  Clustering methods with dimension reduction have been receiving considerable
wide interest in statistics lately and a lot of methods to simultaneously
perform clustering and dimension reduction have been proposed. This work
presents a novel procedure for simultaneously determining the optimal cluster
structure for multivariate binary data and the subspace to represent that
cluster structure. The method is based on a finite mixture model of
multivariate Bernoulli distributions, and each component is assumed to have a
low-dimensional representation of the cluster structure. This method can be
considered an extension of the traditional latent class analysis model.
Sparsity is introduced to the loading values, which produces the
low-dimensional subspace, for enhanced interpretability and more stable
extraction of the subspace. An EM-based algorithm is developed to efficiently
solve the proposed optimization problem. We demonstrate the effectiveness of
the proposed method by applying it to a simulation study and real datasets.
