a b s t r a c tWe present an extension of the recently introduced Generalized Matrix Learning Vector Quantization algorithm. In the original scheme, adaptive square matrices of relevance factors parameterize a discriminative distance measure. We extend the scheme to matrices of limited rank corresponding to low-dimensional representations of the data. This allows to incorporate prior knowledge of the intrinsic dimension and to reduce the number of adaptive parameters efficiently.In particular, for very large dimensional data, the limitation of the rank can reduce computation time and memory requirements significantly. Furthermore, two-or three-dimensional representations constitute an efficient visualization method for labeled data sets. The identification of a suitable projection is not treated as a pre-processing step but as an integral part of the supervised training. Several real world data sets serve as an illustration and demonstrate the usefulness of the suggested method.

Efficient learning of a data analysis task strongly depends on the data representation. Most methods rely on (symmetric) similarity or dissimilarity representations by means of metric inner products or distances, providing easy access to powerful mathematical formalisms like kernel or branch-and-bound approaches. Similarities and dissimilarities are, however, often naturally obtained by nonmetric proximity measures that cannot easily be handled by classical learning algorithms. Major efforts have been undertaken to provide approaches that can either directly be used for such data or to make standard methods available for these types of data. We provide a comprehensive survey for the field of learning with nonmetric proximities. First, we introduce the formalism used in nonmetric spaces and motivate specific treatments for nonmetric proximity data. Second, we provide a systematization of the various approaches. For each category of approaches, we provide a comparative discussion of the individual algorithms and address complexity issues and generalization properties. In a summarizing section, we provide a larger experimental study for the majority of the algorithms on standard data sets. We also address the problem of large-scale proximity learning, which is often overlooked in this context and of major importance to make the method relevant in practice. The algorithms we discuss are in general applicable for proximity-based clustering, one-class classification, classification, regression, and embedding approaches. In the experimental part, we focus on classification tasks.

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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.

We discuss the use of divergences in dissimilarity based classification. Divergences can be employed whenever vectorial data consists of non-negative, potentially normalized features. This is, for instance, the case in spectral data or histograms. In particular, we introduce and study Divergence Based Learning Vector Quantization (DLVQ). We derive cost function based DLVQ schemes for the family of γ-divergences which includes the well-known Kullback-Leibler divergence and the so-called Cauchy-Schwarz divergence as special cases. The corresponding training schemes are applied to two different real world data sets. The first one, a benchmark data set (Wisconsin Breast Cancer) is available in the public domain. In the second problem, color histograms of leaf images are used to detect the presence of Cassava Mosaic Disease in cassava plants. We compare the use of standard Euclidean distances with DLVQ for different parameter settings. We show that DLVQ can yield superior classification accuracies and Receiver Operating Characteristics.

Metric learning constitutes a well-investigated field for vectorial data with successful applications, e.g. in computer vision, information retrieval, or bioinformatics. One particularly promising approach is offered by lowrank metric adaptation integrated into modern variants of learning vector quantization (LVQ). This technique is scalable with respect to both, data dimensionality and the number of data points, and it can be accompanied by strong guarantees of learning theory. Recent extensions of LVQ to general (dis-)similarity data have paved the way towards LVQ classifiers for non-vectorial, possibly discrete, structured objects such as sequences, which are addressed by classical alignment in bioinformatics applications. In this context, the choice of metric parameters plays a crucial role for the result, just as it does in the vectorial setting. In this contribution, we propose a metric learning scheme which allows for an autonomous learning of parameters (such as the underlying scoring matrix in sequence alignments) according to a given discriminative task in relational LVQ. Besides facilitating the often crucial and problematic choice of the scoring parameters in applications, this extension offers an increased interpretability of the results by pointing out structural invariances for the given task. *

Prototype based classifiers are effective algorithms in modeling classification problems and have been applied in multiple domains. While many supervised learning algorithms have been successfully extended to kernels to improve the discrimination power by means of the kernel concept, prototype based classifiers are typically still used with Euclidean distance measures. Kernelized variants of prototype based classifiers are currently too complex to be applied for larger data sets. Here we propose an extension of Kernelized Generalized Learning Vector Quantization (KGLVQ) employing a sparsity and approximation technique to reduce the learning complexity. We provide generalization error bounds and experimental results on real world data, showing that the extended approach is comparable to SVM on different public data.