1,182 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
Exact Controllability of Linear Stochastic Differential Equations and Related Problems
A notion of -exact controllability is introduced for linear controlled
(forward) stochastic differential equations, for which several sufficient
conditions are established. Further, it is proved that the -exact
controllability, the validity of an observability inequality for the adjoint
equation, the solvability of an optimization problem, and the solvability of an
-type norm optimal control problem are all equivalent
Zero-Shot Recognition using Dual Visual-Semantic Mapping Paths
Zero-shot recognition aims to accurately recognize objects of unseen classes
by using a shared visual-semantic mapping between the image feature space and
the semantic embedding space. This mapping is learned on training data of seen
classes and is expected to have transfer ability to unseen classes. In this
paper, we tackle this problem by exploiting the intrinsic relationship between
the semantic space manifold and the transfer ability of visual-semantic
mapping. We formalize their connection and cast zero-shot recognition as a
joint optimization problem. Motivated by this, we propose a novel framework for
zero-shot recognition, which contains dual visual-semantic mapping paths. Our
analysis shows this framework can not only apply prior semantic knowledge to
infer underlying semantic manifold in the image feature space, but also
generate optimized semantic embedding space, which can enhance the transfer
ability of the visual-semantic mapping to unseen classes. The proposed method
is evaluated for zero-shot recognition on four benchmark datasets, achieving
outstanding results.Comment: Accepted as a full paper in IEEE Computer Vision and Pattern
Recognition (CVPR) 201
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