  Cluster analysis faces two problems in high dimensions: first, the `curse of
dimensionality' that can lead to overfitting and poor generalization
performance; and second, the sheer time taken for conventional algorithms to
process large amounts of high-dimensional data. In many applications, only a
small subset of features provide information about the cluster membership of
any one data point, however this informative feature subset may not be the same
for all data points. Here we introduce a `Masked EM' algorithm for fitting
mixture of Gaussians models in such cases. We show that the algorithm performs
close to optimally on simulated Gaussian data, and in an application of `spike
sorting' of high channel-count neuronal recordings.
