1,488 research outputs found
Scalable Sparse Subspace Clustering by Orthogonal Matching Pursuit
Subspace clustering methods based on , or nuclear norm
regularization have become very popular due to their simplicity, theoretical
guarantees and empirical success. However, the choice of the regularizer can
greatly impact both theory and practice. For instance, regularization
is guaranteed to give a subspace-preserving affinity (i.e., there are no
connections between points from different subspaces) under broad conditions
(e.g., arbitrary subspaces and corrupted data). However, it requires solving a
large scale convex optimization problem. On the other hand, and
nuclear norm regularization provide efficient closed form solutions, but
require very strong assumptions to guarantee a subspace-preserving affinity,
e.g., independent subspaces and uncorrupted data. In this paper we study a
subspace clustering method based on orthogonal matching pursuit. We show that
the method is both computationally efficient and guaranteed to give a
subspace-preserving affinity under broad conditions. Experiments on synthetic
data verify our theoretical analysis, and applications in handwritten digit and
face clustering show that our approach achieves the best trade off between
accuracy and efficiency.Comment: 13 pages, 1 figure, 2 tables. Accepted to CVPR 2016 as an oral
presentatio
Provable Self-Representation Based Outlier Detection in a Union of Subspaces
Many computer vision tasks involve processing large amounts of data
contaminated by outliers, which need to be detected and rejected. While outlier
detection methods based on robust statistics have existed for decades, only
recently have methods based on sparse and low-rank representation been
developed along with guarantees of correct outlier detection when the inliers
lie in one or more low-dimensional subspaces. This paper proposes a new outlier
detection method that combines tools from sparse representation with random
walks on a graph. By exploiting the property that data points can be expressed
as sparse linear combinations of each other, we obtain an asymmetric affinity
matrix among data points, which we use to construct a weighted directed graph.
By defining a suitable Markov Chain from this graph, we establish a connection
between inliers/outliers and essential/inessential states of the Markov chain,
which allows us to detect outliers by using random walks. We provide a
theoretical analysis that justifies the correctness of our method under
geometric and connectivity assumptions. Experimental results on image databases
demonstrate its superiority with respect to state-of-the-art sparse and
low-rank outlier detection methods.Comment: 16 pages. CVPR 2017 spotlight oral presentatio
Optical isolation with nonlinear topological photonics
It is shown that the concept of topological phase transitions can be used to
design nonlinear photonic structures exhibiting power thresholds and
discontinuities in their transmittance. This provides a novel route to devising
nonlinear optical isolators. We study three representative designs: (i) a
waveguide array implementing a nonlinear 1D Su-Schrieffer-Heeger (SSH) model,
(ii) a waveguide array implementing a nonlinear 2D Haldane model, and (iii) a
2D lattice of coupled-ring waveguides. In the first two cases, we find a
correspondence between the topological transition of the underlying linear
lattice and the power threshold of the transmittance, and show that the
transmission behavior is attributable to the emergence of a self-induced
topological soliton. In the third case, we show that the topological transition
produces a discontinuity in the transmittance curve, which can be exploited to
achieve sharp jumps in the power-dependent isolation ratio.Comment: 11 pages, 7 figure
Associated production of the heavy charged gauge boson and a top quark at LHC
In the context of topflavor seesaw model, we study the production of the
heavy charged gauge boson associated with a top quark at the LHC.
Focusing on the searching channel , we carry out a full simulation of the signal and the
relevant standard model backgrounds. The kinematical distributions of final
states are presented. It is found that the backgrounds can be significantly
suppressed by sets of kinematic cuts, and the signal of the heavy charged boson
might be detected at the LHC with TeV. With a integrated
luminosity of \LL= 100 , a signal significance can be
achieved for TeV.Comment: 16 pages, 6 figure
Oracle Based Active Set Algorithm for Scalable Elastic Net Subspace Clustering
State-of-the-art subspace clustering methods are based on expressing each
data point as a linear combination of other data points while regularizing the
matrix of coefficients with , or nuclear norms.
regularization is guaranteed to give a subspace-preserving affinity (i.e.,
there are no connections between points from different subspaces) under broad
theoretical conditions, but the clusters may not be connected. and
nuclear norm regularization often improve connectivity, but give a
subspace-preserving affinity only for independent subspaces. Mixed ,
and nuclear norm regularizations offer a balance between the
subspace-preserving and connectedness properties, but this comes at the cost of
increased computational complexity. This paper studies the geometry of the
elastic net regularizer (a mixture of the and norms) and uses
it to derive a provably correct and scalable active set method for finding the
optimal coefficients. Our geometric analysis also provides a theoretical
justification and a geometric interpretation for the balance between the
connectedness (due to regularization) and subspace-preserving (due to
regularization) properties for elastic net subspace clustering. Our
experiments show that the proposed active set method not only achieves
state-of-the-art clustering performance, but also efficiently handles
large-scale datasets.Comment: 15 pages, 6 figures, accepted to CVPR 2016 for oral presentatio
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