COVID data are usually presented in a non-structured format and mainly focused on healthy issues (incidence, mortality, etc). At the same time, Governments have designed a set of measures to deal with the Pandemic. In addition, several institutions have studied the economical e ects of the situation in each country. In this work, we combine these three data sources and illustrate how Formal Concept Analysis can become a useful tool to discover relationships among these three views of the situation: health, politics and economy. Our aim is to provide an implication-driven approach to discover knowledge behind the data.
During 2020 and so far in 2021, the world has been paralysed by the pandemic. The devastating e ects of COVID-19 in terms of loss of human life, the limitations in every country worldwide and the economic downturn constitute a dramatic landmark in the history of humankind.
From the very beginning, individual researchers, universities and institutions
began to accumulate data on the virus incidence oriented to measure the stress of
the health infrastructures and the impact of the Pandemic on mortality.
Simultaneously, governments around the world have implemented several restrictions
to minimise the incidence of the virus. Each country has taken di erent
measures depending on their situation and, as usual, taking into account the political
e ects of these measures on the citizens [
Data scientists have conducted extensive, fast and e ective work, showing
the power of these methods and tools and providing some valuable guidelines
to support the ght against the virus and check its evolution. Most of these
works have been oriented for diagnoses (using image processing or tracking
techniques) or prediction and forecast (time series analysis or machine learning
methods) [
To the best of our knowledge, easy and direct relationships looking at the evolution curve of the number of infected persons and deaths can be extracted if we insert in the evolution curve the major measures taken by governments such as the total closure of companies and the con nement of people to their homes. These classical and quantitative relationships can be considered a good but basic approach. We are not aware of studies that allow studying all the elements involved in the three-dimensional data (health, politics and economy). We need to address the following problem: how to relate all the measures taken to a greater or lesser extent with the changes in the evolution of the number of infected persons, deaths, admissions to intensive care units and the interaction of all this with the economic downturn.
The rst step is to build a comprehensive dataset from reliable sources.
Regarding the disease dimension and its impact, there exist many sources collecting up-to-date data. Mainly, we have used the data from the European Centre for Disease Prevention and Control (ECDC), an agency of the European Union1 because of its trustworthiness. To complete our study, we have integrated economy and politics measures data. On the one hand, we have collected Eurostat data about the Economy. We have used the repository that this institution has mainly created to measure the impact of the crisis in Europe2. On the other hand, we have collected the measures designed for all the EU countries in the di erent waves of the pandemic as well as the number of cases and deceases, hospital occupancy and other related variables3.
Formal concept analysis [
In this work, we are using fcaR software developed in our research group, Malaga-FCA-group, using R language. We propose this tool as a useful tool to approach real problems in FCA and illustrate the bene ts of this solid framework. See https://github.com/Malaga-FCA-group/fcaR for more information.
The paper is organised as follows. In section 2 we describe how to address the import, processing and data curation in this real problem and how to integrate such data to be further used with FCA methods. In Section 3 we explore the discovery of knowledge extracted from the data (using implications) of COVID to establish how to act better in the future to reduce the incidence of the virus and minimise economic losses. We aim to illustrate how implications can be considered a suitable tool to help in decision-making tasks. Section 4 proposes some conclusions and future works. 2
As we have explained in the introduction, we have downloaded the open data regarding health and measures from UE institutions availables in the aforementioned sources. ECDC publishes weekly updates. Brie y, we have collected data about the following information: data on 14-day noti cation rate of new COVID19 cases and deaths, data on hospital and ICU admission rates and occupancy for COVID-19, data on country response measures to COVID-19, data on Harmonised unemployment rates and data on Gross Domestic Product (GDP)
In this rst study, we also have introduced the time dimension to infer conclusions about the Pandemic evolution. Thus, we take the second and third quarters (Q2, Q3) of 2020 as the study periods 4, because of the harshness of the incidence of the virus during these months and because all the EU countries in these two periods have presented signi cant di erences in their situation.
On the other hand, these variables are both numerical and dates, then we
have opted to perform conceptual scaling after normalizing the attributes. We
summarize the data pre-processing we have done to achieve the formal context
being the target of the application of the FCA methods:
{ Each measure adopted in the EU countries in one speci c quarter is stored
in one column. For instance, MEAS Q2 MasksMandatoryClosedSpaces means
that in the second quarter (Q2), masks were mandatory in all closed spaces.
{ We use the NOT token to show the absence of a given measure5. For instance,
MEAS NOT Q2 AdaptationOfWorkplace means that in the second quarter, the
country did not take any action on the adaptation of workplaces.
{ For each quarter (Q2 and Q3), we have discretized the COVID data (deaths
and cumulative cases in percent wrt population), ICU and hospitalization
data, and excess mortality data. For instance, COV Q2 cases low means that
4 Remark that we use somehow a temporal information, but we do not make use of
temporal FCA [
After the pre-processing task, we got an adequate binary formal context to be
explored with FCA. This formal context has 175 attributes and 25 objects. The
dataset has been imported in R using the fcaR package. From this point, we
performed the following steps:
{ First, we remove constant columns, corresponding to attributes (measures
or health or economic parameters) that are present either in none or in all
the objects (the 25 countries in the EU).
{ Then, we perform clari cation on the resulting formal context to identify
equivalent attributes, that is, attributes a, b such that a ) b and b ) a.
{ We compute the Duquenne-Guigues basis of implications and inspect them
to get a complete knowledge representation of the data allowing further
symbolic manipulation of the coronavirus situation in the EU countries.
{ In the last step, we apply the Simpli cation Logic for implications [
The Duquenne-Guigues basis of this formal context has 4086 implications. The average size of its LHS and RHS is 11.297 and 1.594 attributes, respectively. After using the simpli cation logic to remove redundancies, the resulting implication set has 4.472 and 1.188 attributes in the average size in LHS and RHS. The decrease of the implication size eases its reading and interpretation.
In the next subsections, we present the main ndings obtained from the simpli ed basis of implications. Our goal is to illustrate how these implications can be used to get a useful interpretation of the model. 3.1
Some measures weren't taken by any country in the management of the pandemic. Their interpretation depends on the measure or e ect and provides useful information even though its uniform absence seems to induce no information.
For instance, in the 3rd quarter, no country imposed a ban on all events or restrictions on private gatherings or closed restaurants, hotels and entertainment venues. Concerning economic parameters, the unemployment rate wasn't stable in both quarters. It remarks that the strong lockdown measures were not needed in the Q3 period.
It can be observed that the GDP in the second quarter decreased in all countries whereas it increased in the third quarter (summer). And, since there is a common value for all the objects (countries), this progress occurs irrespective of the restriction measures taken. 3.2
We named equivalent attributes those ones that play the same role, and they
can be characterized by using attribute reduction and clari cation methods [
The attributes NOT Q2 EntertainmentVenues and Q3 StayHomeRiskG are found to be equivalent. This means that every country that did not close entertainment venues in the 2nd quarter (Q2) of 2020, in the 3rd quarter (Q3), they had to issue a recommendation to stay home for risk groups (older adults, disabled people or people with other pathologies).
Also, having a high number of deaths in Q2 was equivalent to a high number of deaths in Q3. This is interesting since no matter the measures adopted if the pandemic has led to a high number of deaths during the rst stage, in the summer, the number of deaths remains at a high level, and it was also greater than Europe's average.
A high hospitalization occupancy ratio is shown to be equivalent to the ICU occupation ratio during Q2. This data illustrates that the evolution of patients admitted in the hospitals is not very promising. This is well-known for the health experts that insistently alert us about the risks of this disease, and the FCA analysis also con rms it. 3.3
To illustrate how to get useful knowledge from the implications, we have selected some implications whose interpretation may provide a deeper insight on the pandemic management strategies and the consequences of taking restriction measures. Since the implication set is large, we only show some easily interpretable and with a low number of attributes, and with positive support. In the following, we will simplify attributes' names to allow for a better readability: { Some implications on the in uence of Q2 measures in Q2 COVID cases or deaths (short-term e ects in health):
NOT Q2 MassGather50 ) Q2 cases are high
Q2 AdaptationOfWorkplace ) Q2 cases are medium Q2 RestaurantsCafes, Q2 MasksMandatoryAllSpaces ) Q2 deaths are medium These implications can be interpreted as follows: the countries that didn't constraint mass gatherings of more than 50 people in the Q2 ended this period with a number of COVID cases greater than Europe's average. By contrast, the countries that promoted adaptation of workplaces ended with a number of cases equivalent to the average. However, such promising impact of the virus can also be provided by other measures, and the same situation appears in the countries that did close restaurants and where masks were mandatory in all spaces. { In uence of Q2 measures in Q2 economy (short-term e ects in economy): NOT Q2 WorkplaceClosures ) Q2 UnemploymentChange is increased
NOT Q2 StayHomeOrder ) Q2 UnemploymentChange is increased These implications have a potentially counterintuitive interpretation. Countries that did not close workplaces or didn't order a strict lockdown had their unemployment rate increased; that is, not taking those measures didn't prevent a rise in the unemployment rates. It is important to highlight this relationship that has been discovered with the help of FCA tools.
{ In uence of Q2 measures in Q3 COVID (mid-term e ects in health): NOT Q2 StayHomeRiskG, NOT Q3 MasksVoluntaryAllSpaces ) Q3 ChangeInHospital is increased
Those countries that didn't recommend lockdown for risk groups in Q2 and didn't impose masks in all spaces in Q3, had their number of hospitalizations rise from Q2 to Q3.
{ In uence of Q2 measures in Q3 economy (mid-term e ects in economy): NOT Q2 BanOnAllEvents ) Q3 UnemploymentChange is decreased NOT Q2 StayHomeOrder ) Q3 UnemploymentChange is decreased Q2 PrivateGatheringRestrictions ) Q3 UnemploymentChange is decreased The unemployment decreased in those countries that, in Q2, did not ban all events, nor ordered a strict lockdown nor had restrictions on private gatherings. { In uence of Q3 measures in Q3 COVID:
NOT Q2 StayHomeRiskG, NOT Q3 MasksVoluntaryAllSpaces ) Q3 ChangeInHospital is increased NOT Q2 StayHomeRiskG, NOT Q3 MasksMandatoryAllSpaces ) Q3 ChangeInHospital is increased Q3 StayHomeRiskG ) Q3 inICU is medium, Q3 ChangeInHospital is decreased;
Q3 ExcessMortality is equivalent
The rst two implications tell us that not recommending risk groups to stay home and not suggesting the use of masks in all spaces led to an increase in hospitalizations during summer. The countries that recommended risks groups to stay home ended with an average ICU occupancy rate, a decrease in hospitalizations and a normalization of the mortality excess (that is, the number of deaths in the country is equivalent to the previous years).
To complete the information, we have studied the closure of some interesting attributes. In particular, we want to answer the question `What had in common the countries with a low and a high hospital occupancy rate in the second quarter? '
To answer this question, we will compute the closures of the corresponding attributes (Q2 inHospital is low and Q2 inHospital is high). { The closure of the rst attribute is the following Q2 ClosHigh, Q2 ClosPrim, Q2 MassGather50, Q2 MassGatherAll, Q2 OutdoorOver1000, Q2 EntertainmentVenues, NOT Q2 ClosureOfPublicTransport, NOT Q3 MasksMandatoryAllSpaces, NOT Q3 IndoorOver50, NOT Q3 OutdoorOver50, NOT Q3 Teleworking.
This means that countries that ended Q2 quarter with low occupancy had closed high and primary schools and imposed restrictions on mass gatherings and outdoor. However, in the third quarter, they could relax some restrictions on gatherings because of the low occupancy. { The high occupancy closure provides the following set of attributes: Q2 ClosSec, NOT Q2 HotelsOtherAccommodation, NOT Q2 ClosureOfPublicTransport, NOT Q3 Teleworking, Q2 ExcessMortality is more, Q3 ExcessMortalityChange is decreased.
This result means that they didn't have a common strategy and the only interesting consequence is that in Q3, the mortality excess was decreased. 4
In this work, we have used FCA to address the problem to illustrate the relationships among the government measures, the economic impact and the health situation in the Pandemic. We have combined real public data from all countries in the EU stored in di erent data sets, establishing a data pre-processing task. We have made a knowledge representation through the implications using the fcaR package. Reducing the original Duquenne-Guigues basis using the Simplication logic eases a further examination of the set of implications, allowing to deduce valuable insights about the COVID disease, its impact and the measures that can be used to deal with the virus.
As future works, we plan to collect more data. We intend to consider all
the countries worldwide and collect more attributes for the evolution of the
data in 2021. A more comprehensive conceptual scaling should be performed to
manage such large dataset. In addition, it is of interest the use of generalized
attributes [
To provide more information about the new data, we will also build the
concept lattice that provides other helpful information and a graphical
representation of the information, essential for further navigation among the closure
set of attributes. Since the number of concepts increases when more data were
considered, we will need a ltering method to select those which are most likely
to provide promising information. Stable concepts may provide more insights in
this delicate issue [
Finally, we will also address the negation issue (the relation between contrary
attributes) by means of mixed (negative and positive) attributes [