Recently, regression analysis has become a popular tool for face recognition. Most existing regression methods use the one-dimensional, pixel-based error model, which characterizes the representation error individually, pixel by pixel, and thus neglects the two-dimensional structure of the error image. We observe that occlusion and illumination changes generally lead, approximately, to a low-rank error image. In order to make use of this low-rank structural information, this paper presents a two-dimensional image-matrix-based error model, namely, nuclear norm based matrix regression (NMR), for face representation and classification. NMR uses the minimal nuclear norm of representation error image as a criterion, and the alternating direction method of multipliers (ADMM) to calculate the regression coefficients. We further develop a fast ADMM algorithm to solve the approximate NMR model and show it has a quadratic rate of convergence. We experiment using five popular face image databases: the Extended Yale B, AR, EURECOM, Multi-PIE and FRGC. Experimental results demonstrate the performance advantage of NMR over the state-of-the-art regression-based methods for face recognition in the presence of occlusion and illumination variations.

A novel dimensionality reduction algorithm named "global−local preserving projections" (GLPP) is proposed. Different from locality preserving projections (LPP) and principal component analysis (PCA), GLPP aims at preserving both global and local structures of the data set by solving a dual-objective optimization function. A weighted coefficient is introduced to adjust the trade-off between global and local structures, and an efficient selection strategy of this parameter is proposed. Compared with PCA and LPP, GLPP is more general and flexible in practical applications. Both LPP and PCA can be interpreted under the GLPP framework. A GLPP-based online process monitoring approach is then developed. Two monitoring statistics, i.e., D and Q statistics, are constructed for fault detection and diagnosis. The case study on the Tennessee Eastman process illustrates the effectiveness and advantages of the GLPP-based monitoring method.

A novel method named tensor global–local structure analysis (TGLSA) is proposed for batch process monitoring. Different from principal component analysis (PCA) and locality preserving projections (LPP), TGLSA aims at preserving both global and local structures of data. Consequently, TGLSA has the ability to extract more meaningful information from data than PCA and LPP. Moreover, the tensor-based projection strategy makes TGLSA more applicable for the three-dimensional data than multiway-based methods, such as MPCA and MLPP. A TGLSA-based online monitoring approach is developed by combining TGLSA with a moving window technique. Two new statistics, i.e., SPD and R 2 statistics, are constructed for fault detection and diagnosis. In particular, the R 2 statistic is a novel monitoring statistic, which is proposed based on a support tensor domain description method. The effectiveness and advantages of the TGLSA-based monitoring approach are illustrated by a benchmark fed-batch penicillin fermentation process.

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A novel fuzzy phase partition method and a hybrid modeling strategy are proposed for quality prediction and process monitoring in batch processes with multiple operation phases. The fuzzy phase partition method is proposed on the basis of a sequence-constrained fuzzy c-means (SCFCM) clustering algorithm. It divides the batch process into several fuzzy operation phases by performing the SCFCM algorithm on trajectory data of phase-sensitive process variables. This SCFCM-based partition method not only has high computation efficiency and good partition accuracy but also is easy to implement and popularize. In addition, it generates “soft” partition results, where a “transition” phase exists between two adjacent “steady” operation phases. A hybrid modeling strategy is developed to build appropriate models for all operation phases according to their own characteristics. Phase-based multiway PLS models are built for regular steady phases that have longer durations and stable process behaviors. Just-in-time PLS models are built for those phases with shorter durations but time-varying or nonlinear process behaviors, including all transition phases and several irregular steady phases. This hybrid modeling strategy significantly enhances the modeling accuracy, resulting in better quality prediction and process monitoring performance. Advantages of proposed methods are illustrated by case studies in a fed-batch penicillin fermentation process.