Incremental Linear Discriminant Analysis Using Sufficient Spanning Set Approximations

Abstract

This paper presents a new incremental learning solution for linear discriminant analysis (LDA). We apply the concept of the sufficient spanning set approximation in each update step, i.e. for the between-class scatter matrix, the projected data matrix as well as the total scatter matrix. The algorithm yields a more general and efficient solution to incremental LDA than previous methods. It also significantly reduces the computational complexity while providing a solution which closely agrees with the batch LDA result. The proposed algorithm has a time complexity of O(Nd <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> ) and requires O(Nd) space, where d is the reduced subspace dimension and N the data dimension. We show two applications of incremental LDA: First, the method is applied to semi-supervised learning by integrating it into an EM framework. Secondly, we apply it to the task of merging large databases which were collected during MPEG standardization for face image retrieval.