  Factorial k-means (FKM) clustering is a method for clustering objects in a
low-dimensional subspace. The advantage of this method is that the partition of
objects and the low-dimensional subspace reflecting the cluster structure are
obtained, simultaneously. Conditions that ensure the almost sure convergence of
the estimator of FKM clustering as the sample size increases unboundedly are
derived. The result is proved for a more general model including FKM
clustering.
