# Semi-Supervised GNSS Scintillations Detection Based on DeepInfomax
## 6 Experiments  
In this section, we present experimental results of the DeepInfomax method, compared with the Decision Tree proposed in [11], varying the number of labeled datapoints, by comparing the classification accuracy with respect to the baseline.The dataset used for the experiments is the same as in [11], but we neither train or test the method on the first 63 s of each data collection, due to the necessity of having a full window of samples. For each of the experiments, the labeled datapoints are randomly extracted from the training set. In the following, we present results in terms of standard machine learning performance indicators that we hereafter define. Denote as \(C\) the true class to which a datapoint belongs (0 for non scintillation, 1 for scintillation) and as \(\hat{C}\) the estimated class, i.e., the output of the classifier. We can define four joint probabilities:  
* [noitemsep,topsep=0 pt]
* true positive: \(T_{p}=P\left(\hat{C}=1,\,C=1\right),\)
* false positive: \(F_{p}=P\left(\hat{C}=1,\,C=0\right),\)
* true negative: \(T_{n}=P\left(\hat{C}=0,\,C=0\right),\)
* false negative: \(F_{n}=P\left(\hat{C}=0,\,C=1\right).\)  
Derived from these four quantities are the following ones:  
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* accuracy: \(A=T_{p}+T_{n}\),
* precision: \(P=\frac{T_{p}}{T_{p}+F_{p}}\),
* recall: \(R=\frac{T_{p}}{T_{p}+F_{n}}\),
* F-score: \(F_{sc}=2\frac{RP}{R+P}\).  
Figure 7 reports the main result of this paper: a comparison between the proposed method and the decision tree based one, varying the number of labeled datapoints. For sake of completeness, it is  
Figure 5: Neural Network architecture (Training). The dashed red box contains the unsupervised feature extraction part, while the orange one contains the supervised classification.  
Figure 6: Neural Network architecture (Testing).  
furthermore necessary to clarify that, when dealing with the decision tree classification algorithm, the number of labeled datapoints (\(x\)-axis of Figure 7) coincides with the size of the dataset used for training, since there is no possibility to include unlabeled datapoints in the learning pipeline. Instead, with our approach, the size of the training dataset is always the same (90% of the complete dataset, roughly 150,000 datapoints) but only a portion of the datapoints is labeled.  
The improvement in terms of performance is evident. First, it is worth noticing that the proposed DeepInfomax algorithm outperforms the Decision Tree technique, both in terms of accuracy and of F-score, for the same number of labeled elements. Second, a much lower number of labeled datapoints is required when using DeepInfomax to attain similar levels of accuracy and F-score. As the number of labeled points increases, the accuracy reaches a top value on the test set of 0.9993 for DeepInfomax, compared to the value 0.9824 for the Decision Tree.  
It is important to notice that, even if from a performance point of view, the results are excellent, to attest to the usefulness of the method in a realistic application tests on many different datasets should be performed. It is possible, in fact, that bias is present in the considered data collection on which the networks base their decisions. However, this problem is complex and outside the scope of this paper; see [30].  
Table 1 reports the results of the method for all the performance metrics introduced above. As expected, the performance increases with the increase of number of labeled datapoints, rapidly saturating to excellent levels. It is interesting to notice that the amount of false positives and false negatives is almost equivalent.  
Figure 7: Accuracy and F-score of Deep Infomax (DIM) method and Decision Tree (DT) [11] method.