  Wireless sensor networks are composed of distributed sensors that can be used
for signal detection or classification. The likelihood functions of the
hypotheses are often not known in advance, and decision rules have to be
learned via supervised learning. A specific such algorithm is Fisher
discriminant analysis (FDA), the classification accuracy of which has been
previously studied in the context of wireless sensor networks. Previous work,
however, does not take into account the communication protocol or battery
lifetime of the sensor networks; in this paper we extend the existing studies
by proposing a model that captures the relationship between battery lifetime
and classification accuracy. In order to do so we combine the FDA with a model
that captures the dynamics of the Carrier-Sense Multiple-Access (CSMA)
algorithm, the random-access algorithm used to regulate communications in
sensor networks. This allows us to study the interaction between the
classification accuracy, battery lifetime and effort put towards learning, as
well as the impact of the back-off rates of CSMA on the accuracy. We
characterize the tradeoff between the length of the training stage and
accuracy, and show that accuracy is non-monotone in the back-off rate due to
changes in the training sample size and overfitting.
