This chapter presents a data-driven method for abnormality localization in distributed parameter systems. The cross-correlation order in the spatial domain is first obtained using a cumulants-based identification technique. A spatial augmented matrix is then constructed from the spatio-temporal distribution data, and a dynamic spatial independent component analysis is introduced for independent decomposition. The dominant spatial independent components are extracted, and spatial residuals are generated as reference statistics. Using kernel density estimation, confidence intervals of these statistics under normal (abnormality-free) conditions are established as spatial references. These two references enable reliable spatial localization of abnormalities. Unlike model-based approaches that depend on explicit process models, the proposed method is model-free and relies solely on recorded process data. Experimental studies on two representative DPSs confirm the effectiveness of the approach.