Dunwei Gong

Mei-Xiang Zhao, Zhi-Gang Jia, Dun-Wei Gong et al.

A new data-driven bilateral generalized two-dimensional quaternion principal component analysis (BiG2DQPCA) is presented to extract the features of matrix samples from both row and column directions. This general framework directly works on the 2D color images without vectorizing and well preserves the spatial and color information, which makes it flexible to fit various real-world applications. A generalized ridge regression model of BiG2DQPCA is firstly proposed with orthogonality constrains on aimed features. Applying the deflation technique and the framework of minorization-maximization, a new quaternion optimization algorithm is proposed to compute the optimal features of BiG2DQPCA and a closed-form solution is obtained at each iteration. A new approach based on BiG2DQPCA is presented for color face recognition and image reconstruction with a new data-driven weighting technique. Sufficient numerical experiments are implemented on practical color face databases and indicate the superiority of BiG2DQPCA over the state-of-the-art methods in terms of recognition accuracies and rates of image reconstruction.

Canyun Dai, Xiaoyan Sun, Hejuan Hu et al.

The dispatch optimization of coal mine integrated energy system is challenging due to high dimensionality, strong coupling constraints, and multiobjective. Existing constrained multiobjective evolutionary algorithms struggle with locating multiple small and irregular feasible regions, making them inaplicable to this problem. To address this issue, we here develop a multitask evolutionary algorithm framework that incorporates the dispatch correlated domain knowledge to effectively deal with strong constraints and multiobjective optimization. Possible evolutionary multitask construction strategy based on complex constraint relationship analysis and handling, i.e., constraint coupled spatial decomposition, constraint strength classification and constraint handling technique, is first explored. Within the multitask evolutionary optimization framework, two strategies, i.e., an elite guided knowledge transfer by designing a special crowding distance mechanism to select dominant individuals from each task, and an adaptive neighborhood technology based mutation to effectively balance the diversity and convergence of each optimized task for the differential evolution algorithm, are further developed. The performance of the proposed algorithm in feasibility, convergence, and diversity is demonstrated in a case study of a coal mine integrated energy system by comparing with CPLEX solver and seven constrained multiobjective evolutionary algorithms.

Meixiang Zhao, Zhigang Jia, Yunfeng Cai et al.

The two-dimensional principal component analysis (2DPCA) has become one of the most powerful tools of artificial intelligent algorithms. In this paper, we review 2DPCA and its variations, and propose a general ridge regression model to extract features from both row and column directions. To enhance the generalization ability of extracted features, a novel relaxed 2DPCA (R2DPCA) is proposed with a new ridge regression model. R2DPCA generates a weighting vector with utilizing the label information, and maximizes a relaxed criterion with applying an optimal algorithm to get the essential features. The R2DPCA-based approaches for face recognition and image reconstruction are also proposed and the selected principle components are weighted to enhance the role of main components. Numerical experiments on well-known standard databases indicate that R2DPCA has high generalization ability and can achieve a higher recognition rate than the state-of-the-art methods, including in the deep learning methods such as CNNs, DBNs, and DNNs.

Meixiang Zhao, Zhigang Jia, Dunwei Gong

A sample-relaxed two-dimensional color principal component analysis (SR-2DCPCA) approach is presented for face recognition and image reconstruction based on quaternion models. A relaxation vector is automatically generated according to the variances of training color face images with the same label. A sample-relaxed, low-dimensional covariance matrix is constructed based on all the training samples relaxed by a relaxation vector, and its eigenvectors corresponding to the $r$ largest eigenvalues are defined as the optimal projection. The SR-2DCPCA aims to enlarge the global variance rather than to maximize the variance of the projected training samples. The numerical results based on real face data sets validate that SR-2DCPCA has a higher recognition rate than state-of-the-art methods and is efficient in image reconstruction.