  Non-negative Matrix Factorization (NMF) has proven to be a powerful
unsupervised learning method for uncovering hidden features in complex and
noisy data sets with applications in data mining, text recognition, dimension
reduction, face recognition, anomaly detection, blind source separation, and
many other fields. An important input for NMF is the latent dimensionality of
the data, that is, the number of hidden features, K, present in the explored
data set. Unfortunately, this quantity is rarely known a priori. We utilize a
supervised machine learning approach in combination with a recent method for
model determination, called NMFk, to determine the number of hidden features
automatically. NMFk performs a set of NMF simulations on an ensemble of
matrices, obtained by bootstrapping the initial data set, and determines which
K produces stable groups of latent features that reconstruct the initial data
set well. We then train a Multi-Layer Perceptron (MLP) classifier network to
determine the correct number of latent features utilizing the statistics and
characteristics of the NMF solutions, obtained from NMFk. In order to train the
MLP classifier, a training set of 58,660 matrices with predetermined latent
features were factorized with NMFk. The MLP classifier in conjunction with NMFk
maintains a greater than 95% success rate when applied to a held out test set.
Additionally, when applied to two well-known benchmark data sets, the swimmer
and MIT face data, NMFk/MLP correctly recovered the established number of
hidden features. Finally, we compared the accuracy of our method to the ARD,
AIC and Stability-based methods.
