3,401 research outputs found
Learning Transformations for Clustering and Classification
A low-rank transformation learning framework for subspace clustering and
classification is here proposed. Many high-dimensional data, such as face
images and motion sequences, approximately lie in a union of low-dimensional
subspaces. The corresponding subspace clustering problem has been extensively
studied in the literature to partition such high-dimensional data into clusters
corresponding to their underlying low-dimensional subspaces. However,
low-dimensional intrinsic structures are often violated for real-world
observations, as they can be corrupted by errors or deviate from ideal models.
We propose to address this by learning a linear transformation on subspaces
using matrix rank, via its convex surrogate nuclear norm, as the optimization
criteria. The learned linear transformation restores a low-rank structure for
data from the same subspace, and, at the same time, forces a a maximally
separated structure for data from different subspaces. In this way, we reduce
variations within subspaces, and increase separation between subspaces for a
more robust subspace clustering. This proposed learned robust subspace
clustering framework significantly enhances the performance of existing
subspace clustering methods. Basic theoretical results here presented help to
further support the underlying framework. To exploit the low-rank structures of
the transformed subspaces, we further introduce a fast subspace clustering
technique, which efficiently combines robust PCA with sparse modeling. When
class labels are present at the training stage, we show this low-rank
transformation framework also significantly enhances classification
performance. Extensive experiments using public datasets are presented, showing
that the proposed approach significantly outperforms state-of-the-art methods
for subspace clustering and classification.Comment: arXiv admin note: substantial text overlap with arXiv:1308.0273,
arXiv:1308.027
Coherent dynamics of domain formation in the Bose Ferromagnet
We present a theory to describe domain formation observed very recently in a
quenched Rb-87 gas, a typical ferromagnetic spinor Bose system. An overlap
factor is introduced to characterize the symmetry breaking of M_F=\pm 1
components for the F=1 ferromagnetic condensate. We demonstrate that the domain
formation is a co-effect of the quantum coherence and the thermal relaxation. A
thermally enhanced quantum-oscillation is observed during the dynamical process
of the domain formation. And the spatial separation of domains leads to
significant decay of the M_F=0 component fraction in an initial M_F=0
condensate.Comment: 4 pages, 3 figure
Learning Transformations for Classification Forests
This work introduces a transformation-based learner model for classification
forests. The weak learner at each split node plays a crucial role in a
classification tree. We propose to optimize the splitting objective by learning
a linear transformation on subspaces using nuclear norm as the optimization
criteria. The learned linear transformation restores a low-rank structure for
data from the same class, and, at the same time, maximizes the separation
between different classes, thereby improving the performance of the split
function. Theoretical and experimental results support the proposed framework.Comment: arXiv admin note: text overlap with arXiv:1309.207
The Role of Principal Angles in Subspace Classification
Subspace models play an important role in a wide range of signal processing
tasks, and this paper explores how the pairwise geometry of subspaces
influences the probability of misclassification. When the mismatch between the
signal and the model is vanishingly small, the probability of misclassification
is determined by the product of the sines of the principal angles between
subspaces. When the mismatch is more significant, the probability of
misclassification is determined by the sum of the squares of the sines of the
principal angles. Reliability of classification is derived in terms of the
distribution of signal energy across principal vectors. Larger principal angles
lead to smaller classification error, motivating a linear transform that
optimizes principal angles. The transform presented here (TRAIT) preserves some
specific characteristic of each individual class, and this approach is shown to
be complementary to a previously developed transform (LRT) that enlarges
inter-class distance while suppressing intra-class dispersion. Theoretical
results are supported by demonstration of superior classification accuracy on
synthetic and measured data even in the presence of significant model mismatch
LaneNet: Real-Time Lane Detection Networks for Autonomous Driving
Lane detection is to detect lanes on the road and provide the accurate
location and shape of each lane. It severs as one of the key techniques to
enable modern assisted and autonomous driving systems. However, several unique
properties of lanes challenge the detection methods. The lack of distinctive
features makes lane detection algorithms tend to be confused by other objects
with similar local appearance. Moreover, the inconsistent number of lanes on a
road as well as diverse lane line patterns, e.g. solid, broken, single, double,
merging, and splitting lines further hamper the performance. In this paper, we
propose a deep neural network based method, named LaneNet, to break down the
lane detection into two stages: lane edge proposal and lane line localization.
Stage one uses a lane edge proposal network for pixel-wise lane edge
classification, and the lane line localization network in stage two then
detects lane lines based on lane edge proposals. Please note that the goal of
our LaneNet is built to detect lane line only, which introduces more
difficulties on suppressing the false detections on the similar lane marks on
the road like arrows and characters. Despite all the difficulties, our lane
detection is shown to be robust to both highway and urban road scenarios method
without relying on any assumptions on the lane number or the lane line
patterns. The high running speed and low computational cost endow our LaneNet
the capability of being deployed on vehicle-based systems. Experiments validate
that our LaneNet consistently delivers outstanding performances on real world
traffic scenarios
Magnetic field-line lengths inside interplanetary magnetic flux ropes
We report on the detailed and systematic study of field-line twist and length
distributions within magnetic flux ropes embedded in Interplanetary Coronal
Mass Ejections (ICMEs). The Grad-Shafranov reconstruction method is utilized
together with a constant-twist nonlinear force-free (Gold-Hoyle) flux rope
model to reveal the close relation between the field-line twist and length in
cylindrical flux ropes, based on in-situ Wind spacecraft measurements. We show
that the field-line twist distributions within interplanetary flux ropes are
inconsistent with the Lundquist model. In particular we utilize the unique
measurements of magnetic field-line lengths within selected ICME events as
provided by Kahler et al. (2011) based on energetic electron burst observations
at 1 AU and the associated type III radio emissions detected by the Wind
spacecraft. These direct measurements are compared with our model calculations
to help assess the flux-rope interpretation of the embedded magnetic
structures. By using the different flux-rope models, we show that the in-situ
direct measurements of field-line lengths are consistent with a flux-rope
structure with spiral field lines of constant and low twist, largely different
from that of the Lundquist model, especially for relatively large-scale flux
ropes.Comment: submitted to JGR Special Section: VarSIT
Sparse Dictionary-based Attributes for Action Recognition and Summarization
We present an approach for dictionary learning of action attributes via
information maximization. We unify the class distribution and appearance
information into an objective function for learning a sparse dictionary of
action attributes. The objective function maximizes the mutual information
between what has been learned and what remains to be learned in terms of
appearance information and class distribution for each dictionary atom. We
propose a Gaussian Process (GP) model for sparse representation to optimize the
dictionary objective function. The sparse coding property allows a kernel with
compact support in GP to realize a very efficient dictionary learning process.
Hence we can describe an action video by a set of compact and discriminative
action attributes. More importantly, we can recognize modeled action categories
in a sparse feature space, which can be generalized to unseen and unmodeled
action categories. Experimental results demonstrate the effectiveness of our
approach in action recognition and summarization
The distributional hyper-Jacobian determinants in fractional Sobolev spaces
In this paper we give a positive answer to a question raised by Baer-Jerison
in connection with hyper-Jacobian determinants and associated minors in
fractional Sobolev spaces. Inspired by recent works of Brezis-Nguyen and
Baer-Jerison on the Jacobian and Hessian determinants, we show that the
distributional th-Jacobian minors of degree are weak continuous in
fractional Sobolev spaces , and the result is optimal,
satisfying the necessary conditions, in the frame work of fractional Sobolev
spaces. In particular, the conditions can be removed in case , i.e., the
th-Jacobian minors of degree are well defined in if and only
if in case .Comment: 19 page
Virtual CNN Branching: Efficient Feature Ensemble for Person Re-Identification
In this paper we introduce an ensemble method for convolutional neural
network (CNN), called "virtual branching," which can be implemented with nearly
no additional parameters and computation on top of standard CNNs. We propose
our method in the context of person re-identification (re-ID). Our CNN model
consists of shared bottom layers, followed by "virtual" branches, where neurons
from a block of regular convolutional and fully-connected layers are
partitioned into multiple sets. Each virtual branch is trained with different
data to specialize in different aspects, e.g., a specific body region or pose
orientation. In this way, robust ensemble representations are obtained against
human body misalignment, deformations, or variations in viewing angles, at
nearly no any additional cost. The proposed method achieves competitive
performance on multiple person re-ID benchmark datasets, including Market-1501,
CUHK03, and DukeMTMC-reID
Random Forests Can Hash
Hash codes are a very efficient data representation needed to be able to cope
with the ever growing amounts of data. We introduce a random forest semantic
hashing scheme with information-theoretic code aggregation, showing for the
first time how random forest, a technique that together with deep learning have
shown spectacular results in classification, can also be extended to
large-scale retrieval. Traditional random forest fails to enforce the
consistency of hashes generated from each tree for the same class data, i.e.,
to preserve the underlying similarity, and it also lacks a principled way for
code aggregation across trees. We start with a simple hashing scheme, where
independently trained random trees in a forest are acting as hashing functions.
We the propose a subspace model as the splitting function, and show that it
enforces the hash consistency in a tree for data from the same class. We also
introduce an information-theoretic approach for aggregating codes of individual
trees into a single hash code, producing a near-optimal unique hash for each
class. Experiments on large-scale public datasets are presented, showing that
the proposed approach significantly outperforms state-of-the-art hashing
methods for retrieval tasks
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