Abstract.Many different evaluation measures for dimensionality reduction can be summarized based on the co-ranking framework [6]. Here, we extend this framework in two ways: (i) we show that the current parameterization of the quality shows unpredictable behavior, even in simple settings, and we propose a different parameterization which yields more intuitive results; (ii) we propose how to link the quality to point-wise quality measures which can directly be integrated into the visualization.

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. *

Intelligent tutoring systems (ITSs) typically rely on a formalised model of the underlying domain knowledge in order to provide feedback to learners adaptively to their needs. This approach implies two general drawbacks: the formalisation of a domain-specific model usually requires a huge effort, and in some domains it is not possible at all. In this paper, we propose feedback provision strategies in absence of a formalised domain model, motivated by example-based learning approaches. We demonstrate the feasibility and effectiveness of these strategies in several studies with experts and students. We discuss how, in a set of solutions, appropriate examples can be automatically identified and assigned to given student solutions via machine learning techniques in conjunction with an underlying dissimilarity metric. The plausibility of such an automatic selection is evaluated in an expert survey, while possible choices for domain-agnostic dissimilarity measures are tested in the context of real solution sets of Java programs. The quantitative evidence suggests that the proposed feedback strategies and

We investigate the potential of modern nonlinear dimensionality reduction techniques for an interactive cluster detection in bioinformatics applications. We demonstrate that recent non-parametric techniques such as t-distributed stochastic neighbor embedding (t-SNE) allow a cluster identification which is superior to direct clustering of the original data or cluster detection based on classical parametric dimensionality reduction approaches. Non-parametric approaches, however, display quadratic complexity which makes them unsuitable in interactive devices. As speedup, we propose kernel-t-SNE as a fast parametric counterpart based on t-SNE.

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