Fig 1.
Example Wavelet Functions of Filters From Each Filter Type.
(A–D) Daubechies Extremal Phase filter. (A) Filter with length 2. (B) Filter with length 4. (C) Filter with length 6. (D) Filter with length 8. (E) Daubechies Least Asymmetric filter with length 8. (F) Coiflet filter with length 6.
Fig 2.
Effect of Wavelet Method on Mean and Variance of Correlation Coefficients.
(A, B) Mean correlation coefficients as a function of wavelet filter (Daubechies Extremal Phase, Daubechies Least Asymmetric, and Coiflet families) and wavelet length (2–24) observed when applying the (A) MODWT and (B) DWT. (C, D) Variance of correlation coefficients as a function of wavelet filter (Daubechies Extremal Phase, Daubechies Least Asymmetric, and Coiflet families) and wavelet length (2–24) observed when applying the (C) MODWT and (D) DWT. Wavelet scales are indicated by the color of the lines: scale 1 (approximately 0.125–0.25 Hz) is shown in blue, scale 2 (approximately 0.06–0.125 Hz) in green, scale 3 (approximately 0.03–0.06 Hz) in red, and scale 4 (approximately 0.015–0.03 Hz) in purple. Error bars indicate standard errors of the mean across 29 healthy subjects.
Table 1.
Variation of Diagnostic Values Over Wavelet Lengths t-values and p-values for two-sample t-tests measuring the differences in the sum of the absolute value of differences between graph metrics at consecutive lengths obtained from the MODWT approach as opposed to the DWT approach (df = 28 over the 29 healthy control subjects).
Paired t-tests were performed separately for each filter type (“D” = Daubechies Extremal Phase, “LA” = Daubechies Least Asymmetric, and “C” = Coiflet) for each wavelet scale separately.
Fig 3.
Effect of Wavelet Filter on Graph Metrics in wavelet scale 2 between pairs of wavelet filters with the same length.
(A, B) Weighted graph metrics including (A) mean correlation coefficient and (B) variance of correlation coefficients. (C–F) Binary graph metrics calculated at a graph density of 30% obtained through a cumulative thresholding procedure, including (C) the clustering coefficient, (D) characteristic path length, (E) global efficiency, (F) local efficiency, (G) modularity index Q, and (H) the number of communities. Boxplots indicate the median and quartiles of the data acquired from 29 health subjects. See S1 File for qualitatively similar results obtained at different scales and graph densities.
Fig 4.
Effect of Wavelet Length on Graph Metrics in wavelet scale 2 for all wavelet filters.
(A, B) Weighted graph metrics including (A) mean correlation coefficient and (B) variance of correlation coefficients. (C–F) Binary graph metrics calculated at a graph density of 30% obtained through a cumulative thresholding procedure, including (C) the clustering coefficient, (D) characteristic path length, (E) global efficiency, (F) local efficiency, (G) modularity index Q, and (H) the number of communities. The more saturated curves represent data from the 29 healthy controls, while the less saturated curves represent data from 29 people with schizophrenia. Error bars depict standard errors of the mean across subjects. Note that the range of lengths examined for each wavelet family is sufficient to observe significant trends in graph metrics. See S1 File for qualitatively similar results obtained at different wavelet scales.
Table 2.
Results of Repeated Measures ANOVAs for graph metrics extracted from 29 healthy controls at scale 2 and a graph density of 30%; wavelet length is treated as a factor and graph metric is treated as a repeated measure, separately for each wavelet filter type. Effects that are significant at p < 0.05, uncorrected, are shown in red.
Fig 5.
Effect of Wavelet Filter Type and Length on Statistical Sensitivity in Group Comparisons.
Negative common logarithm of the p-values obtained from two-sample t-tests between graph metric values extracted from healthy control networks versus those extracted from schizophrenia patient networks. Higher values indicate greater group differences and lower values indicate weaker group differences. Graph metrics are calculated for wavelet scale 2; for results in wavelet scale 1, see the SI.
Fig 6.
Effect of Wavelet Filter Type and Length on Classification.
Classification accuracy, sensitivity, and specificity as a function of wavelet filter type and length. Results are based on decision trees (see Methods) and distinguish between healthy controls and people with schizophrenia based on graph metrics computed in wavelet scale 2. Note that we have regarded schizophrenia as positive, which clarifies the direction of the sensitivity and specificity estimates.