Sparse ordinal discriminant analysis.

Ordinal class labels are frequently observed in classification studies across various fields. In medical science, patients' responses to a drug can be arranged in the natural order, reflecting their recovery postdrug administration. The severity of the disease is often recorded using an ordinal scale, such as cancer grades or tumor stages. We propose a method based on the linear discriminant analysis (LDA) that generates a sparse, low-dimensional discriminant subspace reflecting the class orders. Unlike existing approaches that focus on predictors marginally associated with ordinal labels, our proposed method selects variables that collectively contribute to the ordinal labels. We employ the optimal scoring approach for LDA as a regularization framework, applying an ordinality penalty to the optimal scores and a sparsity penalty to the coefficients for the predictors. We demonstrate the effectiveness of our approach using a glioma dataset, where we predict cancer grades based on gene expression. A simulation study with various settings validates the competitiveness of our classification performance and demonstrates the advantages of our approach in terms of the interpretability of the estimated classifier with respect to the ordinal class labels.

Penalized optimal scaling for ordinal variables with an application to international classification of functioning core sets.

Ordinal data occur frequently in the social sciences. When applying principal component analysis (PCA), however, those data are often treated as numeric, implying linear relationships between the variables at hand; alternatively, non-linear PCA is applied where the obtained quantifications are sometimes hard to interpret. Non-linear PCA for categorical data, also called optimal scoring/scaling, constructs new variables by assigning numerical values to categories such that the proportion of variance in those new variables that is explained by a predefined number of principal components (PCs) is maximized. We propose a penalized version of non-linear PCA for ordinal variables that is a smoothed intermediate between standard PCA on category labels and non-linear PCA as used so far. The new approach is by no means limited to monotonic effects and offers both better interpretability of the non-linear transformation of the category labels and better performance on validation data than unpenalized non-linear PCA and/or standard linear PCA. In particular, an application of penalized optimal scaling to ordinal data as given with the International Classification of Functioning, Disability and Health (ICF) is provided.

The Wisdom Acquired During Emergencies Scale - Development and Validity.

The COVID-19 pandemic and its related lockdown restrictions had repercussions on health status, psychological states of mind, and emotion regulation. Attitudes towards these restrictions, beliefs, emotions and behaviours could be wise, as in the acceptance of, and adaptation to, these constraints. On the other hand, they could be unwise, as in the rejection of rules and limitations, denial of the consequences, irrational beliefs, self-accusation, rage and general intolerance. This study aims to introduce the development and validation of the 25-item Wisdom Acquired During Emergencies Scale (WADES). It is a measure to assess the wisdom and self-regulation that are needed to cope with unexpected and unpredictable emergency situations. On the basis of a preliminary study (N1 =212 Italian adults), a multiple-choice scale of 52 items was developed. In the reliability study (N2 =1777), items were scaled, analysed according to the optimal score technique and selected to provide a final and reliable version (Cronbach's α=0.83). The validity study (N3 =1,345, N4 =1,445, N5 = 878) provided correlations with established scales measuring, for example, traditional wisdom, emotion regulation, empathy, post-traumatic growth, collectivism, conscientiousness and satisfaction with life. The results confirmed that high scores on the WADES are associated with the ability to regulate emotions, control impulses and develop goals in emotional situations, to tolerate current difficulties, while developing new attitudes, values and behaviours, entailing changes in self-perception and relationships. It was thus confirmed that high WADES scores indicate a higher degree of acquired wisdom.

Classification of visual comprehension based on EEG data using sparse optimal scoring.

Objective.Understanding and differentiating brain states is an important task in the field of cognitive neuroscience with applications in health diagnostics, such as detecting neurotypical development vs. autism spectrum or coma/vegetative state vs. locked-in state. Electroencephalography (EEG) analysis is a particularly useful tool for this task as EEG data can detect millisecond-level changes in brain activity across a range of frequencies in a non-invasive and relatively inexpensive fashion. The goal of this study is to apply machine learning methods to EEG data in order to classify visual language comprehension across multiple participants.Approach.26-channel EEG was recorded for 24 Deaf participants while they watched videos of sign language sentences played in time-direct and time-reverse formats to simulate interpretable vs. uninterpretable sign language, respectively. Sparse optimal scoring (SOS) was applied to EEG data in order to classify which type of video a participant was watching, time-direct or time-reversed. The use of SOS also served to reduce the dimensionality of the features to improve model interpretability.Main results.The analysis of frequency-domain EEG data resulted in an average out-of-sample classification accuracy of 98.89%, which was far superior to the time-domain analysis. This high classification accuracy suggests this model can accurately identify common neural responses to visual linguistic stimuli.Significance.The significance of this work is in determining necessary and sufficient neural features for classifying the high-level neural process of visual language comprehension across multiple participants.

Group variable selection via ℓp,0 regularization and application to optimal scoring.

The need to select groups of variables arises in many statistical modeling problems and applications. In this paper, we consider the ℓp,0-norm regularization for enforcing group sparsity and investigate a DC (Difference of Convex functions) approximation approach for solving the ℓp,0-norm regularization problem. We show that, with suitable parameters, the original and approximate problems are equivalent. Considering two equivalent formulations of the approximate problem we develop DC programming and DCA (DC Algorithm) for solving them. As an application, we implement the proposed algorithms for group variable selection in the optimal scoring problem. The sparsity is obtained by using the ℓp,0-regularization that selects the same features in all discriminant vectors. The resulting sparse discriminant vectors provide a more interpretable low-dimensional representation of data. The experimental results on both simulated datasets and real datasets indicate the efficiency of the proposed algorithms.

Regularized Group Sparse Discriminant Analysis for P300-Based Brain-Computer Interface.

Event-related potentials (ERPs) especially P300 are popular effective features for brain-computer interface (BCI) systems based on electroencephalography (EEG). Traditional ERP-based BCI systems may perform poorly for small training samples, i.e. the undersampling problem. In this study, the ERP classification problem was investigated, in particular, the ERP classification in the high-dimensional setting with the number of features larger than the number of samples was studied. A flexible group sparse discriminative analysis algorithm based on Moreau-Yosida regularization was proposed for alleviating the undersampling problem. An optimization problem with the group sparse criterion was presented, and the optimal solution was proposed by using the regularized optimal scoring method. During the alternating iteration procedure, the feature selection and classification were performed simultaneously. Two P300-based BCI datasets were used to evaluate our proposed new method and compare it with existing standard methods. The experimental results indicated that the features extracted via our proposed method are efficient and provide an overall better P300 classification accuracy compared with several state-of-the-art methods.