## 1 Introduction
All these factors result in the occurrence of small-sized datasets in either supervised or semi-supervised settings, thus limiting the generalization ability of the end classifier [32]. This challenge is exaggerated in the case of the existence of high intra-class variability [33; 34], which leads to classes of low density in the feature space. In fact, these challenging factors impact clustering algorithms as well [35]. Concurrently, they have a jarring effect on the clusters, creating disjoint subdivisions and hindering the discovery of the class structure in its entirety in space. In our work, the main contribution is proposing a model architecture which fully automates the learning of the transformation function that operates on unseen samples so that they resemble approximations of samples encountered in the training set. There are two aspects evident in our framework. First, we preserve the same feature space as the original data points. Second, we relocate input samples in a subspace while improving the goodness criteria of separability and compactness [36; 37; 38; 39]. To the best of our knowledge, this is the first time these aspects have been combined to carry out the task of selecting the feature vector embedding space. To this end, we train two main network models that, combined, comprise the transformation function. We train an autoencoder for feature extraction and reconstruction of the training samples. We create Cartesian product pairs of the training samples resulting in a set of ordered pairs and extract their embeddings from the encoder of the trained autoencoder. Then, a bridging regression network learns to map the embeddings of the first element in each ordered pair (as input variables to the regression network) to the embeddings of the second element in the pair (as target variables). We use the encoder of the autoencoder, the bridging network, and the decoder from the autoencoder to transform the training and test samples of each class to very similar (template-like) samples of the same class resulting in a reduction in intra-class variance and an increase in the inter-class variance. This helps to enhance the accuracy over the transformed test set of an off-the-shelf classifier trained on the training samples augmented with the transformed training samples. Data augmentation [17] is an effective technique to handle overfitting in the case of small datasets and enhance generalization of the machine learning model, particularly ANNs, by increasing both amount and diversity of data samples. The significance of our work is highlighted in the case of small datasets (\(\left|n\right|\)) with high variability. We fully exploit the samples available in the datasets by a pairing mechanism where we pair each example with all other examples of the same class and we study the samples' inter-relations \(\left|n^{2}\right|\), thus incrementing the learning data pool. In addition, we augment the dataset with reconstructions of latent features of the samples after being subjected to a regression step. Another contribution to this work is the applicability of our proposed model in a semi-supervised clustering setting where a few labeled data samples are utilized to learn clustering of the plentiful unlabeled data in a partially labeled dataset [40,41]. We use the labeled data samples to train our model to learn the transformation function, then we transform the unlabeled data using our trained model. We feed the transformed examples to a clustering technique. We show that not only is the clustering time of the transformed data points significantly reduced compared to using the same clustering techniques on the untransformed data points, but also all clustering metrics used to measure the performance of the clustering techniques notably improve. Several efforts have been proposed in the field of feature engineering in general and in the settings where there is a focus on improving compactness and separability.