Similarity search using multi-space KL

The Karhunen-Loeve transform is probably the most widely used statistical framework for dimensionality reduction in a broad range of scientific fields. Given a set of points in an n-dimensional space (the points can be derived from images, sounds, or other multimedia objects), KL provides a mapping which reduces the dimensionality of the input patterns to k (kε3qn), without altering their structure too much. Unfortunately, KL suffers from some scalability problems: in fact, as the size of the database increases, the efficacy and efficiency of the transform progressively vanish. In this work we introduce the basics of a new generalization of KL (named MultiSpace KL or MKL) which allows the scalability problems to be solved and we show how MKL can be used for similarity searches in multimedia databases. The paper reports some preliminary experiments where MKL outperforms KL as the size of the database increases