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.

Eigenspace models are a convenient way to represent sets of observations with widespread applications, including classification. In this paper we describe a new constructive method for incrementally adding observations to an eigenspace model. Our contribution is to explicitly account for a change in origin as well as a change in the number of eigenvectors needed in the basis set. No other method we have seen considers change of origin, yet both are needed if an eigenspace model is to be used for classification purposes. We empirically compare our incremental method with two alternatives from the literature and show our method is the more useful for classification because it computes the smaller eigenspace model representing the observations. 1 Introduction The contribution of this paper is a method for incrementally computing eigenspace models in the context of using them for classification. Eigenspace models are widely used in computer vision. Applications include: face recognition [...

This paper provides two algorithms; one for adding eigenspaces, another for subtracting them, thus allowing for incremental updating and downdating of data models. Importantly, and unlike previous work, we keep an accurate track of the mean of the data, which allows our methods to be used in classification applications. The result of adding eigenspaces, each made from a set of data, is an approximation to that which would obtain were the sets of data taken together. Subtracting eigenspaces yields a result approximating that which would obtain were a subset of data used. Using our algorithms it is possible to perform "arithmetic" on eigenspaces without reference to the original data. We illustrate the use of our algorithms in three generic applications, including the dynamic construction of Gaussian mixture models.

This paper provides two algorithms: one for adding eigenspaces, another for subtracting them, thus allowing for incremental updating and downdating of data models. Importantly, and unlike previous work, we keep an accurate track of the mean of the data, which allows our methods to be used in classification applications. The result of adding eigenspaces, each made from a set of data, is an approximation to that which would obtain were the sets of data taken together. Subtracting eigenspaces yields a result approximating that which would obtain were a subset of data used. Using our algorithms it is possible to perform "arithmetic" on eigenspaces without reference to the original data. We illustrate the use of our algorithms in three generic applications, including the dynamic construction of Gaussian mixture models. In addition, we mention singular value decomposition as an alternative to eigenvalue decomposition. We show that updating SVD models comes at the cost of space resources, and argue that downdating SVD models is not possible in closedform. Key words: Eigenvalue decomposition, dynamic updating and downdating, Gaussian mixture models, singular value decomposition.