Discriminant diffusion maps analysis: A robust manifold learner for dimensionality reduction and its applications in machine condition monitoring and fault diagnosis

Various features extracted from raw signals usually contain a large amount of redundant information which may impede the practical applications of machine condition monitoring and fault diagnosis. Hence, as a solution, dimensionality reduction is vital for machine condition monitoring. This paper presents a new technique for dimensionality reduction called the discriminant diffusion maps analysis (DDMA), which is implemented by integrating a discriminant kernel scheme into the framework of the diffusion maps. The effectiveness and robustness of DDMA are verified in three different experiments, including a pneumatic pressure regulator experiment, a rolling element bearing test, and an artificial noisy nonlinear test system, with empirical comparisons with both the linear and nonlinear methods of dimensionality reduction, such as principle components analysis (PCA), independent components analysis (ICA), linear discriminant analysis (LDA), kernel PCA, self-organizing maps (SOM), ISOMAP, diffusion maps (DM), Laplacian eigenmaps (LE), locally linear embedding (LLE) analysis, Hessian-based LLE analysis, and local tangent space alignment analysis (LTSA). Results show that DDMA is capable of effectively representing the high-dimensional data in a lower dimensional space while retaining most useful information. In addition, the low-dimensional features generated by DDMA are much better than those generated by most of other state-of-the-art techniques in different situations.

► A discriminant diffusion maps analysis (DDMA) is proposed to reduce feature dimension.
► DDMA integrates a discriminant kernel scheme into the framework of diffusion maps.
► Three different experiments have been carried out to validate DDMA.
► DDMA can effectively represent high dimensional data in a lower dimensional space.
► DDMA can outperform many other dimensionality reduction techniques.