Table 1.
Texture operators.
Fig 1.
Examples of images from best-case scenarios of the four categories in the dataset: (a) Normal chest; (b) COVID-19; (c) Non-COVID-19 viral pneumonia; (d) Lung opacity.
Fig 2.
Examples of images from worst-case scenarios of the four categories in the dataset: (a) Normal chest; (b) COVID-19; (c) Non-COVID-19 viral pneumonia; (d) Lung opacity.
Fig 3.
Block diagram of the proposed method illustrating the processing workflow.
Fig 4.
Example of a Scree plot of singular values, highlighting an elbow at the second component.
Fig 5.
Fit of the non-parametric empirical distribution to the variance-covariance matrix data: Class 0 (normal, blue dots), Class 1 (COVID-19, red dots), Class 2 (viral pneumonia, purple dots), and Class 3 (lung opacity, yellow dots).
Table 2.
Statistics of the smoothing parameter h across all images and classes.
Fig 6.
Scatter plot of the feature vector using the complete dataset: Class 0 (normal, blue dots), Class 1 (COVID-19, red dots), Class 2 (viral pneumonia, purple dots), and Class 3 (lung opacity, yellow dots). (a) Without the tuning weight parameter ω. (d) With the tuning weight parameter ω. The plots have similar shapes but exhibit a drift that aids in differentiating classes.
Fig 7.
Relative feature importance computed by ReliefF using the complete dataset.
(a) Without the tuning weight parameter ω. (b) With the tuning weight parameter ω.
Table 3.
Thresholds for all data with and without the tuning weight parameter (ω). Feature values for SVD (ζ) and the conditional index (η) are different and can serve with a threshold detection scheme.
Table 4.
Performace metrics average: TNR- True Positive Rate (or recall, or sensitivity), FNR- False Negative Rate (FNR), PPV- Positive Predictive Values, FDR- False Discovery Rate, AUC- Area Under Curve, ACC- Accuracy rate, and Total Cost.
Fig 8.
Partial dependency plots of conditional indices during testing, with and without the tuning weight ω: Class 0 (normal, blue dots), Class 1 (COVID-19, red dots), Class 2 (viral pneumonia, purple dots), and Class 3 (lung opacity, yellow dots).
The x-axis values are the conditional indices in (a) and the weighted conditional indices in (b). Values of the y-axis are probabilities of predicting a class. For example, in (a), the probability of predicting COVID-19 is 0 . 9 when the conditional index is around 18. Curves show the variation of the probabilities of predicting each class depending on the values of the feature. Figure (b) shows that for values of the weighted conditional indices starting from 0 . 2, the model is highly confident in predicting COVID-19, with a high probability (more than 0 . 8).
Fig 9.
Partial dependency plots of singular values during testing, with and without the tuning weight ω: Class 0 (normal, blue dots), class 1 (COVID-19, red dots), class 2 (viral pneumonia, purple dots), and class 3 (lung opacity, yellow dots).
The x-axis values are singular values in (a) and weighted singular values in (b). Values of the y-axis are probabilities of predicting a class. For example, in (a), the probability of predicting COVID-19 is 0 . 9 when the singular value is around 0 . 40. Curves show the variation of the probabilities of predicting each class depending on the values of the feature. Comparing plots in (a) and (b), we notice that the behaviour of the model is similar in the range [ 0 , 5 ] . However, Figure (b) shows that for the weighted singular values between [ 0 . 005 , 0 . 010 ] , the model is highly confident in predicting normal chest, with high probability (close to 0 . 8).
Table 5.
State-of-the-art methods for X-ray image classification. Summarised in terms of the classifier, preprocessing, and features extraction used and their performance using the different datasets. CLAHE: Contrast limited adaptive histogram equalization. DT: Decision Tree, HOG: Histogram of Oriented Gradients, WMF: Weighted Median Filtering, LSTM: Long short-term memory. PWLGBP: Weighted Local Gabor Binary Pattern. ENNSA: Ensemble Neural Net Sentinel Algorithm. IGLCM: Insistent Grey Level Co-occurrence Matrix. DF-GAN: Deep Fusion Generative Adversarial Networks. The performance metrics are the True Positive Rate, recall or Sensitivity (TPR), the True Negative Rate, Negative Recall, or Specificity (TNR), and the Accuracy Rate (ACC).