We propose a new method to visualize and detect shape outliers in samples of curves. In functional data analysis, we observe curves defined over a given real interval and shape outliers may be defined as those curves that exhibit a different shape from the rest of the sample. Whereas magnitude outliers, that is, curves that lie outside the range of the majority of the data, are in general easy to identify, shape outliers are often masked among the rest of the curves and thus difficult to detect. In this article, we exploit the relationship between two measures of depth for functional data to help to visualize curves in terms of shape and to develop an algorithm for shape outlier detection. We illustrate the use of the visualization tool, the outliergram, through several examples and analyze the performance of the algorithm on a simulation study. Finally, we apply our method to assess cluster quality in a real set of time course microarray data.

Nowadays, across the most important problems faced by health centers are those caused by the existence of patients who do not attend their appointments. Among others, these patients cause loss of revenue to the health centers and increase the patients’ waiting list. In order to tackle these problems, several scheduling systems have been developed. Many of them require predicting whether a patient will show up for an appointment. However, obtaining these estimates accurately is currently a challenging problem. In this work, a systematic review of the literature on predicting patient no-shows is conducted aiming at establishing the current state-of-the-art. Based on a systematic review following the PRISMA methodology, 50 articles were found and analyzed. Of these articles, 82% were published in the last 10 years and the most used technique was logistic regression. In addition, there is significant growth in the size of the databases used to build the classifiers. An important finding is that only two studies achieved an accuracy higher than the show rate. Moreover, a single study attained an area under the curve greater than the 0.9 value. These facts indicate the difficulty of this problem and the need for further research.

Functional magnetic resonance imaging (fMRI) is a non‐invasive technique that facilitates the study of brain activity by measuring changes in blood flow. Brain activity signals can be recorded during the alternate performance of given tasks, that is, task fMRI (tfMRI), or during resting‐state, that is, resting‐state fMRI (rsfMRI), as a measure of baseline brain activity. This contributes to the understanding of how the human brain is organized in functionally distinct subdivisions. fMRI experiments from high‐resolution scans provide hundred of thousands of longitudinal signals for each individual, corresponding to brain activity measurements over each voxel of the brain along the duration of the experiment. In this context, we propose novel visualization techniques for high‐dimensional functional data relying on depth‐based notions that enable computationally efficient 2‐dim representations of fMRI data, which elucidate sample composition, outlier presence, and individual variability. We believe that this previous step is crucial to any inferential approach willing to identify neuroscientific patterns across individuals, tasks, and brain regions. We present the proposed technique via an extensive simulation study, and demonstrate its application on a motor and language tfMRI experiment.

In functional data analysis, the time warping model aims at representing a set of curves exhibiting phase and amplitude variation with respect to a common continuous process. Many biological processes, when observed across the time among different individuals, fit into this concept. The observed curves are modeled as the composition of an “amplitude process,” which governs the common behavior, and a “warping process” that induces time distortion among the individuals. We aim at characterizing the first one. Because of the phase variation present among the curves, classical sample statistics computed on the observed sample provide poor representations of the amplitude process. Existing methods to estimate the mean behavior of the amplitude process consist on aligning the curves, that is, eliminating time variation, before estimation. However, since they rely on the use of sample means, they are very sensitive to the presence of outliers. In this article, we propose the use of a functional depth-based median as a robust estimator of the central behavior of the amplitude process. We investigate its properties in the time warping model, and we evaluate its performance in different simulation studies where we compare it to existing estimators, and we show its robustness against atypical observations. Finally, we illustrate its use with real data on a yeast time course microarray data set.