Self-Organizing Maps
Laplacian Eigenmaps for dimensionality reduction and data representation
Neural Computation
Principal Manifolds and Nonlinear Dimensionality Reduction via Tangent Space Alignment
SIAM Journal on Scientific Computing
A Nonlinear Mapping for Data Structure Analysis
IEEE Transactions on Computers
Patch Alignment for Dimensionality Reduction
IEEE Transactions on Knowledge and Data Engineering
Curvilinear component analysis: a self-organizing neural network for nonlinear mapping of data sets
IEEE Transactions on Neural Networks
Visual analysis of a cold rolling process using a dimensionality reduction approach
Engineering Applications of Artificial Intelligence
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This paper describes a procedure based on the use of manifold learning algorithms to visualize periodic -or nearly periodic- time series produced by processes with different underlying dynamics. The proposed approach is done in two steps: a feature extraction stage, where a set of descriptors in the frequency domain is extracted, and a manifold learning stage that finds low dimensional structures in the feature space and obtains projections on a low dimensional space for visualization. This approach is applied on vibration data of an electromechanical rotating machine to visualize different vibration conditions under two kinds of asymmetries, using four state-of-the-art manifold learning algorithms for comparison purposes. In all cases, the methods yield consistent results and produce insightful visualizations, suggesting future developments and application in engineering problems.