The supervised sleep staging methods are challenged by their strict requirements of a labelled and large dataset. This study considers an unsupervised dimensionality reduction method, the Deep Boltzmann Machine (DBM), trained to a transient state for binary classification of sleep stages. First, the joint time-frequency domain features from the polysomnographic recordings are extracted. Second, the extracted features are smoothed using 2 min rolling window to include contextual temporal information, and finally, they serve as an input for unsupervised training of DBM_transient. The results show that our method effectively separates the sleep stages in two-dimensional feature space with a large Fisher’s discriminant value. The classification performance by the DBM_transient achieves a 96.1% F1 score, which is higher than DBM converged to an equilibrium state (95.2%), Principal Component Analysis (92.5%), Isometric Feature Mapping (95.9%), t-distributed Stochastic Neighbor Embedding (94.9%), and Uniform Manifold Approximation (95.0%) on the widely used sleep-EDF database. Additionally, Fisher’s discriminant function demonstrates the superiority of the DBM_transient. The significance of the DBM transient lies in its ease of interpretability in two-dimensional space, and future multi-class implementation of the method may facilitate its usage in clinical applications.

Principal component analysis (PCA) is widely adopted in local tangent space alignment (LTSA) to estimate local tangent spaces. These estimates are only accurate when uniformly distributed data lies in or close to linear subspaces. In practice, such conditions are rarely satisfied. Therefore, this approach fails to reveal manifold intrinsic features, resulting in degraded fault detection accuracy. Considering the drawbacks, weighted linear local tangent space alignment (WLLTSA), a manifold learning method is put forward. First, weighted PCA is adopted to provide local tangent space estimates. The parameter selection criterion for the weight matrix is established by taking the context of geometric preservation into account. Second, global low dimensional coordinates are formed by aligning local coordinates with global feature space. Finally, the fault detection model is developed, and KDE is utilized to approximate confidence bounds for T^2 and SPE statistics. WLLTSA is applied to fault detection and feature extraction.

Dimensionality reduction methods based on manifold learning are widely adopted for industrial process monitoring. However, in many situations, these methods fail to preserve manifold intrinsic features in low-dimensional space, resulting in reduced process monitoring efficacy. To overcome this problem, a modified locality preserving projection (MLPP) based on the Riemannian metric is put forward. First, the Riemannian metric, which embodies a manifold’s geometric information, is estimated from process data. Then, the low dimensional embedding coordinates obtained from LPP are supplemented with an estimate of the Riemannian metric. Finally, a process monitoring model is developed, and kernel density estimation is utilized to approximate confidence bounds for T^2 and SPE statistics. The proposed MLPP method is applied to the feature extraction of the Twin-Peaks dataset, fault detection of hot strip mill, steam turbine system and Tennessee Eastman processes. The effectiveness of the MLPP method is compared with both the manifold learning and deep learning approaches. In addition, the proposed method is evaluated under various noisy conditions. The average fault detection rate of 98.9%, 99.6% and 84.4% in hot strip mill, steam turbine system and Tennessee Eastman processes, respectively, are higher than the existing methods. Quantitative results indicate the superiority of the proposed MLPP method.