Time series averaging in dynamic time warping (DTW) spaces has been successfully applied to improve pattern recognition systems. This article proposes and analyzes subgradient methods for the problem of finding a sample mean in DTW spaces. The class of subgradient methods generalizes existing sample mean algorithms such as DTW Barycenter Averaging (DBA). We show that DBA is a majorize-minimize algorithm that converges to necessary conditions of optimality after finitely many iterations. Empirical results show that for increasing sample sizes the proposed stochastic subgradient (SSG) algorithm is more stable and finds better solutions in shorter time than the DBA algorithm on average. Therefore, SSG is useful in online settings and for non-small sample sizes. The theoretical and empirical results open new paths for devising sample mean algorithms: nonsmooth optimization methods and modified variants of pairwise averaging methods.

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The chromosome aberration test is frequently used for the assessment of the potential of chemicals and drugs to elicit genetic damage in mammalian cells in vitro. Due to the limitations of experimental genotoxicity testing in early drug discovery phases, a model to predict the chromosome aberration test yielding high accuracy and providing guidance for structure optimization is urgently needed. In this paper, we describe a machine learning approach for predicting the outcome of this assay based on the structure of the investigated compound. The novelty of the proposed method consists in combining a maximum common subgraph kernel for measuring the similarity of two chemical graphs with the potential support vector machine for classification. In contrast to standard support vector machine classifiers, the proposed approach does not provide a black box model but rather allows to visualize structural elements with high positive or negative contribution to the class decision. In order to compare the performance of different methods for predicting the outcome of the chromosome aberration test, we compiled a large data set exhibiting high quality, reliability, and consistency from public sources and configured a fixed cross-validation protocol, which we make publicly available. In a comparison to standard methods currently used in pharmaceutical industry as well as to other graph kernel approaches, the proposed method achieved significantly better performance.