  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.
