This study proposes a fault detection and diagnosis method for bearing systems using ensemble empirical mode decomposition (EEMD) based feature extraction, in conjunction with particle swarm optimization (PSO), principal component analysis (PCA), and Isomap. First, a mathematical model is assumed to generate vibration signals from damaged bearing components, such as the inner-race, outer-race, ...

The fundamental problem of distance geometry consists in finding a realization of a given weighted graph in a Euclidean space of given dimension, in such a way that vertices are realized as points and edges as straight segments having the same lengths as their given weights. This problem arises in structural proteomics, wireless sensor networks, and clock synchronization protocols to name a few...

Linear methods of dimensionality reduction are useful tools for handling and interpreting high dimensional data. However, the cumulative variance explained by each of the subspaces in which the data space is decomposed may show a slow convergence that makes the selection of a proper minimum number of subspaces for successfully representing the variability of the process ambiguous. The use of no...

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Manifold learning is the process of estimating a low-dimensional structure which underlies a collection of high-dimensional data. Here we review two popular methods for nonlinear dimensionality reduction, locally linear embedding (LLE, [1]) and IsoMap [2]. We also discuss their roots in principal component analysis and multidimensional scaling, and provide a brief comparison of the underlying a...

Manifold Learning learns a low-dimensional embedding of the latent manifold. In this report, we give the definition of distance metric learning, provide the categorization of manifold learning, and describe the essential connection between manifold learning and distance metric learning, with special emphasis on nonlinear manifold learning, including ISOMAP, Laplacian Eigenamp (LE), and Locally ...

In recent years there has been a resurgence of interest in nonlinear dimension reduction methods. Among new proposals are so-called “Local Linear Embedding” (LLE) and “Isomap”. Both use local neighborhood information to construct a global lowdimensional embedding of a hypothetical manifold near which the data fall. In this paper we introduce a family of new nonlinear dimension reduction methods...