  Currently, Coronavirus disease (COVID-19), one of the most infectious
diseases in the 21st century, is diagnosed using RT-PCR testing, CT scans
and/or Chest X-Ray (CXR) images. CT (Computed Tomography) scanners and RT-PCR
testing are not available in most medical centers and hence in many cases CXR
images become the most time/cost effective tool for assisting clinicians in
making decisions. Deep learning neural networks have a great potential for
building COVID-19 triage systems and detecting COVID-19 patients, especially
patients with low severity. Unfortunately, current databases do not allow
building such systems as they are highly heterogeneous and biased towards
severe cases. This paper is three-fold: (i) we demystify the high sensitivities
achieved by most recent COVID-19 classification models, (ii) under a close
collaboration with Hospital Universitario Cl\'inico San Cecilio, Granada,
Spain, we built COVIDGR-1.0, a homogeneous and balanced database that includes
all levels of severity, from normal with Positive RT-PCR, Mild, Moderate to
Severe. COVIDGR-1.0 contains 426 positive and 426 negative PA (PosteroAnterior)
CXR views and (iii) we propose COVID Smart Data based Network (COVID-SDNet)
methodology for improving the generalization capacity of COVID-classification
models. Our approach reaches good and stable results with an accuracy of
$97.72\% \pm 0.95 \%$, $86.90\% \pm 3.20\%$, $61.80\% \pm 5.49\%$ in severe,
moderate and mild COVID-19 severity levels (Paper accepted for publication in
Journal of Biomedical and Health Informatics). Our approach could help in the
early detection of COVID-19. COVIDGR-1.0 along with the severity level labels
are available to the scientific community through this link
https://dasci.es/es/transferencia/open-data/covidgr/.
