NMF and PCA as Applied to Gearbox Fault Data

Both Non-negative matrix factorization (NMF) and Principal component analysis (PCA) are data reduction methods. Both of them act as approximation methods permitting to represent data by lower rank matrices. The two methods differ by their criteria how to obtain the approximation. We show that the main assumption of PCA demanding orthogonal principal components leads to a higher rank approximation as that established by NMF working without that assumption. This can be seen when analyzing a data matrix obtained from vibration signals emitted by a healthy and a faulty gearbox. To our knowledge this fact has not been clearly stated so far and no real example supporting our observation has been shown explicitly.