Mining SOM expression portraits: Feature selection and integrating concepts of molecular function

Background: 
Self organizing maps (SOM) enable the straightforward portraying of high-dimensional data of large sample collections in terms of sample-specific images. The analysis of their texture provides so-called spot-clusters of co-expressed genes which require subsequent significance filtering and functional interpretation. We address feature selection in terms of the gene ranking problem and the interpretation of the obtained spot-related lists using concepts of molecular function.

Results: 
Different expression scores based either on simple fold change-measures or on regularized Students t-statistics are applied to spot-related gene lists and compared with special emphasis on the error characteristics of microarray expression data. The spot-clusters are analyzed using different methods of gene set enrichment analysis with the focus on overexpression and/or overrepresentation of predefined sets of genes. Metagene-related overrepresentation of selected gene sets was mapped into the SOM images to assign gene function to different regions. Alternatively we estimated set-related overexpression profiles over all samples studied using a gene set enrichment score. It was also applied to the spot-clusters to generate lists of enriched gene sets. We used the tissue body index data set, a collection of expression data of human tissues, as an illustrative example. We found that tissue related spots typically contain enriched populations of gene sets well corresponding to molecular processes in the respective tissues. In addition, we display special sets of housekeeping and of consistently weak and highly expressed genes using SOM data filtering. 

Conclusions:
The presented methods allow the comprehensive downstream analysis of SOM-transformed expression data in terms of cluster-related gene lists and enriched gene sets for functional interpretation. SOM clustering implies the ability to define either new gene sets using selected SOM spots or to verify and/or to amend existing ones

Latent Heat Fluxes over Complex Terrain from Airborne Water Vapour and Wind Lidars

Tropospheric profiles of water vapour and wind were measured with a differential absorption lidar (DIAL) and a heterodyne detection Doppler wind lidar collo-cated onboard the DLR Falcon research aircraft in the past two years. The DIAL is a newly developed four-wavelength system operating on three water vapour absorption lines of different strengths, one offline wavelength at 935 nm (each 50 Hz, 40 mJ), and 532 and 1064 nm for aerosol profiling. It is designed as an airborne demonstrator for a possible future space-borne water vapour lidar mission. It operated success-fully during the Convective and Orographically-induced Precipitation Study (COPS) in July 2007 over the Black Forest Mountains in southern Germany, and during the Norwegian THORPEX-IPY field experiment in March 2008 over the European North Sea. For the study of summertime convection initiation over complex terrain and the development of Polar Lows in the North Sea both campaigns included latent heat flux missions where both airborne lidars were pointed nadir-viewing. Using eddy-correlation of the remotely-sensed wind and water vapour fluctuations, a repre-sentative flux profile can be obtained from a single over-flight of the area under investigation. The lidars’ spatial resolution is ~200 m which resolves the domi-nant circulation and flux patterns in a convective boundary layer. This novel instrumentation allows ob-taining profiles of the latent heat flux beneath the air-craft from one single over-flight of any area of interest

Pedestrian Prediction by Planning using Deep Neural Networks

Accurate traffic participant prediction is the prerequisite for collision avoidance of autonomous vehicles. In this work, we predict pedestrians by emulating their own motion planning. From online observations, we infer a mixture density function for possible destinations. We use this result as the goal states of a planning stage that performs motion prediction based on common behavior patterns. The entire system is modeled as one monolithic neural network and trained via inverse reinforcement learning. Experimental validation on real world data shows the system's ability to predict both, destinations and trajectories accurately

Expression cartography of human tissues using self organizing maps

Background: The availability of parallel, high-throughput microarray and sequencing experiments poses a challenge how to best arrange and to analyze the obtained heap of multidimensional data in a concerted way. Self organizing maps (SOM), a machine learning method, enables the parallel sample- and gene-centered view on the data combined with strong visualization and second-level analysis capabilities. The paper addresses aspects of the method with practical impact in the context of expression analysis of complex data sets.
Results: The method was applied to generate a SOM characterizing the whole genome expression profiles of 67 healthy human tissues selected from ten tissue categories (adipose, endocrine, homeostasis, digestion, exocrine, epithelium, sexual reproduction, muscle, immune system and nervous tissues). SOM mapping reduces the dimension of expression data from ten thousands of genes to a few thousands of metagenes where each metagene acts as representative of a minicluster of co-regulated single genes. Tissue-specific and common properties shared between groups of tissues emerge as a handful of localized spots in the tissue maps collecting groups of co-regulated and co-expressed metagenes. The functional context of the spots was discovered using overrepresentation analysis with respect to pre-defined gene sets of known functional impact. We found that tissue related spots typically contain enriched populations of gene sets well corresponding to molecular processes in the respective tissues. Analysis techniques normally used at the gene-level such as two-way hierarchical clustering provide a better signal-to-noise ratio and a better representativeness of the method if applied to the metagenes. Metagene-based clustering analyses aggregate the tissues into essentially three clusters containing nervous, immune system and the remaining tissues. 
Conclusions: The global view on the behavior of a few well-defined modules of correlated and differentially expressed genes is more intuitive and more informative than the separate discovery of the expression levels of hundreds or thousands of individual genes. The metagene approach is less sensitive to a priori selection of genes. It can detect a coordinated expression pattern whose components would not pass single-gene significance thresholds and it is able to extract context-dependent patterns of gene expression in complex data sets.
&#xa

Exact reconstruction and reconstruction from noisy data with anisotropic total variation

It is well-known that point sources with sufficient mutual distance can be reconstructed exactly from finitely many Fourier measurements by solving a convex optimization problem with Tikhonov-regularization (this property is sometimes termed superresolution). In case of noisy measurements one can bound the reconstruction error in unbalanced Wasserstein distances or weak Sobolev-type norms. A natural question is to what other settings the phenomenon of superresolution extends. We here keep the same measurement operator, but replace the regularizer to anisotropic total variation, which is particularly suitable for regularizing piecewise constant images with horizontal and vertical edges. Under sufficient mutual distance between the horizontal and vertical edges we prove exact reconstruction results and $L^1$ error bounds in terms of the measurement noise