The Karhunen-Loeve transform is a key element of many signal processing tasks, including classification and compression. In this paper, we consider distributed signal processing scenarios with limited communication between correlated sources, and we investigate a distributed Karhunen-Loeve transform (KLT). In particular, a partial (where only a subset of sources are observed) and a conditional KLT (where some sources act as side information) are posed and solved in a rate-distortion sense. The partial KLT leads to an original bit allocation problem, while the conditional KLT leads to a Wyner-Ziv solution which is separable at the sources. These two cases can be seen as extreme cases of a distributed KLT.