Structural processing of waveforms as trees

Abstract

Waveforms may be represented symbolically such that their underlying, global structural composition is emphasized. One such symbolic representation is the relational tree. The relational tree is a computer data structure that describes the relative size and placement of peaks and valleys in a waveform. Researchers have developed various distance measures which serve as tree metrics. A tree metric defines a tree space. We are able to cluster groups of trees by their proximity in a tree space. Linear discriminants are used to reduce vector space dimensionality and to improve cluster performance. A tree transformation operating on a regular tree language accomplishes this same goal in a tree space. Under certain restrictions, relational trees form a regular tree language. Combining these concepts yields 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.