146,306 research outputs found
Genus Topology of the Cosmic Microwave Background from the WMAP 3-Year Data
We have independently measured the genus topology of the temperature
fluctuations in the cosmic microwave background seen in the Wilkinson Microwave
Anisotropy Probe (WMAP) 3-year data. A genus analysis of the WMAP data
indicates consistency with Gaussian random-phase initial conditions, as
predicted by standard inflation. We set 95% confidence limits on
non-linearities of -101 < f_{nl} < 107. We also find that the observed low l (l
<= 8) modes show a slight anti-correlation with the Galactic foreground, but
not exceeding 95% confidence, and that the topology defined by these modes is
consistent with that of a Gaussian random-phase distribution (within 95%
confidence).Comment: MNRAS LaTeX style (mn2e.cls), EPS and JPEG figure
Compact Random Feature Maps
Kernel approximation using randomized feature maps has recently gained a lot
of interest. In this work, we identify that previous approaches for polynomial
kernel approximation create maps that are rank deficient, and therefore do not
utilize the capacity of the projected feature space effectively. To address
this challenge, we propose compact random feature maps (CRAFTMaps) to
approximate polynomial kernels more concisely and accurately. We prove the
error bounds of CRAFTMaps demonstrating their superior kernel reconstruction
performance compared to the previous approximation schemes. We show how
structured random matrices can be used to efficiently generate CRAFTMaps, and
present a single-pass algorithm using CRAFTMaps to learn non-linear multi-class
classifiers. We present experiments on multiple standard data-sets with
performance competitive with state-of-the-art results.Comment: 9 page
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