We address the problem of dimension reduction for time series of functional data .X t : t 2 Z/. Such functional time series frequently arise, for example, when a continuous time process is segmented into some smaller natural units, such as days. Then each X t represents one intraday curve. We argue that functional principal component analysis, though a key technique in the field and a benchmark for any competitor, does not provide an adequate dimension reduction in a time series setting. Functional principal component analysis indeed is a static procedure which ignores the essential information that is provided by the serial dependence structure of the functional data under study. Therefore, inspired by Brillinger's theory of dynamic principal components, we propose a dynamic version of functional principal component analysis which is based on a frequency domain approach. By means of a simulation study and an empirical illustration, we show the considerable improvement that the dynamic approach entails when compared with the usual static procedure.

The academic and behavioral progress of children is associated with the timely development of reading and writing skills. Dysgraphia, characterized as a handwriting learning disability, is usually associated with dyslexia, developmental coordination disorder (dyspraxia), or attention deficit disorder, which are all neuro-developmental disorders. Dysgraphia can seriously impair children in their everyday life and require therapeutic care. Early detection of handwriting difficulties is, therefore, of great importance in pediatrics. Since the beginning of the 20th century, numerous handwriting scales have been developed to assess the quality of handwriting. However, these tests usually involve an expert investigating visually sentences written by a subject on paper, and, therefore, they are subjective, expensive, and scale poorly. Moreover, they ignore potentially important characteristics of motor control such as writing dynamics, pen pressure, or pen tilt. However, with the increasing availability of digital tablets, features to measure these ignored characteristics are now potentially available at scale and very low cost. In this work, we developed a diagnostic tool requiring only a commodity tablet. To this end, we modeled data of 298 children, including 56 with dysgraphia. Children performed the BHK test on a digital tablet covered with a sheet of paper. We extracted 53 handwriting features describing various aspects of handwriting, and used the Random Forest classifier to diagnose dysgraphia. Our method achieved 96.6% sensibility and 99.2% specificity. Given the intra-rater and inter-rater levels of agreement in the BHK test, our technique has comparable accuracy for experts and can be deployed directly as a diagnostics tool.

Many neurological and musculoskeletal diseases impair movement, which limits people’s function and social participation. Quantitative assessment of motion is critical to medical decision-making but is currently possible only with expensive motion capture systems and highly trained personnel. Here, we present a method for predicting clinically relevant motion parameters from an ordinary video of a patient. Our machine learning models predict parameters include walking speed ( r = 0.73), cadence ( r = 0.79), knee flexion angle at maximum extension ( r = 0.83), and Gait Deviation Index (GDI), a comprehensive metric of gait impairment ( r = 0.75). These correlation values approach the theoretical limits for accuracy imposed by natural variability in these metrics within our patient population. Our methods for quantifying gait pathology with commodity cameras increase access to quantitative motion analysis in clinics and at home and enable researchers to conduct large-scale studies of neurological and musculoskeletal disorders.

The pedagogical modelling of everyday classroom practice is an interesting kind of evidence, both for educational research and teachers' own professional development. This paper explores the usage of wearable sensors and machine learning techniques to automatically extract orchestration graphs (teaching activities and their social plane over time), on a dataset of 12 classroom sessions enacted by two different teachers in different classroom settings. The dataset included mobile eye-tracking as well as audiovisual and accelerometry data from sensors worn by the teacher. We evaluated both time-independent and time-aware models, achieving median F1 scores of about 0.7-0.8 on leave-one-session-out k-fold cross-validation. Although these results show the feasibility of this approach, they also highlight the need for larger datasets, recorded in a wider variety of classroom settings, to provide automated tagging of classroom practice that can be used in everyday practice across multiple teachers.

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