Randomized nonlinear component analysis

Copyright © (2014) by the International Machine Learning Society (IMLS) All rights reserved. Classical methods such as Principal Component Analysis (PCA) and Canonical Correlation Analysis (CCA) are ubiquitous in statistics. However, these techniques are only able to reveal linear re-lationships in data. Although nonlinear variants of PCA and CCA have been proposed, these are computationally prohibitive in the large scale. In a separate strand of recent research, randomized methods have been proposed to construct features that help reveal nonlinear patterns in data. For basic tasks such as regression or classification, random features exhibit little or no loss in performance, while achieving drastic savings in computational requirements. In this paper we leverage randomness to design scalable new variants of nonlinear PCA and CCA; our ideas extend to key multivariate analysis tools such as spectral clustering or LDA. We demonstrate our algorithms through experiments on real- world data, on which we compare against the state-of-the-art. A simple R implementation of the presented algorithms is provided.

Correlation of transport and magnetic critical currents in melt-processed YBa2Cu3O7-δ thick films

Transport critical current measurements have been carried out on melt-processed thick films of YBa2Cu3O7-δ on yttria-stabilized zirconia in fields of up to 8 T both within grains and across grain boundaries. These measurements yield Jc values of ∼3000 A cm-2 at 4.2 K and zero magnetic field and 400 A cm -2 at 77 K and zero magnetic field, taking the entire sample width as the definitive dimension. Optical and scanning electron microscopy reveals that the thick-film grains consist typically of a central "hub" region ∼50 μm in diameter, which is well connected to radial subgrains or "spokes" which extend ∼1 mm to define the complete grain structure. Attempts have been made to correlate the transport measurements of inter- and intra-hub-and-spoke (H-S) critical current with values of this parameter derived previously from magnetization measurements. Analysis of the transport measurements indicates that current flow through H-S grains is constrained to paths along the spokes via the grain hub. Taking the size of the hub as the definitive dimension yields an intra-H-S grain Jc of ∼60 000 A cm-2 at 4.2 K and 0 T, which is in reasonable agreement with the magnetization data. Experiments in which the hub is removed from individual grains confirm that this feature determines critically the J c of the film.