arXiv subjects

Aleix Alcacer

Publications and source records attributed to Aleix Alcacer.

9 recordsLinked to original sources

arXiv2026

Archetypal analysis of European 10-year government bond yields with multidimensional scaling of two-mode three-way asymmetric dissimilarities

A recent methodology for extracting archetypal profiles from three-way asymmetric proximity data is applied to a dataset comprising 23 x 23 x 3 two-mode, three-way asymmetric dissimilarity matrices. The asymmetric dissimilarities are based on the oriented wavelet squared coherence of 10-year government bond yields among 23 European countries across three time intervals from 2001 to the present. First, the h-plot is computed for the unconditional two-mode three-way data, which is then represented in a unified Euclidean space, providing an intuitive and interpretable visualization. Subsequently, archetypoid analysis is performed. This unsupervised methodology identifies the archetypal countries and expresses all remaining countries as mixtures of these archetypal instances. Additionally, the degree of asymmetry for each country is calculated, offering further insight into the structure of the dissimilarities. The dataset and code are provided to support reproducible research.

stat.ME↗

arXiv2026

Biarchetype analysis for univariate functional data. An application to macroeconomic financial time series

We introduce biarchetype analysis for the first time in the context of univariate functional data. This unsupervised methodology extends archetype analysis by simultaneously identifying archetypal structures across both the cases (countries, in our application) and the temporal argument. Both cases and time points are expressed as mixtures of biarchetypes, yielding a concise and highly interpretable representation of complex functional observations. Although biarchetype analysis is not intended as a clustering technique, it offers superior interpretability compared with biclustering approaches, as it is based on extreme, representative patterns rather than average centroids, thereby enhancing human comprehension. We apply the proposed method to 10-year government bond yields of European countries over the period 2001-2025. The results identify three distinct time regimes (the pre-crisis period, the euro-area sovereign debt crisis, and the post-crisis period), and reveal Germany, Greece, and Hungary as country archetypes.

stat.ME↗

arXiv2026

Archetypal cases for questionnaires with nominal multiple choice questions

Archetypal analysis serves as an exploratory tool that interprets a collection of observations as convex combinations of pure (extreme) patterns. When these patterns correspond to actual observations within the sample, they are termed archetypoids. For the first time, we propose applying archetypoid analysis to nominal observations, specifically for identifying archetypal cases from questionnaires featuring nominal multiple-choice questions with a single possible answer. This approach can enhance our understanding of a nominal data set, similar to its application in multivariate contexts. We compare this methodology with the use of archetype analysis and probabilistic archetypal analysis and demonstrate the benefits of this methodology using a real-world example: the German credit dataset.

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arXiv2026

Representing asymmetric relationships by h-plots. Discovering the archetypal patterns of cross-journal citation relationships

This work approaches the multidimensional scaling problem from a novel angle. We introduce a scalable method based on the h-plot, which inherently accommodates asymmetric proximity data. Instead of embedding the objects themselves, the method embeds the variables that define the proximity to or from each object. It is straightforward to implement, and the quality of the resulting representation can be easily evaluated. The methodology is illustrated by visualizing the asymmetric relationships between the citing and cited profiles of journals on a common map. Two profiles that are far apart (or close together) in the h-plot, as measured by Euclidean distance, are different (or similar), respectively. This representation allows archetypoid analysis (ADA) to be calculated. ADA is used to find archetypal journals (or extreme cases). We can represent the dataset as convex combinations of these archetypal journals, making the results easy to interpret, even for non-experts. Comparisons with other methodologies are carried out, showing the good performance of our proposal. Code and data are available for reproducibility.

stat.AP↗

arXiv2025

Multidimensional scaling of two-mode three-way asymmetric dissimilarities: finding archetypal profiles and clustering

Multidimensional scaling visualizes dissimilarities among objects and reduces data dimensionality. While many methods address symmetric proximity data, asymmetric and especially three-way proximity data (capturing relationships across multiple occasions) remain underexplored. The h-plot enables the analysis of asymmetric and non-reflexive relationships by embedding dissimilarities in a Euclidean space, allowing further techniques like archetypoid analysis to identify representative extreme profiles. However, no existing methods extract archetypal profiles from three-way asymmetric proximity data. This work extends the h-plot methodology to three-way proximity data under both symmetric and asymmetric, conditional and unconditional frameworks. The proposed approach offers several advantages: intuitive interpretability through a unified Euclidean representation; an explicit, eigenvector-based analytical solution free from local minima; scale invariance under linear transformations; computational efficiency for large matrices; and a straightforward goodness-of-fit evaluation. Furthermore, it enables the identification of archetypal profiles and clustering structures for three-way asymmetric proximities. Its performance is compared with existing models for multidimensional scaling and clustering, and illustrated through a financial application. All data and code are provided to facilitate reproducibility.

stat.ME↗

arXiv2025

Incorporating Fairness Constraints into Archetypal Analysis

Archetypal Analysis (AA) is an unsupervised learning method that represents data as convex combinations of extreme patterns called archetypes. While AA provides interpretable and low-dimensional representations, it can inadvertently encode sensitive attributes, leading to fairness concerns. In this work, we propose Fair Archetypal Analysis (FairAA), a modified formulation that explicitly reduces the influence of sensitive group information in the learned projections. We also introduce FairKernelAA, a nonlinear extension that addresses fairness in more complex data distributions. Our approach incorporates a fairness regularization term while preserving the structure and interpretability of the archetypes. We evaluate FairAA and FairKernelAA on synthetic datasets, including linear, nonlinear, and multi-group scenarios, demonstrating their ability to reduce group separability -- as measured by mean maximum discrepancy and linear separability -- without substantially compromising explained variance. We further validate our methods on the real-world ANSUR I dataset, confirming their robustness and practical utility. The results show that FairAA achieves a favorable trade-off between utility and fairness, making it a promising tool for responsible representation learning in sensitive applications.

stat.ML↗

arXiv2025

A Survey on Archetypal Analysis

Archetypal analysis (AA) was originally proposed in 1994 by Adele Cutler and Leo Breiman as a computational procedure for extracting distinct aspects, so-called archetypes, from observations, with each observational record approximated as a mixture (i.e., convex combination) of these archetypes. AA thereby provides straightforward, interpretable, and explainable representations for feature extraction and dimensionality reduction, facilitating the understanding of the structure of high-dimensional data and enabling wide applications across the sciences. However, AA also faces challenges, particularly as the associated optimization problem is non-convex. This is the first survey that provides researchers and data mining practitioners with an overview of the methodologies and opportunities that AA offers, surveying the many applications of AA across disparate fields of science, as well as best practices for modeling data with AA and its limitations. The survey concludes by explaining crucial future research directions concerning AA.

stat.ME↗

arXiv2024

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

We introduce a novel exploratory technique, termed biarchetype analysis, which extends archetype analysis to simultaneously identify archetypes of both observations and features. This innovative unsupervised machine learning tool aims to represent observations and features through instances of pure types, or biarchetypes, which are easily interpretable as they embody mixtures of observations and features. Furthermore, the observations and features are expressed as mixtures of the biarchetypes, which makes the structure of the data easier to understand. We propose an algorithm to solve biarchetype analysis. Although clustering is not the primary aim of this technique, biarchetype analysis is demonstrated to offer significant advantages over biclustering methods, particularly in terms of interpretability. This is attributed to biarchetypes being extreme instances, in contrast to the centroids produced by biclustering, which inherently enhances human comprehension. The application of biarchetype analysis across various machine learning challenges underscores its value, and both the source code and examples are readily accessible in R and Python at https://github.com/aleixalcacer/JA-BIAA.

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arXiv2023

Ordinal classification for interval-valued data and interval-valued functional data

The aim of ordinal classification is to predict the ordered labels of the output from a set of observed inputs. Interval-valued data refers to data in the form of intervals. For the first time, interval-valued data and interval-valued functional data are considered as inputs in an ordinal classification problem. Six ordinal classifiers for interval data and interval-valued functional data are proposed. Three of them are parametric, one of them is based on ordinal binary decompositions and the other two are based on ordered logistic regression. The other three methods are based on the use of distances between interval data and kernels on interval data. One of the methods uses the weighted $k$-nearest-neighbor technique for ordinal classification. Another method considers kernel principal component analysis plus an ordinal classifier. And the sixth method, which is the method that performs best, uses a kernel-induced ordinal random forest. They are compared with naïve approaches in an extensive experimental study with synthetic and original real data sets, about human global development, and weather data. The results show that considering ordering and interval-valued information improves the accuracy. The source code and data sets are available at https://github.com/aleixalcacer/OCFIVD.

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