19,640 research outputs found
Stability of matrix factorization for collaborative filtering
We study the stability vis a vis adversarial noise of matrix factorization
algorithm for matrix completion. In particular, our results include: (I) we
bound the gap between the solution matrix of the factorization method and the
ground truth in terms of root mean square error; (II) we treat the matrix
factorization as a subspace fitting problem and analyze the difference between
the solution subspace and the ground truth; (III) we analyze the prediction
error of individual users based on the subspace stability. We apply these
results to the problem of collaborative filtering under manipulator attack,
which leads to useful insights and guidelines for collaborative filtering
system design.Comment: ICML201
A phase-field model of relaxor ferroelectrics based on random field theory
A mechanically coupled phase-field model is proposed for the first time to
simulate the peculiar behavior of relaxor ferroelectrics. Based on the random
field theory for relaxors, local random fields are introduced to characterize
the effect of chemical disorder. This generic model is developed from a
thermodynamic framework and the microforce theory and is implemented by a
nonlinear finite element method. Simulation results show that the model can
reproduce relaxor features, such as domain miniaturization, small remnant
polarization and large piezoelectric response. In particular, the influence of
random field strength on these features are revealed. Simulation results on
domain structure and hysteresis behavior are discussed and compared with
related experimental results.Comment: 8 figure
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