# Quantum Machine Learning for Security Assessment in the Internet of Medical Things (IoMT)
## 3 Proposed Model and Research Framework
### Semi-Supervised Convolutional Neural Networks  
We combined the supervised CNN and CNN-encoder decoder models to obtain semi-supervised learning for vulnerability prediction in IoMT-based applications. Semi-supervised learning [36] uses a set of labeled pairs (_x_i, _t_i) \(|1\,\mathrm{I}\,\mathrm{N}\) along with unlabeled data xi \(|\mathrm{N}\)+\(1\,\mathrm{I}\,\mathrm{N}\)+\(\mathrm{M}\) to train a classifier. This information was used to teach the classifier. In a semi-supervised CNN-encoder-decoder setup, labeled and unlabeled data can be processed in one of three ways: the clean encoder, noisy encoder, or decoder. The clean encoder path was used to determine the intermediate layer hidden variables, which are marked by z 1 I. This route is used for both labeled and unlabeled clean data. In the noisy encoder path, both labeled and unlabeled data are exposed to Gaussian noise before the noisy encoder converts them into a more abstract representation. The letters z, l, and I represent this representation, respectively. We used the cross-entropy cost to make predictions with the best softmax classifier for the has been labeled data (\(\propto 1\,\mathrm{I}\,\mathrm{I}\,\mathrm{N}\)). In the labeled dataset, the values of x range from 1 to N. Let us assume that the letters y I stand for the expected label. The decoder attempts to return the original, clean input from the noisy, unlabeled data (\(\propto\,\mathrm{i}\), \(\mathrm{N}+1\,\mathrm{I}\,\mathrm{N}+\mathrm{M}\)) (_x_i). The square error is used to measure the size of the reconstruction error. The clean encoder path and noisy encoder path both use the same parameters [37]. The only difference is in the inputs, as shown in Figure 1. (The CNN-Ladder shown in Figure 2 can be simplified to a CNN-Encoder-Decoder structure by only looking at the vertical connections and the cost on the side). The cost function for the CNN-encoder decoder includes both the supervised cross-entropy cost from the labeled data in the supervised CNN and the unsupervised denoising square error cost between the clean input and its noisy reconstruction output. Supervised CNN must pay these two extra costs. This figure shows the cost function.  
\[z_{i}^{(1)},\ldots\ldots,z_{i}^{(L)}=Encoder_{clean}(x_{i}) \tag{4}\]  
\[\underline{x}_{i^{\prime}},\underline{z}_{i}^{(1)},\ldots,\underline{z}_{i}^ {(L)}=Encoder_{noisy}(x_{i}) \tag{5}\]  
\[\hat{x}_{i}=Decoder(\underline{z}_{i}^{(L)}) \tag{6}\]  
Given the input \(x_{i}\), the average cross-entropy of the noisy output y I that meets goal \(t_{i}\) is equal to supervised cost Cs. The average squared error between the reconstructed output xi and original input xi can be considered as the unsupervised cost Cr. If we use a CNN-encoder-decoder that is only partially supervised, we can train both the network and the features simultaneously from the data, as described in Figure 3.  
\[C_{e}=C_{s}+\lambda C_{r}^{(0)}=-\frac{1}{N}\sum_{i=1}^{N}\log\log P(x_{i})+ \frac{\lambda}{M}\sum_{i=N+1}^{N+M}||\underline{x}_{i}-x_{i}||_{2}^{2} \tag{7}\]  
Figure 2: (a) [PERSON] decision process for \(P\) component. (b) [PERSON] decision process for \(R\) component.  
There are two kinds of ties in CNN-Ladder. This kind of connection is shown by the reconstructed cost function C (l) r and the lateral connection g (l). A vertical link is the other kind of link that can be used.