Supervised and unsupervised vector quantization methods for classification and clustering traditionally use dissimilarities, frequently taken as Euclidean distances. In this article, we investigate the applicability of divergences instead, focusing on online learning. We deduce the mathematical fundamentals for its utilization in gradient-based online vector quantization algorithms. It bears on the generalized derivatives of the divergences known as Fréchet derivatives in functional analysis, which reduces in finite-dimensional problems to partial derivatives in a natural way. We demonstrate the application of this methodology for widely applied supervised and unsupervised online vector quantization schemes, including self-organizing maps, neural gas, and learning vector quantization. Additionally, principles for hyperparameter optimization and relevance learning for parameterized divergences in the case of supervised vector quantization are given to achieve improved classification accuracy.

Machine learning strategies are prominent tools for data analysis. Especially in life sciences, they have become increasingly important to handle the growing datasets collected by the scientific community. Meanwhile, algorithms improve in performance, but also gain complexity, and tend to neglect interpretability and comprehensiveness of the resulting models. Generalized Matrix Learning Vector Quantization (GMLVQ) is a supervised, prototype-based machine learning method and provides comprehensive visualization capabilities not present in other classifiers which allow for a fine-grained interpretation of the data. In contrast to commonly used machine learning strategies, GMLVQ is well-suited for imbalanced classification problems which are frequent in life sciences. We present a Weka plug-in implementing GMLVQ. The feasibility of GMLVQ is demonstrated on a dataset of Early Folding Residues (EFR) that have been shown to initiate and guide the protein folding process. Using 27 features, an area under the receiver operating characteristic of 76.6% was achieved which is comparable to other state-of-the-art classifiers. The obtained model is accessible at https://biosciences.hs-mittweida.de/efpred/ . The application on EFR prediction demonstrates how an easy interpretation of classification models can promote the comprehension of biological mechanisms. The results shed light on the special features of EFR which were reported as most influential for the classification: EFR are embedded in ordered secondary structure elements and they participate in networks of hydrophobic residues. Visualization capabilities of GMLVQ are presented as we demonstrate how to interpret the results.

Learning vector quantization (LVQ) is one of the most powerful approaches for prototype based classification of vector data, intuitively introduced by Kohonen. The prototype adaptation scheme relies on its attraction and repulsion during the learning providing an easy geometric interpretability of the learning as well as of the classification decision scheme. Although deep learning architectures and support vector classifiers frequently achieve comparable or even better results, LVQ models are smart alternatives with low complexity and computational costs making them attractive for many industrial applications like intelligent sensor systems or advanced driver assistance systems.Nowadays, the mathematical theory developed for LVQ delivers sufficient justification of the algorithm making it an appealing alternative to other approaches like support vector machines and deep learning techniques.This review article reports current developments and extensions of LVQ starting from the generalized LVQ (GLVQ), which is known as the most powerful cost function based realization of the original LVQ. The cost function minimized in GLVQ is an soft-approximation of the standard classification error allowing gradient descent learning techniques. The GLVQ variants considered in this contribution, cover many aspects like bordersensitive learning, application of non-Euclidean metrics like kernel distances or divergences, relevance learning as well as optimization of advanced statistical classification quality measures beyond the accuracy including sensitivity and specificity or area under the ROC-curve.According to these topics, the paper highlights the basic motivation for these variants and extensions together with the mathematical prerequisites and treatments for integration into the standard GLVQ scheme and compares them to other machine learning approaches. For detailed description and mathematical theory behind all, the reader is referred to the respective original articles.Thus, the intention of the paper is to provide a comprehensive overview of the stateof- the-art serving as a starting point to search for an appropriate LVQ variant in case of a given specific classification problem as well as a reference to recently developed variants and improvements of the basic GLVQ scheme.

.Classification is one of the most frequent tasks in machine learning. However, the variety of classification tasks as well as classifier methods is huge. Thus the question is coming up: which classifier is suitable for a given problem or how can we utilize a certain classifier model for different tasks in classification learning. This paper focuses on learning vector quantization classifiers as one of the most intuitive prototype based classification models. Recent extensions and modifications of the basic learning vector quantization algorithm, which are proposed in the last years, are highlighted and also discussed in relation to particular classification task scenarios like imbalanced and/or incomplete data, prior data knowledge, classification guarantees or adaptive data metrics for optimal classification.

The encounter of large amounts of biological sequence data generated during the last decades and the algorithmic and hardware improvements have offered the possibility to apply machine learning techniques in bioinformatics. While the machine learning community is aware of the necessity to rigorously distinguish data transformation from data comparison and adopt reasonable combinations thereof, this awareness is often lacking in the field of comparative sequence analysis. With realization of the disadvantages of alignments for sequence comparison, some typical applications use more and more so-called alignment-free approaches. In light of this development, we present a conceptual framework for alignment-free sequence comparison, which highlights the delineation of: 1) the sequence data transformation comprising of adequate mathematical sequence coding and feature generation, from 2) the subsequent (dis-)similarity evaluation of the transformed data by means of problem-specific but mathematically consistent proximity measures. We consider coding to be an information-loss free data transformation in order to get an appropriate representation, whereas feature generation is inevitably information-lossy with the intention to extract just the task-relevant information. This distinction sheds light on the plethora of methods available and assists in identifying suitable methods in machine learning and data analysis to compare the sequences under these premises.