  The Principal Component Analysis (PCA) is a data dimensionality reduction
technique well-suited for processing data from sensor networks. It can be
applied to tasks like compression, event detection, and event recognition. This
technique is based on a linear transform where the sensor measurements are
projected on a set of principal components. When sensor measurements are
correlated, a small set of principal components can explain most of the
measurements variability. This allows to significantly decrease the amount of
radio communication and of energy consumption. In this paper, we show that the
power iteration method can be distributed in a sensor network in order to
compute an approximation of the principal components. The proposed
implementation relies on an aggregation service, which has recently been shown
to provide a suitable framework for distributing the computation of a linear
transform within a sensor network. We also extend this previous work by
providing a detailed analysis of the computational, memory, and communication
costs involved. A compression experiment involving real data validates the
algorithm and illustrates the tradeoffs between accuracy and communication
costs.
