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The paper presents a new method of optimization by the Layered Algorithm (LA). The proposed algorithm reduces the initial area to the sub-area containing the optimum. The proposed technique is based on the classification of the optimized function values (data sampled by sensors). The classification method uses a two-dimensional three-state Cellular Automata (CA). The CA classifies all area points ascribed to the CA cells based on their values. Specification of the categorization layers to the data gives a possibility to identify the different levels areas. Consequently, after analysis, a sub-area containing the optimum can be designated. In this paper, the proposed algorithm is applied to find the location of the airborne contaminant source by analyzing the concentration of released substances reported by mobile sensors distributed over the domain of interest. The Gaussian dispersion model simulation of the contaminant dispersion in the urbanized area is applied to generate the data used to verify the efficiency of the proposed Layered Algorithm. The LA successfully estimates the sub-area of the considered domain where the contamination source is located, taking to account data from sensors solely. • Optimization method reducing the initial area to the sub-area containing the optimum. • Verification of the Layered Algorithm (LA) with Selected Benchmark Functions. • Analysis of the LA efficiency to localize the airborne contaminant source. • LA results assessment by the measures: classification and accuracy error, relevance. [ABSTRACT FROM AUTHOR]

Matrix regression uses matrix data as input and directly selects the features from matrix data by employing several couples of left and right regression matrices. However, the existing matrix regression methods do not consider the relationship between different classes of data and cannot get discriminant left/right regression matrix, which results in poor classifications. In this paper, a margin-based discriminant embedding sparse matrix regression (MDESMR) model for image supervised feature selection is proposed. For each matrix data, a margin is first defined as the difference between two types of distances determined by the left/right regression matrix. Maximizing the average margin for all training matrix data can get the nonlinear discriminant embedding. Thus, a nonlinear embedding and its linear approximation can be obtained simultaneously. An alternative iterative optimization algorithm for solving the proposed model is also designed and the corresponding closed-form solutions in each iteration are found. Some experiments on several datasets demonstrate the superiority of our method. • Our model preserves the spatial information of elements in the original image data. • The margin of each matrix data is defined by using left/right regression matrices. • Maximizing the average margin can obtain the non-linear discriminant embedding. • Discriminative features are selected by the row sparsity of transformation matrix. • An iterative optimization algorithm is designed to solve the proposed model. • The effectiveness and superiority of our method are verified on several datasets. [ABSTRACT FROM AUTHOR]