Vector Quantization is useful for data compression. Competitive Learn(cid:173) ing which minimizes reconstruction error is an appropriate algorithm for vector quantization of unlabelled data. Vector quantization of labelled data for classification has a different objective, to minimize the number of misclassifications, and a different algorithm is appropriate. We show that a variant of Kohonen's LVQ2.1 algorithm can be seen as a multi(cid:173) class extension of an algorithm which in a restricted 2 class case can be proven to converge to the Bayes optimal classification boundary. We compare the performance of the LVQ2.1 algorithm to that of a modified version having a decreasing window and normalized step size, on a ten class vowel classification problem.

Decentralised machine learning has recently been proposed as a potential solution to the security issues of the canonical federated learning approach. In this paper, we propose a decentralised and collaborative machine learning framework specially oriented to resource-constrained devices, usual in IoT deployments. With this aim we propose the following construction blocks. First, an incremental learning algorithm based on prototypes that was specifically implemented to work in low-performance computing elements. Second, two random-based protocols to exchange the local models among the computing elements in the network. This proposal was compared to a typical centralized incremental learning approach in terms of accuracy, training time and robustness with very promising results. Decentralized machine learning faces how to use data and models from different sources to build machine learning models that gather the partial knowledge learned by each agent in this network to create, in a collaborative way, a global vision or model of the whole network. This would allow processing large amount of data managed by different computing elements. However, this approach entails several issues that must be considered when proposing solutions for this kind of computing environments. One of the most worrying is how to provide secure and private solutions that protect personal data when building global models. Some approaches have been already proposed to decentralise machine learning algorithms so that a set of networked agents can participate in building a global model.

Machine learning algorithms deployed on edge devices must meet certain resource constraints and efficiency requirements. Random Vector Functional Link (RVFL) networks are favored for such applications due to their simple design and training efficiency. We propose a modified RVFL network that avoids computationally expensive matrix operations during training, thus expanding the network's range of potential applications. Our modification replaces the least-squares classifier with the Generalized Learning Vector Quantization (GLVQ) classifier, which only employs simple vector and distance calculations. The GLVQ classifier can also be considered an improvement upon certain classification algorithms popularly used in the area of Hyperdimensional Computing. The proposed approach achieved state-of-the-art accuracy on a collection of datasets from the UCI Machine Learning Repository - higher than previously proposed RVFL networks. We further demonstrate that our approach still achieves high accuracy while severely limited in training iterations (using on average only 21% of the least-squares classifier computational costs).

Proximities are at the heart of almost all machine learning methods. If the input data are given as numerical vectors of equal lengths, euclidean distance, or a Hilbertian inner product is frequently used in modeling algorithms. In a more generic view, objects are compared by a (symmetric) similarity or dissimilarity measure, which may not obey particular mathematical properties. This renders many machine learning methods invalid, leading to convergence problems and the loss of guarantees, like generalization bounds. In many cases, the preferred dissimilarity measure is not metric, like the earth mover distance, or the similarity measure may not be a simple inner product in a Hilbert space but in its generalization a Krein space. If the input data are non-vectorial, like text sequences, proximity-based learning is used or ngram embedding techniques can be applied. Standard embeddings lead to the desired fixed-length vector encoding, but are costly and have substantial limitations in preserving the original data's full information. As an information preserving alternative, we propose a complex-valued vector embedding of proximity data. This allows suitable machine learning algorithms to use these fixed-length, complex-valued vectors for further processing. The complex-valued data can serve as an input to complex-valued machine learning algorithms. In particular, we address supervised learning and use extensions of prototype-based learning. The proposed approach is evaluated on a variety of standard benchmarks and shows strong performance compared to traditional techniques in processing non-metric or non-psd proximity data.

The amount of real-time communication between agents in an information system has increased rapidly since the beginning of the decade. This is because the use of these systems, e. g. social media, has become commonplace in today's society. This requires analytical algorithms to learn and predict this stream of information in real-time. The nature of these systems is non-static and can be explained, among other things, by the fast pace of trends. This creates an environment in which algorithms must recognize changes and adapt. Recent work shows vital research in the field, but mainly lack stable performance during model adaptation. In this work, a concept drift detection strategy followed by a prototype-based adaptation strategy is proposed. Validated through experimental results on a variety of typical non-static data, our solution provides stable and quick adjustments in times of change.

Nowadays the terms machine learning and artificial neural networks seem to be applied interchangeably. However, when it comes to ML algorithms there is a lot more under the sun than just neural networks. In fact, during university, most of the ML projects I've done did not use neural networks at all. It is true that neural networks can achieve amazing results to very complex problems. There are some key issues, though.

Algorithms are often grouped by similarity in terms of their function (how they work). For example, tree-based methods, and neural network inspired methods. I think this is the most useful way to group algorithms and it is the approach we will use here. This is a useful grouping method, but it is not perfect. There are still algorithms that could just as easily fit into multiple categories like Learning Vector Quantization that is both a neural network inspired method and an instance-based method.

We present a modelling framework for the investigation of prototype-based classifiers in non-stationary environments. Specifically, we study Learning Vector Quantization (LVQ) systems trained from a stream of high-dimensional, clustered data.We consider standard winner-takes-all updates known as LVQ1. Statistical properties of the input data change on the time scale defined by the training process. We apply analytical methods borrowed from statistical physics which have been used earlier for the exact description of learning in stationary environments. The suggested framework facilitates the computation of learning curves in the presence of virtual and real concept drift. Here we focus on timedependent class bias in the training data. First results demonstrate that, while basic LVQ algorithms are suitable for the training in non-stationary environments, weight decay as an explicit mechanism of forgetting does not improve the performance under the considered drift processes.

Adversarial attacks and the development of (deep) neural networks robust against them are currently two widely researched topics. The robustness of Learning Vector Quantization (LVQ) models against adversarial attacks has however not yet been studied to the same extend. We therefore present an extensive evaluation of three LVQ models: Generalized LVQ, Generalized Matrix LVQ and Generalized Tangent LVQ. The evaluation suggests that both Generalized LVQ and Generalized Tangent LVQ have a high base robustness, on par with the current state-of-the-art in robust neural network methods. In contrast to this, Generalized Matrix LVQ shows a high susceptibility to adversarial attacks, scoring consistently behind all other models. Additionally, our numerical evaluation indicates that increasing the number of prototypes per class improves the robustness of the models.

An appropriate choice of the activation function (like ReLU, sigmoid or swish) plays an important role in the performance of (deep) multilayer perceptrons (MLP) for classification and regression learning. Prototype-based classification learning methods like (generalized) learning vector quantization (GLVQ) are powerful alternatives. These models also deal with activation functions but here they are applied to the so-called classifier function instead. In this paper we investigate successful candidates of activation functions known for MLPs for application in GLVQ and their influence on the performance.