Supplemental Materials
I. Sensitivity analysis of dictionary learning model parameters
1.1 Effect of regularization coefficient λ1 and λ2 in Eq. 2
In this work, we have tried using different regularization parameter combinations in the dictionary
learning. Then the learned dictionary was used to derive the eight connectome patterns as shown in Fig.
6. We can then reconstruct the WQCPs using the learned eight connectome patterns. By aiming at
minimizing the reconstruction error, we could finally determine the optimal parameter combination,
which are 0.005 and 0.05 for λ1 and λ2 respectively. In addition, the table below shows how the value
of regularization coefficient would affect the final connectome patterns learned. Each cell in the table
measures the average relative difference between the DICCCOL-based temporally dynamic functional
connectome patterns obtained by using the parameter combination defined by the cell's row and
column header, vs. the connectome patterns obtained using parameter set 0.005 and 0.05. From the
table, it could be seen that within a reasonable range (λ1 from 0.002 to 0.01, λ2 from 0.01 to 0.05) the
model results are similar. However, 1) if λ2 is greater than 0.05, the dictionary learning result would
likely to be degraded to fewer sub-dictionaries thus cannot faithfully represent the original classes; 2)
The model performance would become more unstable when the choice of parameters varies, and it
would be hard to estimate how the results would deviates.
λ2=0.001
0.002
0.005
0.01
0.02
0.05
λ1=0.001
12.07%
10.09%
11.99%
11.80%
5.54%
3.93%
0.002
12.22%
13.02%
10.96%
10.52%
4.36%
3.74%
0.005
11.62%
9.99%
6.56%
6.28%
3.74%
N/A
0.01
10.87%
5.85%
6.68%
4.48%
6.48%
1.96%
0.02
12.82%
12.22%
10.21%
10.52%
9.95%
8.25%
Supplemental Table 1. Relative differences between the results obtained using parameter combination
of (0.005, 0.05) and the results obtained using other parameter combinations indicated by the row and
column header.
1.2 Effect of classification weight (w) parameter in Eq. 3
The weight (w) parameter controls the balance between the reconstruction error and the distance
between coefficient vectors and the mean vector in each class during the classification. In this work, it
is set to 0.1 to ensure that the two values are on the same scale. To investigate how the classification
results change with coefficient w, we tried the classifications using different values of w, and the
results are summarized in the table below. By checking number of WQCPs classified to different
classes comparing with the results obtained at w=0.1, we can see that the classification result would not
be affected much by the value of w. We also examined the connectome patterns derived from each
class with different weight values, and the patterns are consistent.
W
0.01
0.05
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
2
5
10
Number of Classification Difference
0
0
N/A
0
0
0
1
2
2
2
2
2
4
4
4
Supplemental Table 2. Number of WQCPs classified to a different/"wrong" class by using different
values of w, compared with the classification result using w=0.1. Value of 0 means all the WQCPs are
classified into the "correct" class i.e. the classification results perfectly match using two weight values.
1.3 Effect of sliding time window size on the dynamic functional connectivity
To investigate how the sliding time window size would affect the dynamic functional connectivity
results. We randomly selected one subject, applied different window sizes ranging from 10 to 50, and
compared the corresponding dynamic cumulative functional connectivities, which is the average of all
the connectivities over the whole period (time windows), as shown in (a) in the figure below. We also
visualized the corresponding standard deviation of each time point (window) in (b)-(e). It can be
observed that both of the mean strength and the standard deviation of the functional connectivity will
decrease as the length of the time window increases.
Supplemental Figure 1. (a) The mean functional connectivity strength over the whole time points
(windows) when the length of the time window is set to be 10, 14, 25 and 50 time points. (b)-(e) The
standard deviation of the functional connectivity strength of the whole time points (windows) when the
length of the time window is 10, 14, 25 and 50 time points.
1.4 Parameters used in multi-view co-training process
There are two key parameters in the multi-view clustering method: the number of eigenvectors used (k)
for co-training and the N-cut threshold (T) for clustering. The sensitivities of the two parameters in
identifying different resting state networks are detailed below.
The number of eigenvectors used (k): we have tried to use different numbers of k (15, 20, 25, 30, 35,
40) eigenvectors to perform the multi-view co-training and spectral clustering on multiple dynamic
patterns, i.e. multi-pattern clustering. The corresponding clustering results are summarized in the figure
below. The figure shows the corresponding dynamic DICCCOL clusters in the first dynamic temporal
pattern of the brain, i.e. the Fig. 6(a) in our manuscript. The N-cut threshold for spectral clustering is
fixed to be 0.2 for comparison and the optimal iteration number during each co-training procedure is
selected according to ECC criterion in Section 3.3.
Supplemental Figure 2. Multi-view co-training and spectral clustering results by using different
values of k.
From the above figure, it can be found that if small k value was set, some useful information will be
removed (e.g. the high functional connection information in orange the circle when k=15) and will
result in over-training. On the other hand, large k value will retain some uncommon information that
should be removed and thus may cause under-training (the very small cluster in the red circle when
k=40). When k=25 and k=30, both ten clusters were obtained which were almost the same (only 6
DICCCOL nodes are designed to different clusters). When k=35, totally nine clusters were obtained,
where the sixth cluster (the cluster highlighted by the black square box) corresponds to the fifth and the
eighth clusters (pointed by the two black arrows) when k=30. Thus we set k=30, which should be an
appropriate value for our 358 DICCCOL landmarks.
The N-cut threshold (T): the influence of the N-cut threshold is shown in Table 1 in the main
manuscript. This threshold determines whether current cluster could be further divided. For example,
when the threshold is set to be 0.05 and 0.1, nine clusters would be obtained; while the threshold is set
to be 0.2, one of the clusters will be further divided into two sub-groups, and thus the total cluster
number is ten. When the threshold is selected as 0.3, 0.4, and 0.5, no more clusters will be further
divided, thus we chose 0.2 as the threshold as the result was stable at ten clusters.
II. Analysis of the effect of head motion on results
To identify the potential outlier time points caused by the head motion and correct them, we checked
the relative motions of each time point of each subject by using tools provided by the FSL motion
correction kit. Outlier time points were identified by the criteria of relative motion value>0.5mm. For
each subject, averagely 9 time points were identified as outliers out of 200 time points. Then, we
performed linear interpolation on those outlier time points to obtain a new time series, and afterwards
use the new time series for the subsequent functional connectivity strength analysis. An illustration of
the functional connectivity strength pattern obtained from original time series (a) and the new time
series (b) of one randomly selected subject is presented in the figure below. The figure shows no
observable differences between the functional connectivity strength obtained by the original and
interpolated time series. Statistically, the subject-wise average difference of the functional connectivity
strength before and after the outlier detection and linear interpolation is less than 5%.
Supplemental Figure 3. Visualization of the functional connectivity strength matrix before (a) and
after (b) the outlier identification and interpolation. In the figure, X-axis is the time points, while Yaxis is the indices of the 358 DICCCOL ROIs. Each cell is color-coded by the functional connectivity
strength.