3,065 research outputs found
Neural Collaborative Subspace Clustering
We introduce the Neural Collaborative Subspace Clustering, a neural model
that discovers clusters of data points drawn from a union of low-dimensional
subspaces. In contrast to previous attempts, our model runs without the aid of
spectral clustering. This makes our algorithm one of the kinds that can
gracefully scale to large datasets. At its heart, our neural model benefits
from a classifier which determines whether a pair of points lies on the same
subspace or not. Essential to our model is the construction of two affinity
matrices, one from the classifier and the other from a notion of subspace
self-expressiveness, to supervise training in a collaborative scheme. We
thoroughly assess and contrast the performance of our model against various
state-of-the-art clustering algorithms including deep subspace-based ones.Comment: Accepted to ICML 201
Subspace representations in ab initio methods for strongly correlated systems
We present a generalized definition of subspace occupancy matrices in ab
initio methods for strongly correlated materials, such as DFT+U and DFT+DMFT,
which is appropriate to the case of nonorthogonal projector functions. By
enforcing the tensorial consistency of all matrix operations, we are led to a
subspace projection operator for which the occupancy matrix is tensorial and
accumulates only contributions which are local to the correlated subspace at
hand. For DFT+U in particular, the resulting contributions to the potential and
ionic forces are automatically Hermitian, without resort to symmetrization, and
localized to their corresponding correlated subspace. The tensorial invariance
of the occupancies, energies and ionic forces is preserved. We illustrate the
effect of this formalism in a DFT+U study using self-consistently determined
projectors.Comment: 15 pages, 8 figures. This version (v2) matches that accepted for
Physical Review B on 15th April 201
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