Functional Symmetry and Statistical Depth for the Analysis of Movement Patterns in Alzheimer’s Patients

Nieto-Reyes, Alicia; Battey, Heather; Francisci, Giacomo

doi:10.3390/math9080820

Cited by 9 publications

(9 citation statements)

References 29 publications

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“…In the multivariate case, several notions of symmetry exist, for instance central, angular, and halfspace symmetry [12,13]. In the functional case, one proved to be topologically valid exists [10,14], while there have been two proposals in the fuzzy setting [15]. To propose a notion of symmetry in K c (R p ), we make use of the central symmetry notion and of the support function of compact convex random sets.…”

Section: Property 2: Maximality At the Center Of Symmetrymentioning

confidence: 99%

“…Statistical depth functions have become a very useful tool in non-parametric statistics. Nowadays, depth functions are applied in different fields of statistics, such as clustering and classification [9] or real data analysis [10,11]. Given a distribution P in a space, a depth function, D(•; P), orders the elements in the space with respect to P. Roughly speaking, statistical depth functions measure how close an element is to a data cloud, in the sense that, if we move the element to the center of the cloud, its depth increases, and, if we move it out of the center, its depth decreases.…”

Section: Introductionmentioning

confidence: 99%

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Properties of Statistical Depth with Respect to Compact Convex Random Sets: The Tukey Depth

2022

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We study a statistical data depth with respect to compact convex random sets, which is consistent with the multivariate Tukey depth and the Tukey depth for fuzzy sets. In addition, it provides a different perspective to the existing halfspace depth with respect to compact convex random sets. In studying this depth function, we provide a series of properties for the statistical data depth with respect to compact convex random sets. These properties are an adaptation of properties that constitute the axiomatic notions of multivariate, functional, and fuzzy depth-functions and other well-known properties of depth.

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Section: Property 2: Maximality At the Center Of Symmetrymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Properties of Statistical Depth with Respect to Compact Convex Random Sets: The Tukey Depth

2022

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“…According to the recent paper [23], statistical depth is a current hot research topic in statistical analysis [24][25][26][27][28] in some papers on the topic. Given a probability distribution P on R p , a statistical depth function orders the points in R p from the "center of P" to the "outer of P".…”

Section: Statistical Data Depthmentioning

confidence: 99%

A Method to Automate the Prediction of Student Academic Performance from Early Stages of the Course

2021

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The objective of this work is to present a methodology that automates the prediction of students’ academic performance at the end of the course using data recorded in the first tasks of the academic year. Analyzing early student records is helpful in predicting their later results; which is useful, for instance, for an early intervention. With this aim, we propose a methodology based on the random Tukey depth and a non-parametric kernel. This methodology allows teachers and evaluators to define the variables that they consider most appropriate to measure those aspects related to the academic performance of students. The methodology is applied to a real case study obtaining a success rate in the predictions of over the 80%. The case study was carried out in the field of Human-computer Interaction.The results indicate that the methodology could be of special interest to develop software systems that process the data generated by computer-supported learning systems and to warn the teacher of the need to adopt intervention mechanisms when low academic performance is predicted.

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“…This justifies the need to explore research proposals that allow automating the diagnosis of this pathology. Previous related works, including [3][4][5][6], shows that it is possible to make efficient use of modern tools in these areas. In this line, this work presents a methodological proposal that is based on Deep Learning techniques and computer vision to identify apraxias.…”

Section: Introductionmentioning

confidence: 99%

Automatic apraxia detection using Deep Convolutional Neural Networks and similarity methods

Bringas

Nieto-Reyes

Vicedo

et al. 2023

Preprint

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Dementia represents one of the great problems to be solved in medicine for a society that is becoming increasingly long-lived. One of the main causes of dementia is Alzheimer’s disease, which accounts for 80% of cases. There is currently no cure for this disease, although there are treatments to try to alleviate its effects, which is why detecting Alzheimer’s disease in its early stages is crucial to slow down its evolution and thus help sufferers. One of the symptoms of the disease that manifests in its early stages is apraxia, difficulties in carrying out voluntary movements. In the clinical setting, apraxia is typically assessed by asking the patient to imitate hand gestures that are performed by the examiner. To automate this test, this paper proposes a system that, based on a video of the patient making the gesture, evaluates its execution. This evaluation is done in two steps, first extracting the skeleton the skeleton of the hands and then using a similarity function to obtain an objective score Automatic apraxia detection using Deep CNNs and similarity methods of the execution of the gesture. The results obtained in an experiment with several patients performing different gestures are shown, showing the effectiveness of the proposed method. The system is intended to serve as a diagnostic tool, enabling medical experts to detect possible mobility impairments in patients that may be signs of Alzheimer’s disease.

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Functional Symmetry and Statistical Depth for the Analysis of Movement Patterns in Alzheimer’s Patients

Cited by 9 publications

References 29 publications

Properties of Statistical Depth with Respect to Compact Convex Random Sets: The Tukey Depth

Properties of Statistical Depth with Respect to Compact Convex Random Sets: The Tukey Depth

A Method to Automate the Prediction of Student Academic Performance from Early Stages of the Course

Automatic apraxia detection using Deep Convolutional Neural Networks and similarity methods

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