In this paper, we investigate the use of random selection (RS) and random projection (RP) for hyperspectral image analysis, which are data-independent and computationally more efficient than other widely used dimensionality reduction methods. Both anomaly detection and target detection are considered. Due to the random nature, multiple runs of RS or RP are conducted followed by decision fusion to ensure a stable output. Parallel implementations using graphics processing unit (GPU) and clusters are also investigated. The experimental results demonstrated that both RS and RP are capable of providing better target detection performance after decision fusion, while the overall computing time can be greatly decreased with parallel implementations.