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Background Support vector machines (SVM) are a powerful tool to analyze data with a number of predictors approximately equal or larger than the number of observations. However, originally, application of SVM to analyze biomedical data was limited because SVM was not designed to evaluate importance of predictor variables. Creating predictor models based on only the most relevant variables is essential in biomedical research. Currently, substantial work has been done to allow assessment of variable importance in SVM models but this work has focused on SVM implemented with linear kernels. The power of SVM as a prediction model is associated with the flexibility generated by use of non-linear kernels. Moreover, SVM has been extended to model survival outcomes. This paper extends the Recursive Feature Elimination (RFE) algorithm by proposing three approaches to rank variables based on non-linear SVM and SVM for survival analysis. Results The proposed algorithms allows visualization of each one the RFE iterations, and hence, identification of the most relevant predictors of the response variable. Using simulation studies based on time-to-event outcomes and three real datasets, we evaluate the three methods, based on pseudo-samples and kernel principal component analysis, and compare them with the original SVM-RFE algorithm for non-linear kernels. The three algorithms we proposed performed generally better than the gold standard RFE for non-linear kernels, when comparing the truly most relevant variables with the variable ranks produced by each algorithm in simulation studies. Generally, the RFE-pseudo-samples outperformed the other three methods, even when variables were assumed to be correlated in all tested scenarios. Conclusions The proposed approaches can be implemented with accuracy to select variables and assess direction and strength of associations in analysis of biomedical data using SVM for categorical or time-to-event responses. Conducting variable selection and interpreting direction and strength of associations between predictors and outcomes with the proposed approaches, particularly with the RFE-pseudo-samples approach can be implemented with accuracy when analyzing biomedical data. These approaches, perform better than the classical RFE of Guyon for realistic scenarios about the structure of biomedical data.

Background Kernel methods have been proven to be a powerful tool for the integration and analysis of high-throughput technologies generated data. Kernels offer a nonlinear version of any linear algorithm solely based on dot products. The kernelized version of principal component analysis is a valid nonlinear alternative to tackle the nonlinearity of biological sample spaces. This paper proposes a novel methodology to obtain a data-driven feature importance based on the kernel PCA representation of the data. Results The proposed method, kernel PCA Interpretable Gradient (KPCA-IG), provides a data-driven feature importance that is computationally fast and based solely on linear algebra calculations. It has been compared with existing methods on three benchmark datasets. The accuracy obtained using KPCA-IG selected features is equal to or greater than the other methods’ average. Also, the computational complexity required demonstrates the high efficiency of the method. An exhaustive literature search has been conducted on the selected genes from a publicly available Hepatocellular carcinoma dataset to validate the retained features from a biological point of view. The results once again remark on the appropriateness of the computed ranking. Conclusions The black-box nature of kernel PCA needs new methods to interpret the original features. Our proposed methodology KPCA-IG proved to be a valid alternative to select influential variables in high-dimensional high-throughput datasets, potentially unravelling new biological and medical biomarkers.

Smart factories are complex; with the increased complexity of employed cyber-physical systems, the complexity evolves further. Cyber-physical systems produce high amounts of data that are hard to capture and challenging to analyze. Real-time recording of all data is not possible due to limited network capabilities. Limited network capabilities are the reason for a chain of faults introduced via active surveillance during fault diagnosis. These introduced faults may slow down production or lead to an outage of the production line. Here, we present a novel approach to automatically select production-relevant shop floor parameters to decrease the number of surveyed variables and, at the same time, maintain quality in fault diagnosis without overloading the network. We were able to achieve higher throughput, mitigate communication losses and prevent the disruption of factory instructions. Our approach uses an autoencoder ensemble via minority voting to differentiate between normal—always on—variables and production variables that may yield a higher entropy. Our approach has been tested in a production-equal smart factory and was cross-validated by a domain expert.

Lilian Bermejo-Luque has posed these questions:1.What is the relationship between presumption and presumptive inference?2.What are the correctness conditions for presumptions and presumptive inferences?Cohen’s method of relevant variables, Toulmin’s model, and Rescher’s theory of plausibility suggest answers. An inference is presumptive just in case its warrant transfers presumption from its premises to its conclusion. A warrant licencing an inference from the claim that an empirical property φ holds to the claim that some other property ψ holds is backed by observation of a constant conjunction of those properties. The stronger the backing, the stronger the warrant. Warrants may be defeated by instances of φ holding in conjunction with some property χ and ψ not holding. The method of relevant variables directs us to organize such defeating properties into relevant variables. We then test the strength of a warrant by seeing how many variables fail to have a value which defeats the warrant. The more variables with no defeater, the stronger the warrant. We may construct a canonical ordering of the relevant variables by ranking them according to the plausibility of their including defeating values. We may evaluate the strength not only of empirically backed warrants, but warrants backed by institutional rules, such as a branch of law, or by a priori intuited connections between properties. An inference rule will be presumptive just in case the plausibility of its warrant being defeated is below some specified level.

In this article we introduce two procedures for variable selection in cluster analysis and classification rules. One is mainly aimed at detecting the \"noisy\" noninformative variables, while the other also deals with multicolinearity and general dependence. Both methods are designed to be used after a \"satisfactory\" grouping procedure has been carried out. A forward-backward algorithm is proposed to make such procedures feasible in large datasets. A small simulation is performed and some real data examples are analyzed.

Research background: It does not matter if the company is operating in the domestic or in the international environment; its failure has serious impact on its environment. Because of this fact it is not surprising that not only owners of the companies, but also another interested groups are focused on the prediction of the company´s financial health.Purpose of the article: The first studies concerned with this issue are dating back to 1930 but from this time a hundreds of bankruptcy prediction models have been constructed all over the world. Some of them are known world-wide and some of them are known only on the national level. Many researchers share their opinion, that it is not appropriate to use foreign models in the domestic conditions non-critically, because they were constructed in the different conditions. One of the main problems are used variables.Methods: We mention three studies which were focused on the used variables in the bankruptcy prediction models. Our comparative study was concerning with 42 models constructed in the seven chosen transit economics with the aim to realize which variables are relevant and which could be reduce from the bankruptcy prediction models. We focused only on the used variables and abstracted from the used methodology, the date of their construction or the model´s power of relevancy.Findings and Value added: The result of our comparative study is the identification of 20 variables, which were used in three or more prediction models, so we assume that these variables have the best prediction ability in the condition of transit economics and their application should be consider in the construction of new models.

This chapter contains sections titled: Hotelling's T 2 Distribution A T 2 Control Chart Multivariate Chart Versus Individual X̄‐Charts Charts for Detecting Variability and Correlation Shifts Charts Constructed Using Individual Observations When to Use Each Chart Actual Alpha Levels for Multiple Points Requisite Assumptions Effects of Parameter Estimation on ARLs Dimension‐Reduction and Variable Selection Techniques Multivariate CUSUM Charts Multivariate EWMA Charts Effect of Measurement Error Applications of Multivariate Charts Multivariate Process Capability Indices Summary Appendix References Exercises

Research on employee selection has indicated that interviewers are influenced by many variables. This experiment manipulates the attractiveness of male applicants and the perceived relevance of attractiveness for managerial job performance in a 2-by-2 analysis of variance design. An interaction was predicted and was found for the effects of the manipulation on hiring decisions and on job-specific attributions of ability. The first hypothesis held that applicant attractiveness and attractiveness-relevance of the job interact to determine interviewers' decisions and attributions of job-specific characteristics to applicants; it was confirmed. The 2nd posits that applicant attractiveness has a positive effect on the attribution of some general (not job-specific) characteristics; it was not supported.

This chapter contains sections titled: Individual Differences Summary and Conclusions References