Linear discriminant analysis with a generalization of the Moore–Penrose pseudoinverse

Górecki, Tomasz; Łuczak, Maciej

doi:10.2478/amcs-2013-0035

Cited by 18 publications

(10 citation statements)

References 31 publications

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“…Apart from the data spectral analysis, it might find numerous applications in machine learning and artificial intelligence, including supervised classification (e.g., Woźniak and Krawczyk, 2012;Górecki and Łuczak, 2013), clustering (e.g., Kulczycki and Charytanowicz, 2010), and image processing (e.g., Cichocki et al, 2009;Hansen, 1998). Bioucas-Dias, J.M., Plaza, A., Dobigeon, N., Parente, M., Du, Q., Gader, P. and Chanussot, J.…”

Section: Discussionmentioning

confidence: 99%

Regularized nonnegative matrix factorization: Geometrical interpretation and application to spectral unmixing

Zdunek

2014

International Journal of Applied Mathematics and Computer Science

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Nonnegative Matrix Factorization (NMF) is an important tool in data spectral analysis. However, when a mixing matrix or sources are not sufficiently sparse, NMF of an observation matrix is not unique. Many numerical optimization algorithms, which assure fast convergence for specific problems, may easily get stuck into unfavorable local minima of an objective function, resulting in very low performance. In this paper, we discuss the Tikhonov regularized version of the Fast Combinatorial NonNegative Least Squares (FC-NNLS) algorithm (proposed by Benthem and Keenan in 2004), where the regularization parameter starts from a large value and decreases gradually with iterations. A geometrical analysis and justification of this approach are presented. The numerical experiments, carried out for various benchmarks of spectral signals, demonstrate that this kind of regularization, when applied to the FC-NNLS algorithm, is essential to obtain good performance.

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Section: Discussionmentioning

confidence: 99%

Regularized nonnegative matrix factorization: Geometrical interpretation and application to spectral unmixing

Zdunek

2014

International Journal of Applied Mathematics and Computer Science

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“…PseudoInv Algorithm. The PseudoInv algorithm is implemented using the Moore-Penrose generalized inverse [31]. It is often applied to obtain the least norm least squares solution (least squares method) on the nonuniform linear equations and makes the form of the solution simple.…”

Section: Consequent Parameter Optimizationmentioning

confidence: 99%

Soft Sensing Modeling of the SMB Chromatographic Separation Process Based on the Adaptive Neural Fuzzy Inference System

Wang

et al. 2019

Journal of Sensors

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Simulated moving bed (SMB) chromatographic separation technology is a new adsorption separation technology with strong separation ability. Based on the principle of the adaptive neural fuzzy inference system (ANFIS), a soft sensing modeling method was proposed for realizing the prediction of the purity of the extract and raffinate components in the SMB chromatographic separation process. The input data space of the established soft sensor model is divided, and the premise parameters are determined by utilizing the meshing partition method, subtractive clustering algorithm, and fuzzy C-means (FCM) clustering algorithm. The gradient, Kalman, Kaczmarz, and PseudoInv algorithms were used to optimize the conclusion parameters of ANFIS soft sensor models so as to predict the purity of the extract and raffinate components in the SMB chromatographic separation process. The simulation results indicate that the proposed ANFIS soft sensor models can effectively predict the key economic and technical indicators of the SMB chromatographic separation process.

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“…We only take ones and zeros in the diagonal of the matrix M M M because it has been proven (Górecki, Łuczak (2013)) that the value of A A A * M M M depends only on whether the coefficients a i are zeros or not. Each zero in the diagonal trims a part (but not all) of the information about one pair consisting of a class and a classifier.…”

Section: Algorithmmentioning

confidence: 99%

Stacked Regression With a Generalization of the Moore-Penrose Pseudoinverse

Górecki

Łuczak

2017

Statistics in Transition New Series

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In practice, it often happens that there are a number of classification methods. We are not able to clearly determine which method is optimal. We propose a combined method that allows us to consolidate information from multiple sources in a better classifier. Stacked regression (SR) is a method for forming linear combinations of different classifiers to give improved classification accuracy. The Moore-Penrose (MP) pseudoinverse is a general way to find the solution to a system of linear equations.This paper presents the use of a generalization of the MP pseudoinverse of a matrix in SR. However, for data sets with a greater number of features our exact method is computationally too slow to achieve good results: we propose a genetic approach to solve the problem. Experimental results on various real data sets demonstrate that the improvements are efficient and that this approach outperforms the classical SR method, providing a significant reduction in the mean classification error rate.

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Linear discriminant analysis with a generalization of the Moore–Penrose pseudoinverse

Cited by 18 publications

References 31 publications

Regularized nonnegative matrix factorization: Geometrical interpretation and application to spectral unmixing

Regularized nonnegative matrix factorization: Geometrical interpretation and application to spectral unmixing

Soft Sensing Modeling of the SMB Chromatographic Separation Process Based on the Adaptive Neural Fuzzy Inference System

Stacked Regression With a Generalization of the Moore-Penrose Pseudoinverse

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