Top-down approaches to abstract medical time series using linear segments

This work attempts to abstract medical time series using a minimum number of linear segments such that the integral square error between the abstraction and the data is a minimum. The problem is difficult since it involves a multiobjective optimization procedure, and the optimization process is affected by the presence of local minima, noise and outliers. This work proposes a greedy approach, which exploits local and global information for the optimization. Initially, the number of linear segments needed is estimated roughly by detecting the number of cycles in the data set. Then the tendency of each data point to form bends is measured locally in terms of typicality values. A global consensus in terms of clustering is used to select the breakpoints from all the data points with various typicality values. These breakpoints are utilized to partition the data set. Approximating each partition with a linear segment subsequently forms a crude abstraction. The difference between the original data set and the crude abstraction is exploited as feedback information such that the crude abstraction can be split further for refinement. The efficacy of the proposed method is demonstrated on some real life intensive care unit (ICU) data sets