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.

Rheumatoid arthritis (RA) affects millions world-wide. While anti-TNF treatment is widely used to reduce disease progression, treatment fails in ∼one-third of patients. No biomarker currently exists that identifies non-responders before treatment. A rigorous community-based assessment of the utility of SNP data for predicting anti-TNF treatment efficacy in RA patients was performed in the context of a DREAM Challenge (http://www.synapse.org/RA_Challenge). An open challenge framework enabled the comparative evaluation of predictions developed by 73 research groups using the most comprehensive available data and covering a wide range of state-of-the-art modelling methodologies. Despite a significant genetic heritability estimate of treatment non-response trait (h2=0.18, P value=0.02), no significant genetic contribution to prediction accuracy is observed. Results formally confirm the expectations of the rheumatology community that SNP information does not significantly improve predictive performance relative to standard clinical traits, thereby justifying a refocusing of future efforts on collection of other data.

In recent years, a wealth of dimension-reduction techniques for data visualization and preprocessing has been established. Nonparametric methods require additional effort for out-of-sample extensions, because they provide only a mapping of a given finite set of points. In this letter, we propose a general view on nonparametric dimension reduction based on the concept of cost functions and properties of the data. Based on this general principle, we transfer nonparametric dimension reduction to explicit mappings of the data manifold such that direct out-of-sample extensions become possible. Furthermore, this concept offers the possibility of investigating the generalization ability of data visualization to new data points. We demonstrate the approach based on a simple global linear mapping, as well as prototype-based local linear mappings. In addition, we can bias the functional form according to given auxiliary information. This leads to explicit supervised visualization mappings with discriminative properties comparable to state-of-the-art approaches.

Abstract-We present a regularization technique to extend recently proposed matrix learning schemes in learning vector quantization (LVQ). These learning algorithms extend the concept of adaptive distance measures in LVQ to the use of relevance matrices. In general, metric learning can display a tendency towards over-simplification in the course of training. An overly pronounced elimination of dimensions in feature space can have negative effects on the performance and may lead to instabilities in the training. We focus on matrix learning in Generalized LVQ. Extending the cost function by an appropriate regularization term prevents the unfavorable behavior and can help to improve the generalization ability. The approach is first tested and illustrated in terms of artificial model data. Furthermore, we apply the scheme to benchmark classification data sets from the UCI Repository of machine learning. We demonstrate the usefulness of regularization also in the case of rank limited relevance matrices, i.e. matrix learning with an implicit, low dimensional representation of the data.

Flow cytometry is a widely used technique for the analysis of cell populations in the study and diagnosis of human diseases. It yields large amounts of high-dimensional data, the analysis of which would clearly benefit from efficient computational approaches aiming at automated diagnosis and decision support. This article presents our analysis of flow cytometry data in the framework of the DREAM6/FlowCAP2 Molecular Classification of Acute Myeloid Leukemia (AML) Challenge, 2011. In the challenge, example data was provided for a set of 179 subjects, comprising healthy donors and 23 cases of AML. The participants were asked to provide predictions with respect to the condition of 180 patients in a test set. We extracted feature vectors from the data in terms of single marker statistics, including characteristic moments, median and interquartile range of the observed values. Subsequently, we applied Generalized Matrix Relevance Learning Vector Quantization (GMLVQ), a machine learning technique which extends standard LVQ by an adaptive distance measure. Our method achieved the best possible performance with respect to the diagnoses of test set patients. The extraction of features from the flow cytometry data is outlined in detail, the machine learning approach is discussed and classification results are presented. In addition, we illustrate how GMLVQ can provide deeper insight into the problem by allowing to infer the relevance of specific markers and features for the diagnosis.