4,600 research outputs found
A Dictionary-Based Generalization of Robust PCA with Applications to Target Localization in Hyperspectral Imaging
We consider the decomposition of a data matrix assumed to be a superposition
of a low-rank matrix and a component which is sparse in a known dictionary,
using a convex demixing method. We consider two sparsity structures for the
sparse factor of the dictionary sparse component, namely entry-wise and
column-wise sparsity, and provide a unified analysis, encompassing both
undercomplete and the overcomplete dictionary cases, to show that the
constituent matrices can be successfully recovered under some relatively mild
conditions on incoherence, sparsity, and rank. We leverage these results to
localize targets of interest in a hyperspectral (HS) image based on their
spectral signature(s) using the a priori known characteristic spectral
responses of the target. We corroborate our theoretical results and analyze
target localization performance of our approach via experimental evaluations
and comparisons to related techniques.Comment: 21 Pages; Index terms - Low-rank, Matrix Demixing, Dictionary Sparse,
Target Localization, and Robust PC
Robust and Low-Rank Representation for Fast Face Identification with Occlusions
In this paper we propose an iterative method to address the face
identification problem with block occlusions. Our approach utilizes a robust
representation based on two characteristics in order to model contiguous errors
(e.g., block occlusion) effectively. The first fits to the errors a
distribution described by a tailored loss function. The second describes the
error image as having a specific structure (resulting in low-rank in comparison
to image size). We will show that this joint characterization is effective for
describing errors with spatial continuity. Our approach is computationally
efficient due to the utilization of the Alternating Direction Method of
Multipliers (ADMM). A special case of our fast iterative algorithm leads to the
robust representation method which is normally used to handle non-contiguous
errors (e.g., pixel corruption). Extensive results on representative face
databases (in constrained and unconstrained environments) document the
effectiveness of our method over existing robust representation methods with
respect to both identification rates and computational time.
Code is available at Github, where you can find implementations of the
F-LR-IRNNLS and F-IRNNLS (fast version of the RRC) :
https://github.com/miliadis/FIRCComment: IEEE Transactions on Image Processing (TIP), 201
Subspace Learning in The Presence of Sparse Structured Outliers and Noise
Subspace learning is an important problem, which has many applications in
image and video processing. It can be used to find a low-dimensional
representation of signals and images. But in many applications, the desired
signal is heavily distorted by outliers and noise, which negatively affect the
learned subspace. In this work, we present a novel algorithm for learning a
subspace for signal representation, in the presence of structured outliers and
noise. The proposed algorithm tries to jointly detect the outliers and learn
the subspace for images. We present an alternating optimization algorithm for
solving this problem, which iterates between learning the subspace and finding
the outliers. This algorithm has been trained on a large number of image
patches, and the learned subspace is used for image segmentation, and is shown
to achieve better segmentation results than prior methods, including least
absolute deviation fitting, k-means clustering based segmentation in DjVu, and
shape primitive extraction and coding algorithm.Comment: IEEE International Symposium on Circuits and Systems, 201
A Unified Framework for Stochastic Matrix Factorization via Variance Reduction
We propose a unified framework to speed up the existing stochastic matrix
factorization (SMF) algorithms via variance reduction. Our framework is general
and it subsumes several well-known SMF formulations in the literature. We
perform a non-asymptotic convergence analysis of our framework and derive
computational and sample complexities for our algorithm to converge to an
-stationary point in expectation. In addition, extensive experiments
for a wide class of SMF formulations demonstrate that our framework
consistently yields faster convergence and a more accurate output dictionary
vis-\`a-vis state-of-the-art frameworks
Robust Bayesian Method for Simultaneous Block Sparse Signal Recovery with Applications to Face Recognition
In this paper, we present a novel Bayesian approach to recover simultaneously
block sparse signals in the presence of outliers. The key advantage of our
proposed method is the ability to handle non-stationary outliers, i.e. outliers
which have time varying support. We validate our approach with empirical
results showing the superiority of the proposed method over competing
approaches in synthetic data experiments as well as the multiple measurement
face recognition problem.Comment: To appear in ICIP 201
Low-Rank Modeling and Its Applications in Image Analysis
Low-rank modeling generally refers to a class of methods that solve problems
by representing variables of interest as low-rank matrices. It has achieved
great success in various fields including computer vision, data mining, signal
processing and bioinformatics. Recently, much progress has been made in
theories, algorithms and applications of low-rank modeling, such as exact
low-rank matrix recovery via convex programming and matrix completion applied
to collaborative filtering. These advances have brought more and more
attentions to this topic. In this paper, we review the recent advance of
low-rank modeling, the state-of-the-art algorithms, and related applications in
image analysis. We first give an overview to the concept of low-rank modeling
and challenging problems in this area. Then, we summarize the models and
algorithms for low-rank matrix recovery and illustrate their advantages and
limitations with numerical experiments. Next, we introduce a few applications
of low-rank modeling in the context of image analysis. Finally, we conclude
this paper with some discussions.Comment: To appear in ACM Computing Survey
Harvesting Entities from the Web Using Unique Identifiers -- IBEX
In this paper we study the prevalence of unique entity identifiers on the
Web. These are, e.g., ISBNs (for books), GTINs (for commercial products), DOIs
(for documents), email addresses, and others. We show how these identifiers can
be harvested systematically from Web pages, and how they can be associated with
human-readable names for the entities at large scale.
Starting with a simple extraction of identifiers and names from Web pages, we
show how we can use the properties of unique identifiers to filter out noise
and clean up the extraction result on the entire corpus. The end result is a
database of millions of uniquely identified entities of different types, with
an accuracy of 73--96% and a very high coverage compared to existing knowledge
bases. We use this database to compute novel statistics on the presence of
products, people, and other entities on the Web.Comment: 30 pages, 5 figures, 9 tables. Complete technical report for A.
Talaika, J. A. Biega, A. Amarilli, and F. M. Suchanek. IBEX: Harvesting
Entities from the Web Using Unique Identifiers. WebDB workshop, 201
Robust Sparse Coding via Self-Paced Learning
Sparse coding (SC) is attracting more and more attention due to its
comprehensive theoretical studies and its excellent performance in many signal
processing applications. However, most existing sparse coding algorithms are
nonconvex and are thus prone to becoming stuck into bad local minima,
especially when there are outliers and noisy data. To enhance the learning
robustness, in this paper, we propose a unified framework named Self-Paced
Sparse Coding (SPSC), which gradually include matrix elements into SC learning
from easy to complex. We also generalize the self-paced learning schema into
different levels of dynamic selection on samples, features and elements
respectively. Experimental results on real-world data demonstrate the efficacy
of the proposed algorithms.Comment: submitted to AAAI201
A survey of dimensionality reduction techniques
Experimental life sciences like biology or chemistry have seen in the recent
decades an explosion of the data available from experiments. Laboratory
instruments become more and more complex and report hundreds or thousands
measurements for a single experiment and therefore the statistical methods face
challenging tasks when dealing with such high dimensional data. However, much
of the data is highly redundant and can be efficiently brought down to a much
smaller number of variables without a significant loss of information. The
mathematical procedures making possible this reduction are called
dimensionality reduction techniques; they have widely been developed by fields
like Statistics or Machine Learning, and are currently a hot research topic. In
this review we categorize the plethora of dimension reduction techniques
available and give the mathematical insight behind them
A Fast Gradient Method for Nonnegative Sparse Regression with Self Dictionary
A nonnegative matrix factorization (NMF) can be computed efficiently under
the separability assumption, which asserts that all the columns of the given
input data matrix belong to the cone generated by a (small) subset of them. The
provably most robust methods to identify these conic basis columns are based on
nonnegative sparse regression and self dictionaries, and require the solution
of large-scale convex optimization problems. In this paper we study a
particular nonnegative sparse regression model with self dictionary. As opposed
to previously proposed models, this model yields a smooth optimization problem
where the sparsity is enforced through linear constraints. We show that the
Euclidean projection on the polyhedron defined by these constraints can be
computed efficiently, and propose a fast gradient method to solve our model. We
compare our algorithm with several state-of-the-art methods on synthetic data
sets and real-world hyperspectral images
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