Feature eXtraction from sparse time series data

We present a computational methodology for qualitative analysis of sparse and noisy time series. Information about the changes of the signal level within a time series and the number of distinguishable signal levels is extracted and condensed into a pattern string. The qualitative analysis of a time series can be done at several levels of detail to generate pattern strings that encode the sequence of changes within the signal level only, include information about the time points at which these changes took place, or include in addition information about the relative strength of the signal levels. The extraction of the qualitative features is based on standard statistical techniques. One-way analysis of variance is used to detect changes of the signal level and the number of signal levels within a time series. For this reason every pattern string is of well-defined significance. Sparse time series data cannot be used to study the kinetics of a process because they provide qualitative information only. Microarray time series are a typical example of sparse and noisy time series. A single microarray time series experiment provides simultaneous measurements of tens of thousands gene expression levels over time. The algorithms presented here give a reliable and compact description of the qualitative features of each individual time series. The feature extraction algorithms should facilitate a systematic analysis and use of microarray time series data, but they can also be used for time series analysis in general. We illustrate the potential of the methodology by applying it to two microarray time series experiments.