Positive linear decomposition for classifying patterns in dynamic measurements: a case study

The purpose of this article is to show the effectiveness of a positive linear decomposition in the derivation of robust features of high-dimensional dynamic measurements, in order to achieve effective pattern recognition and classification, The method begins with the singular value decomposition, projecting a matrix of dynamic process measurements (taken at uniform intervals over some time-window) onto a low-dimensional subspace. A convex cone, defined by the non-negativity of measurements, is then created. For normalization purposes a polygon, whose corners specify the feature vectors of the data, is formed by intersecting the cone with a plane. This polygon is reduced to a triangle with only the three most representative corners. The net effect of these steps is that the original orthogonal basis of the subspace (consisting of the first three principal components) is replaced by a new, non-orthogonal basis, which offers the advantage of containing only positive measurements and requiring only positive superposition of basis vectors to span the physically meaningful portion of the subspace. One of the vectors in this basis is selected as the feature vector for pattern recognition; a spanning tree created from the feature vectors classifies the patterns. The feature vectors from the new basis are much more robust with respect to changes in the width of the time window, and classification was possible even with feature vectors of differing time windows.