Combining electro- and magnetoencephalography data using directional archetypal analysis

Metastable microstates in electro- and magnetoencephalographic (EEG and MEG) measurements are usually determined using modified k-means accounting for polarity invariant states. However, hard state assignment approaches assume that the brain traverses microstates in a discrete rather than continuous fashion. We present multimodal, multisubject directional archetypal analysis as a scale and polarity invariant extension to archetypal analysis using a loss function based on the Watson distribution. With this method, EEG/MEG microstates are modeled using subject- and modality-specific archetypes that are representative, distinct topographic maps between which the brain continuously traverses. Archetypes are specified as convex combinations of unit norm input data based on a shared generator matrix, thus assuming that the timing of neural responses to stimuli is consistent across subjects and modalities. The input data is reconstructed as convex combinations of archetypes using a subject- and modality-specific continuous archetypal mixing matrix. We showcase the model on synthetic data and an openly available face perception event-related potential data set with concurrently recorded EEG and MEG. In synthetic and unimodal experiments, we compare our model to conventional Euclidean multisubject archetypal analysis. We also contrast our model to a directional clustering model with discrete state assignments to highlight the advantages of modeling state trajectories rather than hard assignments. We find that our approach successfully models scale and polarity invariant data, such as microstates, accounting for intersubject and intermodal variability. The model is readily extendable to other modalities ensuring component correspondence while elucidating spatiotemporal signal variability

Archetypal analysis for ordinal data

Archetypoid analysis (ADA) is an exploratory approach that explains a set of continuous observations as mixtures of pure (extreme) patterns. Those patterns (archetypoids) are actual observations of the sample which makes the results of this technique easily interpretable, even for non-experts. Note that the observations are approximated as a convex combination of the archetypoids. Archetypoid analysis, in its current form, cannot be applied directly to ordinal data. We propose and describe a two-step method for applying ADA to ordinal responses based on the ordered stereotype model. One of the main advantages of this model is that it allows us to convert the ordinal data to numerical values, using a new data-driven spacing that better reflects the ordinal patterns of the data, and this numerical conversion then enables us to apply ADA straightforwardly. The results of the novel method are presented for two behavioural science applications. Finally, the proposed method is also compared with other unsupervised statistical learning methods

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

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

Functional archetype and archetypoid analysis

Archetype and archetypoid analysis can be extended to functional data. Each function is approximated by a convex combination of actual observations (functional archetypoids) or functional archetypes, which are a convex combination of observations in the data set. Well-known Canadian temperature data are used to illustrate the analysis developed. Computational methods are proposed for performing these analyses, based on the coefficients of a basis. Unlike a previous attempt to compute functional archetypes, which was only valid for an orthogonal basis, the proposed methodology can be used for any basis. It is computationally less demanding than the simple approach of discretizing the functions. Multivariate functional archetype and archetypoid analysis are also introduced and applied in an interesting problem about the study of human development around the world over the last 50 years. These tools can contribute to the understanding of a functional data set, as in the classical multivariate case.This work has been partially supported by Grant DPI2013-47279-C2-1-R

Archetype analysis: A new subspace outlier detection approach

The problem of detecting outliers in multivariate data sets with continuous numerical features is addressed by a new method. This method combines projections into relevant subspaces by archetype analysis with a nearest neighbor algorithm, through an appropriate ensemble of the results. Our method is able to detect an anomaly in a simple data set with a linear correlation of two features, while other methods fail to recognize that anomaly. Our method performs among top in an extensive comparison with 23 state-of-the-art outlier detection algorithms with several benchmark data sets. Finally, a novel industrial data set is introduced, and an outlier analysis is carried out to improve the fit of footwear, since this kind of analysis has never been fully exploited in the anthropometric field.Funding for open access charge: CRUE-Universitat Jaume

Robust multivariate and functional archetypal analysis with application to financial time series analysis

The code and data for reproducing the examples are available at http://www3.uji.es/epifanio/RESEARCH/rofada.rar. A preliminary version of this work was presented at the 8th International Conference on Mathematical and Statistical Methods for Actuarial Sciences and Finance (MAF 2018) (Moliner and Epifanio (2018)), where the application data were analyzed in a non-robust way.Archetypal analysis approximates data by means of mixtures of actual extreme cases (archetypoids) or archetypes, which are a convex combination of cases in the data set. Archetypes lie on the boundary of the convex hull. This makes the analysis very sensitive to outliers. A robust methodology by means of M-estimators for classical multivariate and functional data is proposed. This unsupervised methodology allows complex data to be understood even by non-experts. The performance of the new procedure is assessed in a simulation study, where a comparison with a previous methodology for the multivariate case is also carried out, and our proposal obtains favorable results. Finally, robust bivariate functional archetypoid analysis is applied to a set of companies in the S&P 500 described by two time series of stock quotes. A new graphic representation is also proposed to visualize the results. The analysis shows how the information can be easily interpreted and how even non-experts can gain a qualitative understanding of the data

Bivariate Functional Archetypoid Analysis: An Application to Financial Time Series

Treball de Fi de Màster Universitari en Matemàtica Computacional (Pla de 2013). Codi: SIQ027. Curs 2016-2017Archetype Analysis (AA) is a statistical technique that describes individuals of a sample as a convex combination of certain number of elements called Archetypes, which in turn, are convex combinations of the individuals in the sample. For it's part, Archetypoid Analysis (ADA) tries to represent each individual as a convex combination of a certain number of extreme subjects called Archetypoids. It is possible to apply these techniques to functional data applying a basis expansion function and performing AA or ADA to the weighted coe cients in the basis. This document presents an application of Functional Archetypoids Analysis (FADA) to nancial time series. The starting time series consists of daily equity prices of the SP500 stocks. From it, measures of volatility and pro tability are generated in order to characterize listed companies. These variables are converted into functional data through a Fourier basis expansion function and bivariate FADA is applied. By representing subjects through extreme cases, this analysis facilitates the understanding of both the composition and the relationships between listed companies. Finally, a cluster methodology based on a similarity parameter is presented. Therefore, the suitability of this technique for this kind of time series is shown, as well as the robustness of the conclusions drawn

Interictal Network Dynamics in Paediatric Epilepsy Surgery

Epilepsy is an archetypal brain network disorder. Despite two decades of research elucidating network mechanisms of disease and correlating these with outcomes, the clinical management of children with epilepsy does not readily integrate network concepts. For example, network measures are not used in presurgical evaluation to guide decision making or surgical management plans. The aim of this thesis was to investigate novel network frameworks from the perspective of a clinician, with the explicit aim of finding measures that may be clinically useful and translatable to directly benefit patient care. We examined networks at three different scales, namely macro (whole brain diffusion MRI), meso (subnetworks from SEEG recordings) and micro (single unit networks) scales, consistently finding network abnormalities in children being evaluated for or undergoing epilepsy surgery. This work also provides a path to clinical translation, using frameworks such as IDEAL to robustly assess the impact of these new technologies on management and outcomes. The thesis sets up a platform from which promising computational technology, that utilises brain network analyses, can be readily translated to benefit patient care