Extracting Self-affine (Fractal) Features from Physiologic Signals

It has been recognized that many biological systems exhibit complex behavior that is governed by fractal dynamical process. For revealing such dynamics we propose a method based on principal component analysis (PCA) of system´s time series or some other measured and ordered data sequence, embedded in high-dimensional pseudo phase space. It is demonstrated that such mapping, together with projection of data vectors on the successive subspaces, reveals scale invariant statistics in the simple and clear fashion. To illustrate the method and to compare the results with others, such as detrended fluctuation analysis (DFA), we applied it on human heartbeat data series of different lengths and from various groups such as healthy young subjects and subjects with congestive heart failure (PhysioBank data library). Results show that the proposed method is appropriate for detection of fractal dynamics when analyzing limited scale intervals (dimensions) from smaller data sets.