  Dimensionality reduction is considered as an important step for ensuring
competitive performance in unsupervised learning such as anomaly detection.
Non-negative matrix factorization (NMF) is a popular and widely used method to
accomplish this goal. But NMF do not have the provision to include the
neighborhood structure information and, as a result, may fail to provide
satisfactory performance in presence of nonlinear manifold structure. To
address that shortcoming, we propose to consider and incorporate the
neighborhood structural similarity information within the NMF framework by
modeling the data through a minimum spanning tree. We label the resulting
method as the neighborhood structure assisted NMF. We further devise both
offline and online algorithmic versions of the proposed method. Empirical
comparisons using twenty benchmark datasets as well as an industrial dataset
extracted from a hydropower plant demonstrate the superiority of the
neighborhood structure assisted NMF and support our claim of merit. Looking
closer into the formulation and properties of the neighborhood structure
assisted NMF with other recent, enhanced versions of NMF reveals that inclusion
of the neighborhood structure information using MST plays a key role in
attaining the enhanced performance in anomaly detection.
