## 5 Evaluation and Discussion
### Decentralized Data Mining
#### 5.1.2 Simulation Results  
We now first learn a decision tree from the whole training set using the VFDT (Very Fast Decision Tree) [73] implementation of the Hoeffding trees [66] with default parameters in the MOA (Massive On-line Analysis) classifier and evaluate its classification accuracy on the test set. Next, we run the Hoeffding tree learning incrementally by running the same algorithm on the first subset and \"augment\" this initial tree by successively running the algorithm on all other nine subsets (see Figure 2 in Section 4.2). The final tree's classification accuracy is then again evaluated on the same test set. Since we want to show that the sequence in which the nodes are visited in a network does not significantly affect the final decision tree, we repeat the \"incremental\" decision tree learning process 10 times, each time on a different random permutation of training set subsets (keeping the first and last subsets in their place). The sequence of this random permutation of the subsets is represented in Table 2.  
The results of the test-runs of the Hoeffding tree algorithm are presented in Table 3. The table includes the classification accuracies and sizes (number of leaves in the tree) for each of the 10 runs of the incremental Hoeffding tree (R1...R10) + the classification accuracy and size of the Hoeffding tree learned from all the training data (ALL). The average and standard deviation of all classification accuracies and sizes is also provided.  
\begin{table}
\begin{tabular}{c c} \hline
**Run** & **Subsets Sequence** \\ \hline R1 & \(1\to 2\to 3\to 4\to 5\to 6\to 7\to 8\to 9\to 10\) \\ R2 & \(1\to 3\to 4\to 5\to 6\to 7\to 8\to 9\to 2\to 10\) \\ R3 & \(1\to 4\to 5\to 6\to 7\to 8\to 9\to 2\to 3\to 10\) \\ R4 & \(1\to 5\to 6\to 7\to 8\to 9\to 2\to 3\to 4\to 10\) \\ R5 & \(1\to 6\to 7\to 8\to 9\to 2\to 3\to 4\to 5\to 10\) \\ R6 & \(1\to 7\to 8\to 9\to 2\to 3\to 4\to 5\to 6\to 7\to 10\) \\ R7 & \(1\to 8\to 9\to 2\to 3\to 4\to 5\to 6\to 7\to 10\) \\ R8 & \(1\to 9\to 2\to 3\to 4\to 5\to 6\to 7\to 8\to 10\) \\ R9 & \(1\to 6\to 3\to 5\to 4\to 7\to 2\to 9\to 8\to 10\) \\ R10 & \(1\to 8\to 4\to 9\to 5\to 6\to 7\to 3\to 2\to 10\) \\ \hline \end{tabular}
\end{table}
Table 2: Ten runs of the incremental Hoeffding tree learning process—the subsets sequence.  
\begin{table}
\begin{tabular}{c c c} \hline
**Run** & **Accuracy (\%)** & **Size (\# Leaves)** \\ \hline R1 & 65.34 & 285 \\ R2 & 63.12 & 291 \\ R3 & 66.01 & 280 \\ R4 & 67.88 & 279 \\ R5 & 64.32 & 285 \\ R6 & 63.76 & 290 \\ R7 & 64.91 & 281 \\ R8 & 65.50 & 292 \\ R9 & 67.46 & 291 \\ R10 & 66.72 & 285 \\ ALL & 64.15 & 291 \\ \hline Avg. & 65.38 & 286.36 \\ Std. & 1.46 & 4.66 \\ \hline \end{tabular}
\end{table}
Table 3: Results for 10 runs of the incremental Hoeffding tree learning process—the subsets sequence.  
The results in Table 3 show that the trees from different test-runs of the incremental Hoeffding tree algorithm, as well as the Hoeffding tree learned in batch from the complete training set, are very similar regarding classification accuracies and sizes (observe the very low standard deviation of the results in Table 3). This confirms our hypothesis that Hoeffding trees learned in an incremental way do not differ much from their batch counterparts learned from a large \"joint dataset\". Moreover, the sequence in which the nodes are visited in a WSN does not affect the final incremental Hoeffding tree.