# A Framework for Frugal Supervised Learning with Incremental Neural Networks
### Prototype-Based Neural Networks  
Prototype-based methods aim to represent a dataset through a small set of exemplars, which are called prototypes. These prototypes are chosen to be representative of the data in the sense that they capture the essential characteristics of the data distribution. Research studies have demonstrated the effectiveness of prototype-based classifiers in learning from small datasets. For instance, a study [4] showed that prototype-based classifiers such as k-NN and learning vector quantization (LVQ) achieved a higher accuracy with smaller training datasets than traditional machine learning methods such as support vector machines (SVMs) and artificial neural networks (ANNs). Similarly, in [5], it was found that prototype-based classifiers such as adaptive resonance theory (ART) neural networks outperformed traditional methods in recognizing patterns in small datasets with high noise levels.  
A commonly taken example of prototype-based neural network is the adaptive resonance theory network, which was introduced by [PERSON] in 1976 [6]. The ART network was initially designed to perform unsupervised learning and was capable of learning and recognizing patterns from noisy or ambiguous data. The network consists of two layers: the input layer and the recognition layer. The input layer is fed with input patterns, while the recognition layer contains a set of prototype vectors that represent each category. At training time, the network can adjust the prototype vectors to best represent the input data. During testing, the input pattern is computed to each prototype, and the category with the closest prototype is selected as the output.  
Another example of a prototype-based neural network is the learning vector quantization (LVQ) network, which was introduced by [PERSON] in 1982 [7]. The LVQ network is a supervised learning algorithm that learns a set of prototypes to represent each class in the input data. During training, the network adjusts the prototype vectors to minimize the classification error. During testing, the input pattern is compared to each prototype, and the closest prototype is selected as the output.  
Despite their relatively old origins, prototype-based classifiers still find recent use cases where they are preferred to cutting-edge methods, such as deep learning methods. In 2022, [PERSON], et al. [8] proposed a model architecture of a prototype-based classifier to detect melanoma from images. It is worth noting that their approach was not motivated by outperforming the latest classifier, but by providing an explainable framework to dermatologists. In another attempt, [PERSON], et al. [9] proposed to extend an imperialist competitive algorithm (ICA) prototype-based classification technique and compared their results with state-of-the-art ICA algorithms. Their proposition provided encouraging results.  
In a previous work [10], the incremental neural network (further called INN) used is a three-layer feedforward neural network that uses prototypes (or _exemplars_) to perform classification tasks (see Figure 1). Traditional artificial neural networks learn weights for every feature in the input. INNs use a set of representative examples (the prototypes) to model each class. The prototypes are stored in the network's memory--the networks's weights--and used to classify new inputs by measuring the similarity between an input and each prototype.  
The use of a neural network as support to a prototype-based classifier draws its inspiration from both [PERSON]'s and [PERSON]'s work. The motivation behind the attempt is to provide a frugal technique to classify labeled data, while providing an explainable approach. Indeed, unlike most neural methods that could be referred to as \"deep\", the INN has some features that facilitate its use in an interdisciplinary context.