5,464 research outputs found
SamBaTen: Sampling-based Batch Incremental Tensor Decomposition
Tensor decompositions are invaluable tools in analyzing multimodal datasets.
In many real-world scenarios, such datasets are far from being static, to the
contrary they tend to grow over time. For instance, in an online social network
setting, as we observe new interactions over time, our dataset gets updated in
its "time" mode. How can we maintain a valid and accurate tensor decomposition
of such a dynamically evolving multimodal dataset, without having to re-compute
the entire decomposition after every single update? In this paper we introduce
SaMbaTen, a Sampling-based Batch Incremental Tensor Decomposition algorithm,
which incrementally maintains the decomposition given new updates to the tensor
dataset. SaMbaTen is able to scale to datasets that the state-of-the-art in
incremental tensor decomposition is unable to operate on, due to its ability to
effectively summarize the existing tensor and the incoming updates, and perform
all computations in the reduced summary space. We extensively evaluate SaMbaTen
using synthetic and real datasets. Indicatively, SaMbaTen achieves comparable
accuracy to state-of-the-art incremental and non-incremental techniques, while
being 25-30 times faster. Furthermore, SaMbaTen scales to very large sparse and
dense dynamically evolving tensors of dimensions up to 100K x 100K x 100K where
state-of-the-art incremental approaches were not able to operate
Online and Differentially-Private Tensor Decomposition
In this paper, we resolve many of the key algorithmic questions regarding
robustness, memory efficiency, and differential privacy of tensor
decomposition. We propose simple variants of the tensor power method which
enjoy these strong properties. We present the first guarantees for online
tensor power method which has a linear memory requirement. Moreover, we present
a noise calibrated tensor power method with efficient privacy guarantees. At
the heart of all these guarantees lies a careful perturbation analysis derived
in this paper which improves up on the existing results significantly.Comment: 19 pages, 9 figures. To appear at the 30th Annual Conference on
Advances in Neural Information Processing Systems (NIPS 2016), to be held at
Barcelona, Spain. Fix small typos in proofs of Lemmas C.5 and C.
Lattice Boltzmann simulations of droplet dynamics in time-dependent flows
We study the deformation and dynamics of droplets in time-dependent flows
using 3D numerical simulations of two immiscible fluids based on the lattice
Boltzmann model (LBM). Analytical models are available in the literature, which
assume the droplet shape to be an ellipsoid at all times (P.L. Maffettone, M.
Minale, J. Non-Newton. Fluid Mech 78, 227 (1998); M. Minale, Rheol. Acta 47,
667 (2008)). Beyond the practical importance of using a mesoscale simulation to
assess ab-initio the robustness and limitations of such theoretical models, our
simulations are also key to discuss - in controlled situations - some relevant
phenomenology related to the interplay between the flow time scales and the
droplet time scales regarding the transparency transition for high enough shear
frequencies for an external oscillating flow. This work may be regarded as a
step forward to discuss extensions towards a novel DNS approach, describing the
mesoscale physics of small droplets subjected to a generic hydrodynamical
strain field, possibly mimicking the effect of a realistic turbulent flow on
dilute droplet suspensions
Lattice Boltzmann Thermohydrodynamics
We introduce a lattice Boltzmann computational scheme capable of modeling
thermohydrodynamic flows of monatomic gases. The parallel nature of this
approach provides a numerically efficient alternative to traditional methods of
computational fluid dynamics. The scheme uses a small number of discrete
velocity states and a linear, single-time-relaxation collision operator.
Numerical simulations in two dimensions agree well with exact solutions for
adiabatic sound propagation and Couette flow with heat transfer.Comment: 11 pages, Physical Review E: Rapid Communications, in pres
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