147,996 research outputs found
In Search of Non-Gaussian Components of a High-Dimensional Distribution
Finding non-Gaussian components of high-dimensional data is an important preprocessing step for effcient information processing. This article proposes a new linear method to identify the ``non-Gaussian subspace´´ within a very general semi-parametric framework. Our proposed method, called NGCA (Non-Gaussian Component Analysis), is essentially based on a linear operator which, to any arbitrary nonlinear (smooth) function, associates a vector which belongs to the low dimensional non-Gaussian target subspace up to an estimation error. By applying this operator to a family of different nonlinear functions, one obtains a family of different vectors lying in a vicinity of the target space. As a final step, the target space itself is estimated by applying PCA to this family of vectors. We show that this procedure is consistent in the sense that the estimaton error tends to zero at a parametric rate, uniformly over the family, Numerical examples demonstrate the usefulness of our method.non-Gaussian components, dimension reduction
A reliable order-statistics-based approximate nearest neighbor search algorithm
We propose a new algorithm for fast approximate nearest neighbor search based
on the properties of ordered vectors. Data vectors are classified based on the
index and sign of their largest components, thereby partitioning the space in a
number of cones centered in the origin. The query is itself classified, and the
search starts from the selected cone and proceeds to neighboring ones. Overall,
the proposed algorithm corresponds to locality sensitive hashing in the space
of directions, with hashing based on the order of components. Thanks to the
statistical features emerging through ordering, it deals very well with the
challenging case of unstructured data, and is a valuable building block for
more complex techniques dealing with structured data. Experiments on both
simulated and real-world data prove the proposed algorithm to provide a
state-of-the-art performance
History Matching Using Principal Component Analysis
Imperial Users onl
A coherent triggered search for single spin compact binary coalescences in gravitational wave data
In this paper we present a method for conducting a coherent search for single
spin compact binary coalescences in gravitational wave data and compare this
search to the existing coincidence method for single spin searches. We propose
a method to characterize the regions of the parameter space where the single
spin search, both coincident and coherent, will increase detection efficiency
over the existing non-precessing search. We also show example results of the
coherent search on a stretch of data from LIGO's fourth science run but note
that a set of signal based vetoes will be needed before this search can be run
to try to make detections.Comment: 14 pages, 4 figure
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