## 1 Introduction
The AdaBoost algorithm, introduced by [PERSON] and [PERSON] [27], is an iterative algorithm that can boost weak classifiers into a strong classifier and improve the final accuracy. In each iteration, a feature is working as a weak classifier and the best feature is selected to minimize the average training error. Afterwards, the weights on training samples are redistributed in such a way that the weight of accurately classified samples will be reduced while the weight of ill classified samples is raised. Therefore, AdaBoost focuses on the most \"difficult\" ones [28]. The final classifier aggregates the selected weak classifier from each iteration, and the weight for each weak classifier depends on its error rate. However, AdaBoost can be sensitive to noise and may introduce the overfitting problem. Random forests (RF) is a classifier that combines many decision trees [29]. Each tree depends on values of a random vector sampled independently and with equal distribution. Each tree casts a unit vote for the most popular case at input, and random forests outputs the class that is the mode of the \begin{table}
\begin{tabular}{l c} \hline
**Authors** & **\# Of Patients** \\ \hline [PERSON] _et al._[20] & 2 \\ [PERSON] _et al._[2] & 2 \\ [PERSON] _et al._[21] & 10 \\ [PERSON] _et al._[22] & 20 \\ [PERSON] _et al._[23] & 34 \\ \hline \end{tabular}
\end{table} 
Table 2: Summary of related methods in GBM tumor treatment response using DWI. classes output by individual trees. [PERSON] suggests the generalization error for forests converges to a limit as the number of trees in the forest becomes large [30]. The error of a forest of tree classifiers depends on the strength of the individual trees in the forest and the correlation between them. Using a random selection of features to split each node yields error rates that compare favorably to Adaboost but are more robust with respect to noise. Support vector machines (SVMs) are a set of related supervised learning methods used for classification and regression [31, 32]. Viewing input data as two sets of vectors in an n-dimensional space, an SVM will construct a separating hyperplane in that space, one which maximizes the margin between the two data sets. To calculate the margin, two parallel hyperplanes are constructed, one on each side of the separating hyperplane, which are \"pushed up against\" the two data sets. Intuitively, a good separation is achieved by the hyperplane that has the largest distance to the neighboring data points of both classes, since in general the larger the margin the lower the generalization error of the classifier [33]. SVM have been reported to work well for pharmaceutical data analysis [34]. There are two main challenges in this work. One challenge is the two competing effects in ADC changes after treatment. In general, water movement inside cells is more restricted than outside. Thus, increased cell density tends to lower ADC values, whereas increased edema (more interstitial water) results in higher ADC values. Therefore, theoretically, ADC values in treated brain tumors could not only increase due to the cell kill (and thus reduced cell density), but also decrease due to inhibition of edema. None of the listed studies above have specified the separate effects. Thus, we applied a two-component model to fit the tumor ADC histogram [25]. The other challenge is that it is difficult to directly identify GBM brain tumors on ADC maps. We developed a semi-automated framework to achieve that goal. There are several contributions in this work. First, we developed a computer-aided method to semi-automatically identify tumors on ADC maps. Second, we explored the changes of different statistical features of the whole tumor ADC histogram. Moreover, we applied a two-component Gaussian mixture modeling to fit the tumor ADC histogram to overcome the two competing effects. Next, we used earth mover's distance (EMD) to directly measure the distance between the pre- and post-treatment tumor ADC histograms.