We explore the effect of dimensionality on the nearest neighbor problem. We show that under a broad set of conditions (much broader than independent and identically distributed dimensions), as dimensionality increases, the distance to the nearest data point approaches the distance to the farthest data point. To provide a practical perspective, we present empirical results on both real and synthetic data sets that demonstrate that this effect can occur for as few as 10-15 dimensions. These results should not be interpreted to mean that high-dimensional indexing is never meaningful; we illustrate this point by identifying some high-dimensional workloads for which this effect does not occur. However, our results do emphasize that the methodology used almost universally in the database literature to evaluate high-dimensional indexing techniques is flawed, and should be modified. In particular, most such techniques proposed in the literature are not evaluated versus simple linear scan, and are evaluated over workloads for which nearest neighbor is not meaningful. Often, even the reported experiments, when analyzed carefully, show that linear scan would outperform the techniques being proposed on the workloads studied in high (10-15) dimensionality!.

When is nearest neighbor meaningful

Bearing fault diagnosis method based on adaptive maximum cyclostationarity blind deconvolution

Blind filters based on envelope spectrum sparsity indicators for bearing and gear vibration-based condition monitoring

A review on the application of blind deconvolution in machinery fault diagnosis

Blind deconvolution based on cyclostationarity maximization and its application to fault identification

Motion analysis of a linear vibratory feeder: Dynamic modeling and experimental verification

A vibration-based method for contact pattern assessment in straight bevel gears

The gear fault diagnosis on multistage gearboxes by vibration analysis is a challenging task due to the complexity of the vibration signal. The localization of the gear fault occurring in a wheel located in the intermediate shaft can be particularly complex due to the superposition of the vibration signature of the synchronous wheels. Indeed, the gear fault detection is commonly restricted to the identification of the stage containing the faulty gear rather than the faulty gear itself. In this context, the paper advances a methodology which combines the Empirical Mode Decomposition and the Time Synchronous Average in order to separate the vibration signals of the synchronous gears mounted on the same shaft. The physical meaningful modes are selected by means of a criterion based on Pearson’s coefficients and the fault detection is performed by dedicated condition indicators. The proposed method is validated taking into account simulated vibrations signals and real ones.

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Marco Buzzoni

Papers

Blind deconvolution based on cyclostationarity maximization and its application to fault identification

Motion analysis of a linear vibratory feeder: Dynamic modeling and experimental verification

A vibration-based method for contact pattern assessment in straight bevel gears

Diagnosis of Localized Faults in Multistage Gearboxes: A Vibrational Approach by Means of Automatic EMD-Based Algorithm

A CWT-based methodology for piston slap experimental characterization