14,801 research outputs found
Optimisation of on-line principal component analysis
Different techniques, used to optimise on-line principal component analysis,
are investigated by methods of statistical mechanics. These include local and
global optimisation of node-dependent learning-rates which are shown to be very
efficient in speeding up the learning process. They are investigated further
for gaining insight into the learning rates' time-dependence, which is then
employed for devising simple practical methods to improve training performance.
Simulations demonstrate the benefit gained from using the new methods.Comment: 10 pages, 5 figure
Similarity-Aware Spectral Sparsification by Edge Filtering
In recent years, spectral graph sparsification techniques that can compute
ultra-sparse graph proxies have been extensively studied for accelerating
various numerical and graph-related applications. Prior nearly-linear-time
spectral sparsification methods first extract low-stretch spanning tree from
the original graph to form the backbone of the sparsifier, and then recover
small portions of spectrally-critical off-tree edges to the spanning tree to
significantly improve the approximation quality. However, it is not clear how
many off-tree edges should be recovered for achieving a desired spectral
similarity level within the sparsifier. Motivated by recent graph signal
processing techniques, this paper proposes a similarity-aware spectral graph
sparsification framework that leverages efficient spectral off-tree edge
embedding and filtering schemes to construct spectral sparsifiers with
guaranteed spectral similarity (relative condition number) level. An iterative
graph densification scheme is introduced to facilitate efficient and effective
filtering of off-tree edges for highly ill-conditioned problems. The proposed
method has been validated using various kinds of graphs obtained from public
domain sparse matrix collections relevant to VLSI CAD, finite element analysis,
as well as social and data networks frequently studied in many machine learning
and data mining applications
The great turn-of-the-century housing boom
This article explains the recent high levels of residential investment and rates of homeownership.Home ownership ; Housing - Finance ; Housing - Prices
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