An efficient heuristic for geometric analysis of cell deformations

Sickle cell disease causes erythrocytes to become sickle-shaped, affecting their movement in the bloodstream and reducing oxygen delivery. It has a high global prevalence and places a significant burden on healthcare systems, especially in resource-limited regions. Automated classification of sickle cells in blood images is crucial, allowing the specialist to reduce the effort required and avoid errors when quantifying the deformed cells and assessing the severity of a crisis. Recent studies have proposed various erythrocyte representation and classification methods. Since classification depends solely on cell shape, a suitable approach models erythrocytes as closed planar curves in shape space. This approach employs elastic distances between shapes, which are invariant under rotations, translations, scaling, and reparameterizations, ensuring consistent distance measurements regardless of the curves' position, starting point, or traversal speed. While previous methods exploiting shape space distances had achieved high accuracy, we refined the model by considering the geometric characteristics of healthy and sickled erythrocytes. Our method proposes (1) to employ a fixed parameterization based on the major axis of each cell to compute distances and (2) to align each cell with two templates using this parameterization before computing distances. Aligning shapes to templates before distance computation, a concept successfully applied in areas such as molecular dynamics, and using a fixed parameterization, instead of minimizing distances across all possible parameterizations, simplifies calculations. This strategy achieves 96.03\% accuracy rate in both supervised classification and unsupervised clustering. Our method ensures efficient erythrocyte classification, maintaining or improving accuracy over shape space models while significantly reducing computational costs.

Biarchetype analysis: simultaneous learning of observations and features based on extremes

A new exploratory technique called biarchetype analysis is defined. We extend archetype analysis to find the archetypes of both observations and features simultaneously. The idea of this new unsupervised machine learning tool is to represent observations and features by instances of pure types (biarchetypes) that can be easily interpreted as they are mixtures of observations and features. Furthermore, the observations and features are expressed as mixtures of the biarchetypes, which also helps understand the structure of the data. We propose an algorithm to solve biarchetype analysis. We show that biarchetype analysis offers advantages over biclustering, especially in terms of interpretability. This is because byarchetypes are extreme instances as opposed to the centroids returned by biclustering, which favors human understanding. Biarchetype analysis is applied to several machine learning problems to illustrate its usefulness.

Unsupervised classification of children's bodies using currents

Object classification according to their shape and size is of key importance in many scientific fields. This work focuses on the case where the size and shape of an object is characterized by a current}. A current is a mathematical object which has been proved relevant to the modeling of geometrical data, like submanifolds, through integration of vector fields along them. As a consequence of the choice of a vector-valued Reproducing Kernel Hilbert Space (RKHS) as a test space for integrating manifolds, it is possible to consider that shapes are embedded in this Hilbert Space. A vector-valued RKHS is a Hilbert space of vector fields; therefore, it is possible to compute a mean of shapes, or to calculate a distance between two manifolds. This embedding enables us to consider size-and-shape classification algorithms. These algorithms are applied to a 3D database obtained from an anthropometric survey of the Spanish child population with a potential application to online sales of children's wear.