# Few-Shot Wideband Tympanometry Classification in
## 2 Material and Method
### Gaussian Processes-Guided Domain Adaptation (GPGDA) Algorithm  
In this study, the approach of WBT classification in tostclerosis was based on deep transfer learning, which usually involves two problems, that is, how to generate the source dataset and how to transfer from the source dataset to the target dataset. We mainly focused on optimizing the transfer strategies for our diagnosis task by considering the domain shift between source dataset and target dataset. The source datasets were generated by several data augmentation schemes including _nearest neighbor interpolation_[28], _additive noise_[29], and _mixup_[30], named as _SynDatal_, _SynDatalN_, and _SynDatalM_[5], respectively. They were dependent on training data (realistic) but independent of testing data (realistic). _SynDatal_ and _SynDatalN_ had deterministic hard labels, and _SynDatalM_ had probabilistic soft labels. The adopted backbone network was a lightweight LeNet-like architecture (Figure 1), where the number of channels was 12 and 24 for conv1 and conv2, respectively; the kernel size was \(2\times 4\) and \(4\times 5\) for convolutional layers and pooling layers, respectively; and the size of the hidden layer in the classifier (the output of fc3) was 32. In addition, no padding operation was employed for all convolutional and pooling layers in the backbone. The whole pipeline was conventionally divided into a training phase to optimize the parameters of the backbone network and a testing phase to evaluate the final performance. Figure 1: The adopted CNN architecture. First, conv1 and conv2 (convolution filters or feature extractors) processed the WBT image for feature extraction; then, fc3 and fc4 (classifiers) classified the features to yield the final diagnosis. The network included convolutional (Conv) layers, batch normalization (BatchNorm) layers, ReLU layers, MaxPooling layers, fully connected (FC) layers, and a SoftMax layer. The GPGDA algorithm ran during the training phase using both the realistic target and the synthetic source datasets to guide the parameter optimization (Figure 2). The test phase was the same as routine. Specifically, the deep neural network transformed the data \(\mathbf{x}\) (with its actual label \(y\), unified as \((\mathbf{x},y)\)) into a feature space via the feature extraction layers to obtain the latent variable \(\mathbf{z}\); then classified \(\mathbf{z}\) via a SoftMax layer to yield the final classification output. This algorithm considered adapting the distributions to make \(p(\{y^{s}\},\{\mathbf{z}^{s}\}|\{\mathbf{x}^{s}\})\) on the realistic dataset and \(p(\{y^{s}\},\{\mathbf{z}^{s}\}|\{\mathbf{x}^{s}\})\) on the synthetic dataset as close as possible via GP. First, we hypothesized that the relationship between \(y\) and \(\mathbf{z}\) could be modeled as  
\[y=\mathcal{GP}(0,k(\mathbf{z},\mathbf{z}^{\prime}))+\epsilon,\quad\epsilon\sim\mathcal{ N}(0,\sigma_{\epsilon}^{2}), \tag{6}\]  
where \(\epsilon\) is the modeling error. Naturally, the low-dimensional manifold on which \(p(\{y^{s}\},\{\mathbf{z}^{s}\}|\{\mathbf{x}^{s}\})\) lies could be fitted with (6).