Supervised learning of short and high-dimensional temporal sequences for life science measurements

The analysis of physiological processes over time are often given by spectrometric or gene expression profiles over time with only few time points but a large number of measured variables. The analysis of such temporal sequences is challenging and only few methods have been proposed. The information can be encoded time independent, by means of classical expression differences for a single time point or in expression profiles over time. Available methods are limited to unsupervised and semi-supervised settings. The predictive variables can be identified only by means of wrapper or post-processing techniques. This is complicated due to the small number of samples for such studies. Here, we present a supervised learning approach, termed Supervised Topographic Mapping Through Time (SGTM-TT). It learns a supervised mapping of the temporal sequences onto a low dimensional grid. We utilize a hidden markov model (HMM) to account for the time domain and relevance learning to identify the relevant feature dimensions most predictive over time. The learned mapping can be used to visualize the temporal sequences and to predict the class of a new sequence. The relevance learning permits the identification of discriminating masses or gen expressions and prunes dimensions which are unnecessary for the classification task or encode mainly noise. In this way we obtain a very efficient learning system for temporal sequences. The results indicate that using simultaneous supervised learning and metric adaptation significantly improves the prediction accuracy for synthetically and real life data in comparison to the standard techniques. The discriminating features, identified by relevance learning, compare favorably with the results of alternative methods. Our method permits the visualization of the data on a low dimensional grid, highlighting the observed temporal structure

Mathematical Foundations of the Self Organized Neighbor Embedding ({SONE}) for Dimension Reduction and Visualization

Abstract. In this paper we propose the generalization of the recently introduced Neighbor Embedding Exploratory Observation Machine (NE-XOM) for dimension reduction and visualization. We provide a general mathematical framework called Self Organized Neighbor Embedding (SONE).Ittreatsthecomponents, likedatasimilarity measures andneighborhood functions, independently and easily changeable. And it enables the utilization of different divergences, based on the theory of Fréchet derivatives. In this way we propose a new dimension reduction and visualization algorithm, which can be easily adapted to the user specific request and the actual problem.

Low-Rank Subspace Override for Unsupervised Domain Adaptation

Current supervised learning models cannot generalize well across domain boundaries, which is a known problem in many applications, such as robotics or visual classification. Domain adaptation methods are used to improve these generalization properties. However, these techniques suffer either from being restricted to a particular task, such as visual adaptation, require a lot of computational time and data, which is not always guaranteed, have complex parameterization, or expensive optimization procedures. In this work, we present an approach that requires only a well-chosen snapshot of data to find a single domain invariant subspace. The subspace is calculated in closed form and overrides domain structures, which makes it fast and stable in parameterization. By employing low-rank techniques, we emphasize on descriptive characteristics of data. The presented idea is evaluated on various domain adaptation tasks such as text and image classification against state of the art domain adaptation approaches and achieves remarkable performance across all tasks

Anisotropy and chemical composition of ultra-high energy cosmic rays using arrival directions measured by the Pierre Auger Observatory

The Pierre Auger Collaboration has reported evidence for anisotropy in the distribution of arrival directions of the cosmic rays with energies $E>E_{th}=5.5\times 10^{19}$ eV. These show a correlation with the distribution of nearby extragalactic objects, including an apparent excess around the direction of Centaurus A. If the particles responsible for these excesses at $E>E_{th}$ are heavy nuclei with charge $Z$, the proton component of the sources should lead to excesses in the same regions at energies $E/Z$. We here report the lack of anisotropies in these directions at energies above $E_{th}/Z$ (for illustrative values of $Z=6,\ 13,\ 26$). If the anisotropies above $E_{th}$ are due to nuclei with charge $Z$, and under reasonable assumptions about the acceleration process, these observations imply stringent constraints on the allowed proton fraction at the lower energies