40,954 research outputs found
Generalized residual vector quantization for large scale data
Vector quantization is an essential tool for tasks involving large scale
data, for example, large scale similarity search, which is crucial for
content-based information retrieval and analysis. In this paper, we propose a
novel vector quantization framework that iteratively minimizes quantization
error. First, we provide a detailed review on a relevant vector quantization
method named \textit{residual vector quantization} (RVQ). Next, we propose
\textit{generalized residual vector quantization} (GRVQ) to further improve
over RVQ. Many vector quantization methods can be viewed as the special cases
of our proposed framework. We evaluate GRVQ on several large scale benchmark
datasets for large scale search, classification and object retrieval. We
compared GRVQ with existing methods in detail. Extensive experiments
demonstrate our GRVQ framework substantially outperforms existing methods in
term of quantization accuracy and computation efficiency.Comment: published on International Conference on Multimedia and Expo 201
Quantum Statistical Physics - A New Approach
The new scheme employed (throughout the thermodynamic phase space), in the
statistical thermodynamic investigation of classical systems, is extended to
quantum systems. Quantum Nearest Neighbor Probability Density Functions are
formulated (in a manner analogous to the classical case) to provide a new
quantum approach for describing structure at the microscopic level, as well as
characterize the thermodynamic properties of material systems. A major point of
this paper is that it relates the free energy of an assembly of interacting
particles to Quantum Nearest Neighbor Probability Density Functions. Also. the
methods of this paper reduces to a great extent, the degree of difficulty of
the original equilibrium quantum statistical thermodynamic problem without
compromising the accuracy of results. Application to the simple case of dilute,
weakly degenerate gases has been outlined.Comment: Submitted for publication in Physica A journa
The -matching problem on bipartite graphs
The -matching problem on bipartite graphs is studied with a local
algorithm. A -matching () on a bipartite graph is a set of matched
edges, in which each vertex of one type is adjacent to at most matched edge
and each vertex of the other type is adjacent to at most matched edges. The
-matching problem on a given bipartite graph concerns finding -matchings
with the maximum size. Our approach to this combinatorial optimization are of
two folds. From an algorithmic perspective, we adopt a local algorithm as a
linear approximate solver to find -matchings on general bipartite graphs,
whose basic component is a generalized version of the greedy leaf removal
procedure in graph theory. From an analytical perspective, in the case of
random bipartite graphs with the same size of two types of vertices, we develop
a mean-field theory for the percolation phenomenon underlying the local
algorithm, leading to a theoretical estimation of -matching sizes on
coreless graphs. We hope that our results can shed light on further study on
algorithms and computational complexity of the optimization problem.Comment: 15 pages, 3 figure
Tree-Independent Dual-Tree Algorithms
Dual-tree algorithms are a widely used class of branch-and-bound algorithms.
Unfortunately, developing dual-tree algorithms for use with different trees and
problems is often complex and burdensome. We introduce a four-part logical
split: the tree, the traversal, the point-to-point base case, and the pruning
rule. We provide a meta-algorithm which allows development of dual-tree
algorithms in a tree-independent manner and easy extension to entirely new
types of trees. Representations are provided for five common algorithms; for
k-nearest neighbor search, this leads to a novel, tighter pruning bound. The
meta-algorithm also allows straightforward extensions to massively parallel
settings.Comment: accepted in ICML 201
The Random Walk in Generalized Quantum Theory
One can view quantum mechanics as a generalization of classical probability
theory that provides for pairwise interference among alternatives. Adopting
this perspective, we ``quantize'' the classical random walk by finding, subject
to a certain condition of ``strong positivity'', the most general Markovian,
translationally invariant ``decoherence functional'' with nearest neighbor
transitions.Comment: 25 pages, no figure
Next nearest neighbour Ising models on random graphs
This paper develops results for the next nearest neighbour Ising model on
random graphs. Besides being an essential ingredient in classic models for
frustrated systems, second neighbour interactions interactions arise naturally
in several applications such as the colour diversity problem and graphical
games. We demonstrate ensembles of random graphs, including regular
connectivity graphs, that have a periodic variation of free energy, with either
the ratio of nearest to next nearest couplings, or the mean number of nearest
neighbours. When the coupling ratio is integer paramagnetic phases can be found
at zero temperature. This is shown to be related to the locked or unlocked
nature of the interactions. For anti-ferromagnetic couplings, spin glass phases
are demonstrated at low temperature. The interaction structure is formulated as
a factor graph, the solution on a tree is developed. The replica symmetric and
energetic one-step replica symmetry breaking solution is developed using the
cavity method. We calculate within these frameworks the phase diagram and
demonstrate the existence of dynamical transitions at zero temperature for
cases of anti-ferromagnetic coupling on regular and inhomogeneous random
graphs.Comment: 55 pages, 15 figures, version 2 with minor revisions, to be published
J. Stat. Mec
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