28,880 research outputs found
K-nearest Neighbor Search by Random Projection Forests
K-nearest neighbor (kNN) search has wide applications in many areas,
including data mining, machine learning, statistics and many applied domains.
Inspired by the success of ensemble methods and the flexibility of tree-based
methodology, we propose random projection forests (rpForests), for kNN search.
rpForests finds kNNs by aggregating results from an ensemble of random
projection trees with each constructed recursively through a series of
carefully chosen random projections. rpForests achieves a remarkable accuracy
in terms of fast decay in the missing rate of kNNs and that of discrepancy in
the kNN distances. rpForests has a very low computational complexity. The
ensemble nature of rpForests makes it easily run in parallel on multicore or
clustered computers; the running time is expected to be nearly inversely
proportional to the number of cores or machines. We give theoretical insights
by showing the exponential decay of the probability that neighboring points
would be separated by ensemble random projection trees when the ensemble size
increases. Our theory can be used to refine the choice of random projections in
the growth of trees, and experiments show that the effect is remarkable.Comment: 15 pages, 4 figures, 2018 IEEE Big Data Conferenc
Investigate the interaction between dark matter and dark energy
In this paper we investigate the interaction between dark matter and dark
energy by considering two different interacting scenarios, i.e. the cases of
constant interaction function and variable interaction function. By fitting the
current observational data to constrain the interacting models, it is found
that the interacting strength is non-vanishing, but weak for the case of
constant interaction function, and the interaction is not obvious for the case
of variable interaction function. In addition, for seeing the influence from
interaction we also investigate the evolutions of interaction function,
effective state parameter for dark energy and energy density of dark matter. At
last some geometrical quantities in the interacting scenarios are discussed.Comment: 14 pages, 6 figure
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