Working with short time series

Although many sections of the time-series analysis literature has worked to develop methods for quantifying complex temporal structure in long time-series recordings, many time series that are analyzed in practice are relatively short. *hctsa* has been successfully applied to time-series classification problems in the data mining literature, which includes datasets of time series as short as 60 samples (link to paper). However, time-series data are sometimes even shorter, including yearly economic data across perhaps six years, or biological data measured at say 10 points across a lifespan. Although many features in *hctsa* will not give a meaningful output when applied to a short time series, *hctsa* includes methods for filtering such features (cf.

`TS_Normalize`

), after which the remaining features can be used for analysis.The number of features with a meaningful output, from time series as short as 5 samples, up to those with as many as 500 samples, is shown below (where the maximum set of 7749 is shown as a dashed horizontal line): â€‹

In each case, over 3000 features can be computed. Note that one must be careful when representing a 5-dimensional object with thousands of features, the vast majority of which will be highly intercorrelated.

To demonstrate the feasibility of running *hctsa* analysis on datasets of short time series, we applied *hctsa* to gene expression data in the cerebellar brain region, r1A, across seven developmental time points (from the Allen Institute's Developing Mouse Brain Atlas), for a subset of 50 genes. After filtering and normalizing (

`TS_Normalize`

), then clustering (`TS_Cluster`

), we plotted the clustered time-series data matrix (`TS_PlotDataMatrix('cl')`

):Inspecting the time series plots to the left of the colored matrix, we can see that genes with similar temporal expression profiles are clustered together based on their 2829-long feature vector representations. Thus, these feature-based representations provide a meaningful representation of these short time series. Further, while these 2829-long feature vectors are shorter than those that can be computed from longer time series, they still constitute a highly comprehensive representation that can be used as the starting point to obtain interpretable understanding in addressing specific domain questions.

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