Search

A functional linear discriminant analysis approach to classify a set of kinematic data (human movement curves of individuals performing different physical activities) is performed. Kinematic data, usually collected in linear acceleration or angular rotation format, can be identified with functions in a continuous domain (time, percentage of gait cycle, etc.). Since kinematic curves are measured in the same sample of individuals performing different activities, they are a clear example of functional data with repeated measures. On the other hand, the sample curves are observed with noise. Then, a roughness penalty might be necessary in order to provide a smooth estimation of the discriminant functions, which would make them more interpretable. Moreover, because of the infinite dimension of functional data, a reduction dimension technique should be considered. To solve these problems, we propose a multi-class approach for penalized functional partial least squares (FPLS) regression. Then linear discriminant analysis (LDA) will be performed on the estimated FPLS components. This methodology is motivated by two case studies. The first study considers the linear acceleration recorded every two seconds in 30 subjects, related to three different activities (walking, climbing stairs and down stairs). The second study works with the triaxial angular rotation, for each joint, in 51 children when they completed a cycle walking under three conditions (walking, carrying a backpack and pulling a trolley). A simulation study is also developed for comparing the performance of the proposed functional LDA with respect to the corresponding multivariate and non-penalized approaches. [ABSTRACT FROM AUTHOR]

This paper focuses on the problems of estimation and variable selection in the functional linear regression model (FLM) with functional response and scalar covariates. To this end, two different types of regularization (L1 and L2) are considered in this paper. On the one hand, a sample approach for functional LASSO in terms of basis representation of the sample values of the response variable is proposed. On the other hand, we propose a penalized version of the FLM by introducing a P‐spline penalty in the least squares fitting criterion. But our aim is to propose P‐splines as a powerful tool simultaneously for variable selection and functional parameters estimation. In that sense, the importance of smoothing the response variable before fitting the model is also studied. In summary, penalized (L1 and L2) and nonpenalized regression are combined with a presmoothing of the response variable sample curves, based on regression splines or P‐splines, providing a total of six approaches to be compared in two simulation schemes. Finally, the most competitive approach is applied to a real data set based on the graft‐versus‐host disease, which is one of the most frequent complications (30% –50%) in allogeneic hematopoietic stem‐cell transplantation. [ABSTRACT FROM AUTHOR]

Functional regression modelling has become one of the most vibrant areas of research in the last years. This discussion provides some alternative approaches to one of the key issues of functional data analysis: the basis representation of curves, and in particular, of functional random effects. First, we propose the estimation of functional principal components by penalizing the norm, and as an alternative, we provide an efficient and unified approach based on B-spline basis and quadratic penalties. [ABSTRACT FROM AUTHOR]

The aim of this article is to improve the quality of cookies production by classifying them as good or bad from the curves of resistance of dough observed during the kneading process. As the predictor variable is functional, functional classification methodologies such as functional logit regression and functional discriminant analysis are considered. A P-spline approximation of the sample curves is proposed to improve the classification ability of these models and to suitably estimate the relationship between the quality of cookies and the resistance of dough. Inference results on the functional parameters and related odds ratios are obtained using the asymptotic normality of the maximum likelihood estimators under the classical regularity conditions. Finally, the classification results are compared with alternative functional data analysis approaches such as componentwise classification on the logit regression model. [ABSTRACT FROM PUBLISHER]

This paper introduces stringing via Manifold Learning (ML-stringing), an alternative to the original stringing based on Unidimensional Scaling (UDS). Our proposal is framed within a wider class of methods that map high-dimensional observations to the infinite space of functions, allowing the use of Functional Data Analysis (FDA). Stringing handles general high-dimensional data as scrambled realizations of an unknown stochastic process. Therefore, the essential feature of the method is a rearrangement of the observed values. Motivated by the linear nature of UDS and the increasing number of applications to biosciences (e.g., functional modeling of gene expression arrays and single nucleotide polymorphisms, or the classification of neuroimages) we aim to recover more complex relations between predictors through ML. In simulation studies, it is shown that ML-stringing achieves higher-quality orderings and that, in general, this leads to improvements in the functional representation and modeling of the data. The versatility of our method is also illustrated with an application to a colon cancer study that deals with high-dimensional gene expression arrays. This paper shows that ML-stringing is a feasible alternative to the UDS-based version. Also, it opens a window to new contributions to the field of FDA and the study of high-dimensional data. [ABSTRACT FROM AUTHOR]

Over the last decade, regularized regression methods have offered alternatives for performing multi-marker analysis and feature selection in a whole genome context. The process of defining a list of genes that will characterize an expression profile remains unclear. It currently relies upon advanced statistics and can use an agnostic point of view or include some a priori knowledge, but overfitting remains a problem. This paper introduces a methodology to deal with the variable selection and model estimation problems in the high-dimensional set-up, which can be particularly useful in the whole genome context. Results are validated using simulated data and a real dataset from a triple-negative breast cancer study. [ABSTRACT FROM AUTHOR]

Diabetes is a very complex condition affecting millions of people around the world. Its occurrence, always accompanied by sustained hyperglycemia, leads to many medical complications that can be greatly mitigated when the disease is treated in its earliest stage. In this paper, a novel sensing approach for the early non-invasive detection and monitoring of sustained hyperglycemia is presented. The sensing principle is based on millimeter-wave transmission spectroscopy through the skin and subsequent statistical analysis of the amplitude data. A classifier based on functional principal components for sustained hyperglycemia prediction was validated on a sample of twelve mice, correctly classifying the condition in diabetic mice. Using the same classifier, sixteen mice with drug-induced diabetes were studied for two weeks. The proposed sensing approach was capable of assessing the glycemic states at different stages of induced diabetes, providing a clear transition from normoglycemia to hyperglycemia typically associated with diabetes. This is believed to be the first presentation of such evolution studies using non-invasive sensing. The results obtained indicate that gradual glycemic changes associated with diabetes can be accurately detected by non-invasively sensing the metabolism using a millimeter-wave spectral sensor, with an observed temporal resolution of around four days. This unprecedented detection speed and its non-invasive character could open new opportunities for the continuous control and monitoring of diabetics and the evaluation of response to treatments (including new therapies), enabling a much more appropriate control of the condition. [ABSTRACT FROM AUTHOR]

HbA1c is the gold standard test for monitoring medium/long term glycemia conditions in diabetes care, which is a critical factor in reducing the risk of chronic diabetes complications. Current technologies for measuring HbA1c concentration are invasive and adequate assays are still limited to laboratory-based methods that are not widely available worldwide. The development of a non-invasive diagnostic tool for HbA1c concentration can lead to the decrease of the rate of undiagnosed cases and facilitate early detection in diabetes care. We present a preliminary validation diagnostic study of W-band spectroscopy for detection and monitoring of sustained hyperglycemia, using the HbA1c concentration as reference. A group of 20 patients with type 1 diabetes mellitus and 10 healthy subjects were non-invasively assessed at three different visits over a period of 7 months by a millimeter-wave spectrometer (transmission mode) operating across the full W-band. The relationship between the W-band spectral profile and the HbA1c concentration is studied using longitudinal and non-longitudinal functional data analysis methods. A potential blind discrimination between patients with or without diabetes is obtained, and more importantly, an excellent relation (R-squared = 0.97) between the non-invasive assessment and the HbA1c measure is achieved. Such results support that W-band spectroscopy has great potential for developing a non-invasive diagnostic tool for in-vivo HbA1c concentration monitoring in humans., Competing Interests: The authors declare no conflicts of interest., (© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement.)