## 3 Methodology  
Algorithm selection has been shown to have excellent results with meta-features [7; 18; 26] and some success with regular features [13; 14; 27]. In both cases, analyzing the whole dataset can provide valuable statistics-based meta-features, but it also requires having a lot of labeled data. In order to avoid this problem, we study the Algorithm selection training using synthetic dataset. The overall approach is shown in Figure 1. We focus on medical image classification. The task is defined as a mapping \(C:I\to L\); for each image \(i\in I\), determine the label \(l\in L\). The Algorithm selection approach improves performance by dynamically choosing the optimal Algorithm for each input instance [28; 29]. Unlike ensembles that combine multiple Algorithm outputs, Algorithm selection chooses a single best Algorithm for each specific input, leveraging the complementary strengths of different Algorithms across the input space [7]. This meta-learning strategy works by training a selector that learns to map input features to the most suitable Algorithm from a portfolio of pretrained component Algorithms [30]. The selector essentially learns which Algorithm performs best on which types of inputs, allowing the system to achieve higher overall accuracy than any single Algorithm could achieve alone [8; 9]. The method starts with a set of pretrained Algorithms or by training a set of Algorithms \(\mathbb{A}=\{a_{1},\ldots,a_{k}\}\) for the classification task defined by mapping \(C\). We prepare an initial set of data \(\mathbb{D}\) by separating them into three subsets: \(\mathbb{D}_{t}\cap\mathbb{D}_{V}\cap\mathbb{D}_{T}=\mathbb{D}\), training, validation, and testing, respectively. Using the training dataset \(\mathbb{D}_{t}=\{(i_{1},l_{p})\ldots(i_{n},l_{q})\}\), we train a set of binary classifiers \(\mathbb{A}\). Each Algorithm \(a\in\mathbb{A}\) is evaluated on a validation dataset \(\mathbb{D}_{V}\), and its accuracy \(acc(a)\) is recorded. The Algorithms \(a\in\mathbb{A}\) are all trained on the same training dataset \(\mathbb{D}_{t}\) and will be referred to as component Algorithms. Next, from the validation dataset \(\mathbb{D}_{V}\), we use a subset of samples to create a subset, referred to as the seed dataset \(\mathbb{D}_{E}\subset\mathbb{D}_{V}\). Using \(\mathbb{D}_{E}\), we train a Generative Adversarial Network (GAN). Then, using the trained GAN, we create a new set of synthetic images \(\mathbb{I}_{5}\). For each label in the dataset \(\mathbb{D}\), we train a new GAN and generate a target number of synthetic images. For each sample of the resulting dataset \(x\in\mathbb{I}_{S}\), we determine the best Algorithm. The best Algorithm is any Algorithm \(a\in\mathcal{A}\) that classifies \(x\) correctly: \(a(x)=l^{\prime}\), where \(l^{\prime}\) is the ground-truth label for the input image \(x\). For synthetic images,  
Figure 1: A schematic representation of the whole system. it is important to note that we generate them class by class. When training the GAN on images of a specific class, e.g., \"pneumonia\" or \"healthy\", the generated synthetic images inherit the same class label as their training data source. Thus, when we refer to an Algorithm classifying a synthetic image \"correctly\", we mean it assigns the image to the same class used to train the GAN that generated it. This approach provides unambiguous ground-truth labels for all synthetic images used in our experimental evaluation. Using the synthetic images and the best Algorithms, we build the Algorithm selector training dataset \(\mathbb{D}_{S}=\{(x_{1},a_{k}),\ldots,(x_{N},a_{j})\}\). The inputs in \(\mathbb{D}_{S}\) are the synthetic images, and the outputs are the Algorithm names represented by the label set \(\mathbb{L}_{S}\). Using \(\mathbb{D}_{s}\), we train the Algorithm selector \(\mathcal{S}\) for the mapping \(\mathbb{I}_{s}\rightarrow\mathbb{L}_{s}\). Once the Algorithm selector is trained, we evaluate its accuracy and compare it to the accuracy of the individual Algorithms using the \(\mathbb{D}_{T}\) dataset.