Table 2 Results from Robust PCA.

From: A data-driven approach to measuring epidemiological susceptibility risk around the world

Method

Number of PC

Mean explained variance

Mean \(R^2\)

Mean \(R^2\) on 99th

Mean \(R^2\) on 95th

Augmented Dickey–Fuller

PCA

1

49.9 ± 0.9%

49.9 ± 0.9%

57.3 ± 1.1%

65.3 ± 0.9%

\(\ll 0.01\)

RobPCA

1

87 ± 0.9%

94.8 ± 0.3%

95.4 ± 0.2%

96.5 ± 0.2%

\(\ll 0.01\)

RobSparPCA

1

50.2 ± 0.9%

28.5 ± 3%

33.6 ± 3.6%

38.2 ± 4.5%

\(\ll 0.01\)

  1. Mean is evaluated over years. Mean Explained Variance is evaluated from the eigenvalues of PCA, \(R^2\) is reported for the full dataset and for the 99th and 95th percentiles. In analogy with the classical \(R^2\), we compute the RSS term as the squared residuals given after the reconstruction step using only the retained principal components and the TSS term as the total variance contained in the original variables. Augmented Dickey–Fuller test for stationarity of the ESR index as well.
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