316 research outputs found
Toward a generic representation of random variables for machine learning
This paper presents a pre-processing and a distance which improve the
performance of machine learning algorithms working on independent and
identically distributed stochastic processes. We introduce a novel
non-parametric approach to represent random variables which splits apart
dependency and distribution without losing any information. We also propound an
associated metric leveraging this representation and its statistical estimate.
Besides experiments on synthetic datasets, the benefits of our contribution is
illustrated through the example of clustering financial time series, for
instance prices from the credit default swaps market. Results are available on
the website www.datagrapple.com and an IPython Notebook tutorial is available
at www.datagrapple.com/Tech for reproducible research.Comment: submitted to Pattern Recognition Letter
A proposal of a methodological framework with experimental guidelines to investigate clustering stability on financial time series
We present in this paper an empirical framework motivated by the practitioner
point of view on stability. The goal is to both assess clustering validity and
yield market insights by providing through the data perturbations we propose a
multi-view of the assets' clustering behaviour. The perturbation framework is
illustrated on an extensive credit default swap time series database available
online at www.datagrapple.com.Comment: Accepted at ICMLA 201
The sensitivity of rapidly rotating Rayleigh--B\'enard convection to Ekman pumping
The dependence of the heat transfer, as measured by the nondimensional
Nusselt number , on Ekman pumping for rapidly rotating Rayleigh-B\'enard
convection in an infinite plane layer is examined for fluids with Prandtl
number . A joint effort utilizing simulations from the Composite
Non-hydrostatic Quasi-Geostrophic model (CNH-QGM) and direct numerical
simulations (DNS) of the incompressible fluid equations has mapped a wide range
of the Rayleigh number - Ekman number parameter space within the
geostrophic regime of rotating convection. Corroboration of the -
relation at from both methods along with higher covered by
DNS and lower by the asymptotic model allows for this range of the heat
transfer results. For stress-free boundaries, the relation has the dissipation-free scaling of for all
. This is directly related to a geostrophic turbulent interior
that throttles the heat transport supplied to the thermal boundary layers. For
no-slip boundaries, the existence of ageostrophic viscous boundary layers and
their associated Ekman pumping yields a more complex 2D surface in
parameter space. For results suggest that the surface can be
expressed as indicating the
dissipation-free scaling law is enhanced by Ekman pumping by the multiplicative
prefactor where . It follows for
that the geostrophic turbulent interior remains the flux bottleneck
in rapidly rotating Rayleigh-B\'enard convection. For , where DNS
and asymptotic simulations agree quantitatively, it is found that the effects
of Ekman pumping are sufficiently strong to influence the heat transport with
diminished exponent and .Comment: 9 pages, 14 figure
The effects of Ekman pumping on quasi-geostrophic Rayleigh-Benard convection
Numerical simulations of 3D, rapidly rotating Rayleigh-Benard convection are
performed using an asymptotic quasi-geostrophic model that incorporates the
effects of no-slip boundaries through (i) parameterized Ekman pumping boundary
conditions, and (ii) a thermal wind boundary layer that regularizes the
enhanced thermal fluctuations induced by pumping. The fidelity of the model,
obtained by an asymptotic reduction of the Navier-Stokes equations that
implicitly enforces a pointwise geostrophic balance, is explored for the first
time by comparisons of simulations against the findings of direct numerical
simulations and laboratory experiments. Results from these methods have
established Ekman pumping as the mechanism responsible for significantly
enhancing the vertical heat transport. This asymptotic model demonstrates
excellent agreement over a range of thermal forcing for Pr ~1 when compared
with results from experiments and DNS at maximal values of their attainable
rotation rates, as measured by the Ekman number (E ~ 10^{-7}); good qualitative
agreement is achieved for Pr > 1. Similar to studies with stress-free
boundaries, four spatially distinct flow morphologies exists. Despite the
presence of frictional drag at the upper and/or lower boundaries, a strong
non-local inverse cascade of barotropic (i.e., depth-independent) kinetic
energy persists in the final regime of geostrophic turbulence and is dominant
at large scales. For mixed no-slip/stress-free and no-slip/no-slip boundaries,
Ekman friction is found to attenuate the efficiency of the upscale energy
transport and, unlike the case of stress-free boundaries, rapidly saturates the
barotropic kinetic energy. For no-slip/no-slip boundaries, Ekman friction is
strong enough to prevent the development of a coherent dipole vortex
condensate. Instead vortex pairs are found to be intermittent, varying in both
time and strength.Comment: 20 pages, 10 figure
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