Dynamic Cerebral Contrast-enhanced Perfusion MRI - Biomedical Signal Analysis: Contemporary Methods and Applications - page 304

operating characteristic (ROC) analysis;
The implementation of a quantitative ROC analysis demonstrating
the performance of the presented clustering paradigms is reported in
the following. Besides the four clustering techniques - “neural gas” net-
work, Kohonen's self-organizing map (SOM), fuzzy clustering based on
deterministic annealing, and fuzzy c -means vector quantization - for the
last, two different implementations are employed: fuzzy c -means with
unsupervised codebook initialization (FSM) and the fuzzy c -means al-
gorithm (FVQ) with random codebook initialization. The two relevant
parameters in an ROC study, sensitivity and specificity, are explained
in the following for evaluating the dynamic perfusion MRI data. In the
study, sensitivity is the proportion of the activation site identified cor-
rectly, and specificity is the proportion of the inactive region identified
correctly. Both sensitivity and specificity are functions of the two thresh-
old values Δ 1 and Δ 2 , representing the thresholds for the reference and
compared partitions, respectively. Δ 2 is varied over its whole range while
Δ 1 is kept constant. By plotting the trajectory of these two parameters
(sensitivity and specificity), the ROC curve is obtained. In the ideal case,
sensitivity and specificity are both 1, and thus any curve corresponding
to a certain method closest to the uppermost left corner of the ROC plot
will be the method of choice. The results of quantitative ROC analysis
presented in figure 11.14 show large values of the areas under the ROC
curves as a quantitative criterion of diagnostic validity (i.e. agreement
between clustering results and parametric maps).
The threshold value Δ 1 in table 11.1 was carefully determined for
both performance metrics, regional cerebral blood volume (rCBV; left
column), and mean transit time (MTT): Δ 1 waschosenastheone
that maximizes the AUC of the ROC curves of experimental series. The
optimal threshold value Δ 1 is given individually for each data set (see
table 11.1) and corresponds to the maximum of the sum over all ROC
areas for each possible threshold value.
The ground truth used for the ROCanalysisisgivenbytheseg-
mentation obtained for the parameter values of the time series of each
individual pixel (i.e. the conventional analysis). The implemented pro-
cedure is as follows: (a) Select a threshold Δ 1 . (b) Then, determine the
ground truth: for the time series of each individual pixel, compare the
MTT value to Δ 1 . If the MTT value of this specific pixel is less than Δ 1 ,
assign this pixel to the active ground truth region; otherwise, assign it