Neighborhood Structure Assisted Non-negative Matrix Factorization and its Application in Unsupervised Point-wise Anomaly Detection

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 algorithm