The taxonomy of foot shapes or other parts of the body is important, especially for design purposes. We propose a methodology based on archetypoid analysis (ADA) that overcomes the weaknesses of previous methodologies used to establish typologies. ADA is an objective, data-driven methodology that seeks extreme patterns, the archetypal profiles in the data. ADA also explains the data as percentages of the archetypal patterns, which makes this technique understandable and accessible even for non-experts. Clustering techniques are usually considered for establishing taxonomies, but we will show that finding the purest or most extreme patterns is more appropriate than using the central points returned by clustering techniques. We apply the methodology to an anthropometric database of 775 3D right foot scans representing the Spanish adult female and male population for footwear design. Each foot is described by a 5626 × 3 configuration matrix of landmarks. No multivariate features are used for establishing the taxonomy, but all the information gathered from the 3D scanning is employed. We use ADA for shapes described by landmarks. Women's and men's feet are analyzed separately. We have analyzed 3 archetypal feet for both men and women. These archetypal feet could not have been recovered using multivariate techniques.

In this paper we propose several methodologies for handling missing or incomplete data in Archetype analysis (AA) and Archetypoid analysis (ADA). AA seeks to find archetypes, which are convex combinations of data points, and to approximate the samples as mixtures of those archetypes. In ADA, the representative archetypal data belong to the sample, i.e. they are actual data points. With the proposed procedures, missing data are not discarded or previously filled by imputation and the theoretical properties regarding location of archetypes are guaranteed, unlike the previous approaches. The new procedures adapt the AA algorithm either by considering the missing values in the computation of the solution or by skipping them. In the first case, the solutions of previous approaches are modified in order to fulfill the theory and a new procedure is proposed, where the missing values are updated by the fitted values. In this second case, the procedure is based on the estimation of dissimilarities between samples and the projection of these dissimilarities in a new space, where AA or ADA is applied, and those results are used to provide a solution in the original space. A comparative analysis is carried out in a simulation study, with favorable results. The methodology is also applied to two real data sets: a well-known climate data set and a global development data set. We illustrate how these unsupervised methodologies allow complex data to be understood, even by non-experts.

The correct implementation of Ambulatory Surgery must be accompanied by an accurate monitoring of the patient post-discharge state. We fit different statistical models to predict the first hours postoperative status of a discharged patient. We will also be able to predict, for any discharged patient, the probability of needing a closer follow-up, or of having a normal progress at home.BackgroundThe status of a discharged patient is predicted during the first 48 hours after discharge by using variables routinely used in Ambulatory Surgery. The models fitted will provide the physician with an insight into the post-discharge progress. These models will provide valuable information to assist in educating the patient and their carers about what to expect after discharge as well as to improve their overall level of satisfaction.MethodsA total of 922 patients from the Ambulatory Surgery Unit of the Dr. Peset University Hospital (Valencia, Spain) were selected for this study. Their post-discharge status was evaluated through a phone questionnaire. We pretend to predict four variables which were self-reported via phone interviews with the discharged patient: sleep, pain, oral tolerance of fluid/food and bleeding status. A fifth variable called phone score will be built as the sum of these four ordinal variables. The number of phone interviews varies between patients, depending on the evolution. The proportional odds model was used. The predictors were age, sex, ASA status, surgical time, discharge time, type of anaesthesia, surgical specialty and ambulatory surgical incapacity (ASI). This last variable reflects, before the operation, the state of incapacity and severity of symptoms in the discharged patient.ResultsAge, ambulatory surgical incapacity and the surgical specialty are significant to explain the level of pain at the first call. For the first two phone calls, ambulatory surgical incapacity is significant as a predictor for all responses except for sleep at the first call.ConclusionsThe variable ambulatory surgical incapacity proved to be a good predictor of the patient's status at home. These predictions could be used to assist in educating patients and their carers about what to expect after discharge, as well as to improve their overall level of satisfaction.

Summary We introduce generalized partially linear models with covariates on Riemannian manifolds. These models, like ordinary generalized linear models, are a generalization of partially linear models on Riemannian manifolds that allow for scalar response variables with error distribution models other than a normal distribution. Partially linear models are particularly useful when some of the covariates of the model are elements of a Riemannian manifold, because the curvature of these spaces makes it difficult to define parametric models. The model was developed to address an interesting application: the prediction of children's garment fit based on three‐dimensional scanning of their bodies. For this reason, we focus on logistic and ordinal models and on the important and difficult case where the Riemannian manifold is the three‐dimensional case of Kendall's shape space. An experimental study with a well‐known three‐dimensional database is carried out to check the goodness of the procedure. Finally, it is applied to a three‐dimensional database obtained from an anthropometric survey of the Spanish child population. A comparative study with related techniques is carried out.

Fitting cloth is a problem for both the customer and the apparel industry, but analysis of anthropometric data can be useful to define better sizing systems. In 2006, the Spanish Ministry of Health coordinated a study to obtain 3D anthropometric data of the Spanish women. Our aim in this work is to develop a statistical methodology to define prototypes based on the 3D clouds of points obtained from 3D scans of a great number of women and apply it to the 3D anthropometric survey of the Spanish female population. To build the prototypes, 3D images will be built, and after registration, homologous 2D sections will be averaged, and a 3D "mean" shape will be reconstructed from them.