Matrix factorization algorithms are frequently used in the machine
learning community to find low dimensional representations
of data. We introduce a novel generative Bayesian
probabilistic model for unsupervised matrix and tensor factorization.
The model consists of several interacting LDA
models, one for each modality. We describe an efficient collapsed
Gibbs sampler for inference. We also derive the nonparametric
form of the model where interacting LDA models
are replaced with interacting HDP models. Experiments
demonstrate that the model is useful for prediction of missing
data with two or more modalities as well as learning the latent
structure in the data.