augmentation statistics as well as the sampling strategy, which guarantee the superiority of the sampling performance over existing methods. Simulations under various scenarios and two real case studies are also conducted to evaluate and validate the performance of the proposed method.