Sparse HJ Biplot: A New Methodology via Elastic Net

Cubilla‐Montilla, Mitzi; Librero, Ana Belén Nieto; Galindo-Villardón, Purificación; Torres-Cubilla, Carlos A.

doi:10.3390/math9111298

Cited by 14 publications

(9 citation statements)

References 40 publications

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“…In this article, a new technical contribution to three-way data analysis is developed using the elastic net regularization method. The advantage of this method, which combines the properties of ridge and lasso regularization, consists mainly in the selection of the most relevant variables, providing efficient solutions when studying multidimensional data [24] or data sets in which the number of observations is greater than the number of variables.…”

Section: Conclusion and Discussionmentioning

confidence: 99%

“…This new terminology and methodology propose applying restrictions to penalize the loads and produce sparse factorial axes; that is, derive axes that are a combination of the relevant variables [23]. The richness of this new method, from the exploratory point of view, consists in the clarity with which it is possible to visualize the main relationships between the dimensions, in addition to reproducing a two-dimensional structure [24]. In addition to the proposed method, a package has been implemented in the R programming language to give practical support to the new algorithm [25].…”

Section: Introductionmentioning

confidence: 99%

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Sparse STATIS-Dual via Elastic Net

et al. 2021

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Multi-set multivariate data analysis methods provide a way to analyze a series of tables together. In particular, the STATIS-dual method is applied in data tables where individuals can vary from one table to another, but the variables that are analyzed remain fixed. However, when you have a large number of variables or indicators, interpretation through traditional multiple-set methods is complex. For this reason, in this paper, a new methodology is proposed, which we have called Sparse STATIS-dual. This implements the elastic net penalty technique which seeks to retain the most important variables of the model and obtain more precise and interpretable results. As a complement to the new methodology and to materialize its application to data tables with fixed variables, a package is created in the R programming language, under the name Sparse STATIS-dual. Finally, an application to real data is presented and a comparison of results is made between the STATIS-dual and the Sparse STATIS-dual. The proposed method improves the informative capacity of the data and offers more easily interpretable solutions.

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Section: Conclusion and Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Sparse STATIS-Dual via Elastic Net

et al. 2021

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“…The first technique utilized is ELB which identifies the presence or absence of indicators of the social dimension in each of the selected companies. The second technique applied is the HJ-Biplot [41] to evaluate the similarities between the countries that serve the companies in the study, since, unlike other techniques, it makes it easier to visually detect the behaviour of geographic areas with respect to various dimensions (GRI social indicators) [42], in addition to achieving the highest quality of representation for rows and columns in the same reference system [43].…”

Section: Introductionmentioning

confidence: 99%

Using HJ-Biplot and External Logistic Biplot as Machine Learning Methods for Corporate Social Responsibility Practices for Sustainable Development

et al. 2021

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In recent years, social responsibility has been revolutionizing sustainable development. After the development of new mathematical techniques, the improvement of computers’ processing capacity and the greater availability of possible explanatory variables, the analysis of these topics is moving towards the use of different machine learning techniques. However, within the field of machine learning, the use of Biplot techniques is little known for these analyses. For this reason, in this paper we explore the performance of two of the most popular techniques in multivariate statistics: External Logistic Biplot and the HJ-Biplot, to analyse the data structure in social responsibility studies. The results obtained from the sample of companies representing the Fortune Global 500 list indicate that the most frequently reported indicators are related to the social aspects are labour practices and decent work and society. On the contrary, the disclosure of indicators is less frequently related to human rights and product responsibility. Additionally, we have identified the countries and sectors with the highest CSR in social matters. We discovered that both machine learning algorithms are extremely competitive and practical to apply in CSR since they are simple to implement and work well with relatively big datasets.

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“…The biplot methods allow the simultaneous representation of the individuals and variables of a data matrix [14]. Biplots have proven to be very useful for analyzing multivariate continuous data [15][16][17][18][19] and have also been implemented to visualize the results of other multivariate techniques such as multidimensional scaling, MANOVA, canonical analysis, correspondence analysis, generalized bilinear models, and the HJ-Biplot, among many others [14,[20][21][22][23][24].…”

Section: Introductionmentioning

confidence: 99%

Logistic Biplot by Conjugate Gradient Algorithms and Iterated SVD

Babativa-Márquez

Villardón

2021

Mathematics

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Multivariate binary data are increasingly frequent in practice. Although some adaptations of principal component analysis are used to reduce dimensionality for this kind of data, none of them provide a simultaneous representation of rows and columns (biplot). Recently, a technique named logistic biplot (LB) has been developed to represent the rows and columns of a binary data matrix simultaneously, even though the algorithm used to fit the parameters is too computationally demanding to be useful in the presence of sparsity or when the matrix is large. We propose the fitting of an LB model using nonlinear conjugate gradient (CG) or majorization–minimization (MM) algorithms, and a cross-validation procedure is introduced to select the hyperparameter that represents the number of dimensions in the model. A Monte Carlo study that considers scenarios with several sparsity levels and different dimensions of the binary data set shows that the procedure based on cross-validation is successful in the selection of the model for all algorithms studied. The comparison of the running times shows that the CG algorithm is more efficient in the presence of sparsity and when the matrix is not very large, while the performance of the MM algorithm is better when the binary matrix is balanced or large. As a complement to the proposed methods and to give practical support, a package has been written in the R language called BiplotML. To complete the study, real binary data on gene expression methylation are used to illustrate the proposed methods.

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Sparse HJ Biplot: A New Methodology via Elastic Net

Cited by 14 publications

References 40 publications

Sparse STATIS-Dual via Elastic Net

Sparse STATIS-Dual via Elastic Net

Using HJ-Biplot and External Logistic Biplot as Machine Learning Methods for Corporate Social Responsibility Practices for Sustainable Development

Logistic Biplot by Conjugate Gradient Algorithms and Iterated SVD

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