MKL-Tree: A Hierarchical Data Structure for Indexing Multidimensional Data

Abstract

Recently, multidimensional point indexing has generated a great deal of interest in applications where objects are usually represented through feature vectors belonging to high-dimensional spaces and are searched by similarity according to a given example. Unfortunately, although traditional data structures and access methods work well for low-dimensional spaces, they perform poorly as dimensionality increases. The application of a dimensionality reduction approach, such as the Karhunen-Loève transform, is often not very effective to deal with the indexing problem, since the substantial loss of information does not allow patterns to be sufficiently discriminated in the reduced space. In this work we present a novel hierarchical data structure based on the Multispace KL transform, a generalization of the KL transform, specifically designed to cope with locally correlated data. In the MKL-tree, dimensionality reduction is performed at each node, allowing more selective features to be extracted and thus increasing the discriminant power of the index. In this work the mathematical foundations and the algorithms on which the MKL-tree is based are presented and preliminary experimental results are reported.