684,679 research outputs found
Graph kernels between point clouds
Point clouds are sets of points in two or three dimensions. Most kernel
methods for learning on sets of points have not yet dealt with the specific
geometrical invariances and practical constraints associated with point clouds
in computer vision and graphics. In this paper, we present extensions of graph
kernels for point clouds, which allow to use kernel methods for such ob jects
as shapes, line drawings, or any three-dimensional point clouds. In order to
design rich and numerically efficient kernels with as few free parameters as
possible, we use kernels between covariance matrices and their factorizations
on graphical models. We derive polynomial time dynamic programming recursions
and present applications to recognition of handwritten digits and Chinese
characters from few training examples
Mining Point Cloud Local Structures by Kernel Correlation and Graph Pooling
Unlike on images, semantic learning on 3D point clouds using a deep network
is challenging due to the naturally unordered data structure. Among existing
works, PointNet has achieved promising results by directly learning on point
sets. However, it does not take full advantage of a point's local neighborhood
that contains fine-grained structural information which turns out to be helpful
towards better semantic learning. In this regard, we present two new operations
to improve PointNet with a more efficient exploitation of local structures. The
first one focuses on local 3D geometric structures. In analogy to a convolution
kernel for images, we define a point-set kernel as a set of learnable 3D points
that jointly respond to a set of neighboring data points according to their
geometric affinities measured by kernel correlation, adapted from a similar
technique for point cloud registration. The second one exploits local
high-dimensional feature structures by recursive feature aggregation on a
nearest-neighbor-graph computed from 3D positions. Experiments show that our
network can efficiently capture local information and robustly achieve better
performances on major datasets. Our code is available at
http://www.merl.com/research/license#KCNetComment: Accepted in CVPR'18. *indicates equal contributio
Error Metrics for Learning Reliable Manifolds from Streaming Data
Spectral dimensionality reduction is frequently used to identify
low-dimensional structure in high-dimensional data. However, learning
manifolds, especially from the streaming data, is computationally and memory
expensive. In this paper, we argue that a stable manifold can be learned using
only a fraction of the stream, and the remaining stream can be mapped to the
manifold in a significantly less costly manner. Identifying the transition
point at which the manifold is stable is the key step. We present error metrics
that allow us to identify the transition point for a given stream by
quantitatively assessing the quality of a manifold learned using Isomap. We
further propose an efficient mapping algorithm, called S-Isomap, that can be
used to map new samples onto the stable manifold. We describe experiments on a
variety of data sets that show that the proposed approach is computationally
efficient without sacrificing accuracy
Active Sampling of Pairs and Points for Large-scale Linear Bipartite Ranking
Bipartite ranking is a fundamental ranking problem that learns to order
relevant instances ahead of irrelevant ones. The pair-wise approach for
bi-partite ranking construct a quadratic number of pairs to solve the problem,
which is infeasible for large-scale data sets. The point-wise approach, albeit
more efficient, often results in inferior performance. That is, it is difficult
to conduct bipartite ranking accurately and efficiently at the same time. In
this paper, we develop a novel active sampling scheme within the pair-wise
approach to conduct bipartite ranking efficiently. The scheme is inspired from
active learning and can reach a competitive ranking performance while focusing
only on a small subset of the many pairs during training. Moreover, we propose
a general Combined Ranking and Classification (CRC) framework to accurately
conduct bipartite ranking. The framework unifies point-wise and pair-wise
approaches and is simply based on the idea of treating each instance point as a
pseudo-pair. Experiments on 14 real-word large-scale data sets demonstrate that
the proposed algorithm of Active Sampling within CRC, when coupled with a
linear Support Vector Machine, usually outperforms state-of-the-art point-wise
and pair-wise ranking approaches in terms of both accuracy and efficiency.Comment: a shorter version was presented in ACML 201
Proximal Iteratively Reweighted Algorithm with Multiple Splitting for Nonconvex Sparsity Optimization
This paper proposes the Proximal Iteratively REweighted (PIRE) algorithm for
solving a general problem, which involves a large body of nonconvex sparse and
structured sparse related problems. Comparing with previous iterative solvers
for nonconvex sparse problem, PIRE is much more general and efficient. The
computational cost of PIRE in each iteration is usually as low as the
state-of-the-art convex solvers. We further propose the PIRE algorithm with
Parallel Splitting (PIRE-PS) and PIRE algorithm with Alternative Updating
(PIRE-AU) to handle the multi-variable problems. In theory, we prove that our
proposed methods converge and any limit solution is a stationary point.
Extensive experiments on both synthesis and real data sets demonstrate that our
methods achieve comparative learning performance, but are much more efficient,
by comparing with previous nonconvex solvers
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