Smart Visualization of Mixed Data

Abstract

In this work, we propose a new protocol that integrates robust classification and visualization techniques to analyze mixed data. This protocol is based on the combination of the Forward Search Distance-Based (FS-DB) algorithm (Grané, Salini, and Verdolini 2020) and robust clustering. The resulting groups are visualized via MDS maps and characterized through an analysis of several graphical outputs. The methodology is illustrated on a real dataset related to European COVID-19 numerical health data, as well as the policy and restriction measurements of the 2020–2021 COVID-19 pandemic across the EU Member States. The results show similarities among countries in terms of incidence and the management of the emergency across several waves of the disease. With the proposed methodology, new smart visualization tools for analyzing mixed data are provided.

Dynamic Mixed Data Analysis and Visualization

“…In Grané et al [ 11 ], we divided the epidemiological time series into three periods: the first one corresponds to the first wave of the pandemic with western EU countries more affected than eastern EU countries (from the end of February 2020 to mid-June 2020), the second one to the summer of 2020 when the pandemic was less strong almost in every EU country, and the final one corresponds to the second pandemic wave which affected almost all the EU countries (from mid-September 2020 to end of November 2020). The three periods are referred to as Wave 1, Wave 2 and Wave 3 in the following.…”

“…Second, it is a not robust metric; thus, it can lead to non-stable MDS configurations [ 5 , 8 ]. Finally, outliers cannot be easily located in MDS configurations obtained with Gower’s metric [ 5 , 11 ].…”

“…To circumvent these problems, Grané et al [ 11 ] proposed a robustification of Gower’s distance, by taking as a robust Mahalanobis distance, instead of range-normalized city-block distance, and they left and unchanged.…”

“…Their proposal was successful in discarding redundant information from a given set of variables, unlike classical Gower’s distance [ 10 ], although the metric’s computation can be computationally expensive. For this purpose, Grané et al [ 11 ] proposed a protocol based on the combination of this algorithm and robust clustering, by means of a robustified version of Gower’s metric.…”

“…The main task of this paper is to extend Grané et al,’s protocol [ 11 ] for similarity (dissimilarity) comparisons over time. In particular, given a time and a set of n individuals with heterogeneous measurements, we performed the comparisons over time using robust distance matrices for mixed data evaluated at each time t , and developed tools for smart visualization to monitor the evolution of inter-distances over time.…”