Two important limitations of approximate query answering in OLAP are recognized and investigated. These limitations are: (i) scalability of the techniques, i.e. their reliabiliy on highly-dimensional data cubes, and (ii) need for guarantees on the degree of approximation of the answers. In this paper, we focus on the first limitation, and propose adopting the well-known Karhunen-Loeve Transform (KLT) to obtain dimensionality reduction of data cubes, thus devising a transformation methodology that is independent by the number of dimensions of the data cubes. To tailor the KLT for the specific OLAP context, effective optimizations are also proposed, by taking into account the query-consciousness feature. Finally, some encouraging preliminary experimental results are presented.