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Abstract Robust principal component analysis (RPCA) is a widely used method for recovering low‐rank structure from data matrices corrupted by significant and sparse outliers. These corruptions may arise from occlusions, malicious tampering, or other causes for anomalies, and the joint identification of such corruptions with low‐rank background is critical for process monitoring and diagnosis. However, existing RPCA methods and their extensions largely do not account for the underlying probabilistic distribution for the data matrices, which in many applications are known and can be highly non‐Gaussian. We thus propose a new method called RPCA for exponential family distributions (), which can perform the desired decomposition into low‐rank and sparse matrices when such a distribution falls within the exponential family. We present a novel alternating direction method of multiplier optimization algorithm for efficient decomposition, under either its natural or canonical parametrization. The effectiveness of is then demonstrated in two applications: the first for steel sheet defect detection and the second for crime activity monitoring in the Atlanta metropolitan area. 

Abstract Background The spatiotemporal variation of observed trace gases (NO 2 , SO 2 , O 3 ) and particulate matter (PM 2.5 , PM 10 ) were investigated over cities of Yangtze River Delta (YRD) region including Nanjing, Hefei, Shanghai and Hangzhou. Furthermore, the characteristics of different pollution episodes, i.e., haze events (visibility < 7 km, relative humidity < 80%, and PM 2.5  > 40 µg/m 3 ) and complex pollution episodes (PM 2.5  > 35 µg/m 3 and O 3  > 160 µg/m 3 ) were studied over the cities of the YRD region. The impact of China clean air action plan on concentration of aerosols and trace gases is examined. The impacts of trans-boundary pollution and different meteorological conditions were also examined. Results The highest annual mean concentrations of PM 2.5 , PM 10 , NO 2 and O 3 were found for 2019 over all the cities. The annual mean concentrations of PM 2.5 , PM 10 , and NO 2 showed continuous declines from 2019 to 2021 due to emission control measures and implementation of the Clean Air Action plan over all the cities of the YRD region. The annual mean O 3 levels showed a decline in 2020 over all the cities of YRD region, which is unprecedented since the beginning of the China’s National environmental monitoring program since 2013. However, a slight increase in annual O 3 was observed in 2021. The highest overall means of PM 2.5 , PM 10 , SO 2 , and NO 2 were observed over Hefei, whereas the highest O 3 levels were found in Nanjing. Despite the strict control measures, PM 2.5 and PM 10 concentrations exceeded the Grade-1 National Ambient Air Quality Standards (NAAQS) and WHO (World Health Organization) guidelines over all the cities of the YRD region. The number of haze days was higher in Hefei and Nanjing, whereas the complex pollution episodes or concurrent occurrence of O 3 and PM 2.5 pollution days were higher in Hangzhou and Shanghai. The in situ data for SO 2 and NO 2 showed strong correlation with Tropospheric Monitoring Instrument (TROPOMI) satellite data. Conclusions Despite the observed reductions in primary pollutants concentrations, the secondary pollutants formation is still a concern for major metropolises. The increase in temperature and lower relative humidity favors the accumulation of O 3 , while low temperature, low wind speeds and lower relative humidity favor the accumulation of primary pollutants. This study depicts different air pollution problems for different cities inside a region. Therefore, there is a dire need to continuous monitoring and analysis of air quality parameters and design city-specific policies and action plans to effectively deal with the metropolitan pollution.