Merging and Splitting Eigenspace Models

We present new deterministic methods that given two eigenspace models, each representing a set of n-dimensional observations will: (1) merge the models to yield a representation of the union of the sets; (2) split one model from another to represent the difference between the sets; as this is done, we accurately keep track of the mean. These methods are more efficient than computing new eigenspace models directly from the observations when the eigenmodels are dimensionally small compared to the total number of observations. Such methods are important because they provide a basis for novel techniques in machine learning, using a dynamic split-andmerge paradigm to optimally cluster observations. Here we present a theoretical derivation of the methods, empirical results relating to the efficiency and accuracy of the techniques, and three general applications, including the on-line construction of Gaussian mixture models.