Archetypal Analysis With Missing Data: See All Samples by Looking at a Few Based on Extreme Profiles

Abstract

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.

Archetype analysis: A new subspace outlier detection approach

“…On the other hand, we have considered only complete instances, but in real problems not all the cases are complete. We could easily extend the methodology for data sets with missing data, taking into account the proposal of [23]. We could also extend the methodology to other kind of data, such as multivariate time series and compare with recent literature on deep learning based methods for outlier detection in this field [75,7].…”

“…We propose a new method for unsupervised (no labels are available) detection of outliers in continuous multivariate data. It can be categorized into several of those categories, mainly (1) and ( 4), because it uses an unsupervised learning technique (a subspace technique), which can also be used as a clustering technique [23], and it also relies on NN-based techniques. Note that techniques based on distances are very popular due to their good results, conceptual simplicity and interpretability.…”

A data-driven classification of 3D foot types by archetypal shapes based on landmarks

“…AA and ADA applications have been growing at a great rate and they can be found in a diverse range of disciplines, such as biology [39], computer vision [40][41][42][43][44][45], developmental psychology [46], engineering [11,13,47,48], finance [49], genetics [50], global development [51], machine learning problems [52], market research [53], multi-document summarization [54], neuroscience [55,56] and sports [57][58][59].…”

Robust archetypoids for anomaly detection in big functional data

“…Evidence of this is the number of successful applications, both with classical continuous multivariate data, functional data and other kind of data (binary data, shapes, etc. ), such as ergonomy and anthropometry (Vinué et al, 2015;Epifanio et al, 2018;Alcacer et al, 2020), weather temperatures and the study of human development around the world (Epifanio, 2016;Epifanio et al, 2020), hyperspectral imagery (Sun et al, 2017;Cabero and Epifanio, 2019), sports (Vinué andEpifanio, 2017, 2019), social sciences (Cabero and Epifanio, 2020), financial time series (Moliner and Epifanio, 2019) and water networks (Millán-Roures et al, 2018). However, there are still two open questions in archetypoids theory: exploiting its use for anomaly detection and scalability.…”