The successive projections algorithm

Soares, Sófacles Figueredo Carreiro; Gomes, A. A.; Araújo, Mário César Ugulino de; Filho, Arlindo Rodrigues Galvão; Galvão, Roberto Kawakami Harrop

doi:10.1016/j.trac.2012.09.006

Cited by 228 publications

(98 citation statements)

References 74 publications

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“…Second, from the results of the multi-linear regression (MLR) model assessed by cross-validation or by applying a separate validation set, the algorithm evaluates candidate subsets of variables on the basis of the value of the root mean square error (RMSE). Finally, a variable elimination procedure is carried out to remove uninformative variables without significant loss of predictive power [31,32]. SPA has been successfully applied in hyperspectral image analysis for multivariate calibration in food safety and quality evaluation [33,34].…”

Section: Wavelength Selectionmentioning

confidence: 99%

Black Heart Detection in White Radish by Hyperspectral Transmittance Imaging Combined with Chemometric Analysis and a Successive Projections Algorithm

Song

Sun

et al. 2016

Applied Sciences

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Radishes with black hearts will lose edible value and cause food safety problems, so it is important to detect and remove the defective ones before processing and consumption. A hyperspectral transmittance imaging system with 420 wavelengths was developed to capture images from white radishes. A successive-projections algorithm (SPA) was applied with 10 wavelengths selected to distinguish defective radishes with black hearts from normal samples. Pearson linear correlation coefficients were calculated to further refine the set of wavelengths with 4 wavelengths determined. Four chemometric classifiers were developed for classification of normal and defective radishes, using 420, 10 and 4 wavelengths as input variables. The overall classifying accuracy based on the four classifiers were 95.6%-100%. The highest classification with 100% was obtained with a back propagation artificial neural network (BPANN) for both calibration and prediction using 420 and 10 wavelengths. Overall accuracies of 98.4% and 97.8% were obtained for calibration and prediction, respectively, with Fisher's linear discriminant analysis (FLDA) based on 4 wavelengths, and was better than the other three classifiers. This indicated that the developed hyperspectral transmittance imaging was suitable for black heart detection in white radishes with the optimal wavelengths, which has potential for fast on-line discrimination before food processing or reaching storage shelves.

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Section: Wavelength Selectionmentioning

confidence: 99%

Black Heart Detection in White Radish by Hyperspectral Transmittance Imaging Combined with Chemometric Analysis and a Successive Projections Algorithm

Song

Sun

et al. 2016

Applied Sciences

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“…O APSé um procedimento iterativo bastante utilizado para a seleção de variáveis em modelos de calibração. Dado uma variável inicial, uma nova variávelé inserida no subconjunto de dados caso tenha uma maior projeção ortogonal em relaçãoà variável anterior [13]. Esse procedimentó e realizado até que um número máximo m seja atingido [12].…”

Section: Algoritmo Das Projeções Sucessivasunclassified

“…O APSé utilizado com sucesso para a seleção de variáveis no contexto de diferentes aplicações como, por exemplo, calibração multivariada [12]; classificação e detecção de falhas quando o objetivoé minimizar a multicolinearidade [2]; e melhorar a capacidade predtiva dos modelos de calibração [13]. Este trabalho apresenta os resultados obtidos com uma implementação paralela do APS, denominada APS-SR-CUDA, para reduzir o tempo computacional do APS original.…”

Section: Introductionunclassified

Paralelização do algoritmo das projeções sucessivas em GPU usando uma implementação das regressões sequenciais para seleção de variáveis em problemas de calibração multivariada

Paula¹,

Soares²,

Soares³

et al. 2015

Proceeding Series of the Brazilian Society of Computational and Applied Mathematics

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“…In such analysis, it is assessed the prediction error of the property of interest as well as the number of selected variables (Galvao et al, 2011;Sofacles et al, 2012). Nevertheless, both objectives were not used in the proposal of Goodarzi and dos Santos Coelho (2014).…”

Section: Introductionmentioning

confidence: 99%

Modern Metaheuristic with Multi-Objective Formulation for the Variable Selection Problem

Paula

Soares

et al. 2017

Journal of Computer Science

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The development of efficient algorithms for variable selection becomes important to deal with large and complex datasets. Most works in quantitative chemical analysis have used Genetic Algorithms (GAs) as a reference method to select variables. On the other hand, new advances in metaheuristic techniques provide novel possibilities in this task Moreover, the application of Multi-Objective Optimization (MOO) may significantly contribute to efficiently construct an accurate model in the context of multivariate calibration. MOO has showed itself as an efficiently and successful tool to dealing with conflicting objective-functions. For instance, the use of MOO may be considered as a good choice to treat the reducing of prediction error and the number of selected variables in a calibration model. In this paper, we present a modern metaheuristic implementation called Multi-Objective Firefly Algorithm (MOFA) for variable selection in multivariate calibration models. The goal is to propose an optimization to reduce the prediction error of the property of interest in the analysed sample as well as reducing the number of selected variables. However, the outcomes are remarkably promising compared with the previous work. Based on the results obtained, it is possible to demonstrate that our proposal is a viable alternative in order to deal with such conflicting objectives. Additionally, we compare MOFA with a traditional GA implementation and show that MOFA is more efficient for the variable selection problem.

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The successive projections algorithm

Cited by 228 publications

References 74 publications

Black Heart Detection in White Radish by Hyperspectral Transmittance Imaging Combined with Chemometric Analysis and a Successive Projections Algorithm

Black Heart Detection in White Radish by Hyperspectral Transmittance Imaging Combined with Chemometric Analysis and a Successive Projections Algorithm

Paralelização do algoritmo das projeções sucessivas em GPU usando uma implementação das regressões sequenciais para seleção de variáveis em problemas de calibração multivariada

Modern Metaheuristic with Multi-Objective Formulation for the Variable Selection Problem

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