16,264 research outputs found
Manifold Elastic Net: A Unified Framework for Sparse Dimension Reduction
It is difficult to find the optimal sparse solution of a manifold learning
based dimensionality reduction algorithm. The lasso or the elastic net
penalized manifold learning based dimensionality reduction is not directly a
lasso penalized least square problem and thus the least angle regression (LARS)
(Efron et al. \cite{LARS}), one of the most popular algorithms in sparse
learning, cannot be applied. Therefore, most current approaches take indirect
ways or have strict settings, which can be inconvenient for applications. In
this paper, we proposed the manifold elastic net or MEN for short. MEN
incorporates the merits of both the manifold learning based dimensionality
reduction and the sparse learning based dimensionality reduction. By using a
series of equivalent transformations, we show MEN is equivalent to the lasso
penalized least square problem and thus LARS is adopted to obtain the optimal
sparse solution of MEN. In particular, MEN has the following advantages for
subsequent classification: 1) the local geometry of samples is well preserved
for low dimensional data representation, 2) both the margin maximization and
the classification error minimization are considered for sparse projection
calculation, 3) the projection matrix of MEN improves the parsimony in
computation, 4) the elastic net penalty reduces the over-fitting problem, and
5) the projection matrix of MEN can be interpreted psychologically and
physiologically. Experimental evidence on face recognition over various popular
datasets suggests that MEN is superior to top level dimensionality reduction
algorithms.Comment: 33 pages, 12 figure
Locality Preserving Projections for Grassmann manifold
Learning on Grassmann manifold has become popular in many computer vision
tasks, with the strong capability to extract discriminative information for
imagesets and videos. However, such learning algorithms particularly on
high-dimensional Grassmann manifold always involve with significantly high
computational cost, which seriously limits the applicability of learning on
Grassmann manifold in more wide areas. In this research, we propose an
unsupervised dimensionality reduction algorithm on Grassmann manifold based on
the Locality Preserving Projections (LPP) criterion. LPP is a commonly used
dimensionality reduction algorithm for vector-valued data, aiming to preserve
local structure of data in the dimension-reduced space. The strategy is to
construct a mapping from higher dimensional Grassmann manifold into the one in
a relative low-dimensional with more discriminative capability. The proposed
method can be optimized as a basic eigenvalue problem. The performance of our
proposed method is assessed on several classification and clustering tasks and
the experimental results show its clear advantages over other Grassmann based
algorithms.Comment: Accepted by IJCAI 201
Discriminative Scale Space Tracking
Accurate scale estimation of a target is a challenging research problem in
visual object tracking. Most state-of-the-art methods employ an exhaustive
scale search to estimate the target size. The exhaustive search strategy is
computationally expensive and struggles when encountered with large scale
variations. This paper investigates the problem of accurate and robust scale
estimation in a tracking-by-detection framework. We propose a novel scale
adaptive tracking approach by learning separate discriminative correlation
filters for translation and scale estimation. The explicit scale filter is
learned online using the target appearance sampled at a set of different
scales. Contrary to standard approaches, our method directly learns the
appearance change induced by variations in the target scale. Additionally, we
investigate strategies to reduce the computational cost of our approach.
Extensive experiments are performed on the OTB and the VOT2014 datasets.
Compared to the standard exhaustive scale search, our approach achieves a gain
of 2.5% in average overlap precision on the OTB dataset. Additionally, our
method is computationally efficient, operating at a 50% higher frame rate
compared to the exhaustive scale search. Our method obtains the top rank in
performance by outperforming 19 state-of-the-art trackers on OTB and 37
state-of-the-art trackers on VOT2014.Comment: To appear in TPAMI. This is the journal extension of the
VOT2014-winning DSST tracking metho
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