Structural processing of waveforms as trees

Waveforms can be represented symbolically in such a manner that their underlying global structural composition is emphasized. The authors consider one such symbolic representation: a computer data structure, known as the relational tree, that describes the relative size and placement of peaks and valleys in a waveform. To analyze the relational tree, the authors examine various distance measures which serve as tree metrics. These metrics make it possible to cluster groups of trees by their proximity in tree space. In traditional cluster analysis, linear discriminants are used to reduce vector space dimensionality and to improve cluster performance. A tree transformation accomplishes this same goal operating on relational trees in a tree space. By combining these concepts, the authors have developed a waveform recognition system. This system recognizes waveforms even when they have undergone a monotonic transformation of the time axis. The system performs well with high signal-to-noise ratios, but further refinements are necessary for a working waveform interpretation system. The technique is illustrated by application to seismic and electrocardiographic data