15,805 research outputs found
Signal Classification under structure sparsity constraints
Object Classification is a key direction of research in signal and image
processing, computer vision and artificial intelligence. The goal is to come up
with algorithms that automatically analyze images and put them in predefined
categories. This dissertation focuses on the theory and application of sparse
signal processing and learning algorithms for image processing and computer
vision, especially object classification problems. A key emphasis of this work
is to formulate novel optimization problems for learning dictionary and
structured sparse representations. Tractable solutions are proposed
subsequently for the corresponding optimization problems.
An important goal of this dissertation is to demonstrate the wide
applications of these algorithmic tools for real-world applications. To that
end, we explored important problems in the areas of:
1. Medical imaging: histopathological images acquired from mammalian tissues,
human breast tissues, and human brain tissues.
2. Low-frequency (UHF to L-band) ultra-wideband (UWB) synthetic aperture
radar: detecting bombs and mines buried under rough surfaces.
3. General object classification: face, flowers, objects, dogs, indoor
scenes, etc.Comment: PhD Thesi
Structured Dictionary Learning for Classification
Sparsity driven signal processing has gained tremendous popularity in the
last decade. At its core, the assumption is that the signal of interest is
sparse with respect to either a fixed transformation or a signal dependent
dictionary. To better capture the data characteristics, various dictionary
learning methods have been proposed for both reconstruction and classification
tasks. For classification particularly, most approaches proposed so far have
focused on designing explicit constraints on the sparse code to improve
classification accuracy while simply adopting -norm or -norm for
sparsity regularization. Motivated by the success of structured sparsity in the
area of Compressed Sensing, we propose a structured dictionary learning
framework (StructDL) that incorporates the structure information on both group
and task levels in the learning process. Its benefits are two-fold: (i) the
label consistency between dictionary atoms and training data are implicitly
enforced; and (ii) the classification performance is more robust in the cases
of a small dictionary size or limited training data than other techniques.
Using the subspace model, we derive the conditions for StructDL to guarantee
the performance and show theoretically that StructDL is superior to -norm
or -norm regularized dictionary learning for classification. Extensive
experiments have been performed on both synthetic simulations and real world
applications, such as face recognition and object classification, to
demonstrate the validity of the proposed DL framework
Exploring Structure-Adaptive Graph Learning for Robust Semi-Supervised Classification
Graph Convolutional Neural Networks (GCNNs) are generalizations of CNNs to
graph-structured data, in which convolution is guided by the graph topology. In
many cases where graphs are unavailable, existing methods manually construct
graphs or learn task-driven adaptive graphs. In this paper, we propose Graph
Learning Neural Networks (GLNNs), which exploit the optimization of graphs (the
adjacency matrix in particular) from both data and tasks. Leveraging on
spectral graph theory, we propose the objective of graph learning from a
sparsity constraint, properties of a valid adjacency matrix as well as a graph
Laplacian regularizer via maximum a posteriori estimation. The optimization
objective is then integrated into the loss function of the GCNN, which adapts
the graph topology to not only labels of a specific task but also the input
data. Experimental results show that our proposed GLNN outperforms
state-of-the-art approaches over widely adopted social network datasets and
citation network datasets for semi-supervised classification
On The Projection Operator to A Three-view Cardinality Constrained Set
The cardinality constraint is an intrinsic way to restrict the solution
structure in many domains, for example, sparse learning, feature selection, and
compressed sensing. To solve a cardinality constrained problem, the key
challenge is to solve the projection onto the cardinality constraint set, which
is NP-hard in general when there exist multiple overlapped cardinality
constraints. In this paper, we consider the scenario where the overlapped
cardinality constraints satisfy a Three-view Cardinality Structure (TVCS),
which reflects the natural restriction in many applications, such as
identification of gene regulatory networks and task-worker assignment problem.
We cast the projection into a linear programming, and show that for TVCS, the
vertex solution of this linear programming is the solution for the original
projection problem. We further prove that such solution can be found with the
complexity proportional to the number of variables and constraints. We finally
use synthetic experiments and two interesting applications in bioinformatics
and crowdsourcing to validate the proposed TVCS model and method
Learning Discriminative Multilevel Structured Dictionaries for Supervised Image Classification
Sparse representations using overcomplete dictionaries have proved to be a
powerful tool in many signal processing applications such as denoising,
super-resolution, inpainting, compression or classification. The sparsity of
the representation very much depends on how well the dictionary is adapted to
the data at hand. In this paper, we propose a method for learning structured
multilevel dictionaries with discriminative constraints to make them well
suited for the supervised pixelwise classification of images. A multilevel
tree-structured discriminative dictionary is learnt for each class, with a
learning objective concerning the reconstruction errors of the image patches
around the pixels over each class-representative dictionary. After the initial
assignment of the class labels to image pixels based on their sparse
representations over the learnt dictionaries, the final classification is
achieved by smoothing the label image with a graph cut method and an erosion
method. Applied to a common set of texture images, our supervised
classification method shows competitive results with the state of the art
Weakly-supervised Dictionary Learning
We present a probabilistic modeling and inference framework for
discriminative analysis dictionary learning under a weak supervision setting.
Dictionary learning approaches have been widely used for tasks such as
low-level signal denoising and restoration as well as high-level classification
tasks, which can be applied to audio and image analysis. Synthesis dictionary
learning aims at jointly learning a dictionary and corresponding sparse
coefficients to provide accurate data representation. This approach is useful
for denoising and signal restoration, but may lead to sub-optimal
classification performance. By contrast, analysis dictionary learning provides
a transform that maps data to a sparse discriminative representation suitable
for classification. We consider the problem of analysis dictionary learning for
time-series data under a weak supervision setting in which signals are assigned
with a global label instead of an instantaneous label signal. We propose a
discriminative probabilistic model that incorporates both label information and
sparsity constraints on the underlying latent instantaneous label signal using
cardinality control. We present the expectation maximization (EM) procedure for
maximum likelihood estimation (MLE) of the proposed model. To facilitate a
computationally efficient E-step, we propose both a chain and a novel tree
graph reformulation of the graphical model. The performance of the proposed
model is demonstrated on both synthetic and real-world data
Classifying Multi-channel UWB SAR Imagery via Tensor Sparsity Learning Techniques
Using low-frequency (UHF to L-band) ultra-wideband (UWB) synthetic aperture
radar (SAR) technology for detecting buried and obscured targets, e.g. bomb or
mine, has been successfully demonstrated recently. Despite promising recent
progress, a significant open challenge is to distinguish obscured targets from
other (natural and manmade) clutter sources in the scene. The problem becomes
exacerbated in the presence of noisy responses from rough ground surfaces. In
this paper, we present three novel sparsity-driven techniques, which not only
exploit the subtle features of raw captured data but also take advantage of the
polarization diversity and the aspect angle dependence information from
multi-channel SAR data. First, the traditional sparse representation-based
classification (SRC) is generalized to exploit shared information of classes
and various sparsity structures of tensor coefficients for multi-channel data.
Corresponding tensor dictionary learning models are consequently proposed to
enhance classification accuracy. Lastly, a new tensor sparsity model is
proposed to model responses from multiple consecutive looks of objects, which
is a unique characteristic of the dataset we consider. Extensive experimental
results on a high-fidelity electromagnetic simulated dataset and radar data
collected from the U.S. Army Research Laboratory side-looking SAR demonstrate
the advantages of proposed tensor sparsity models
Collaborative Multi-sensor Classification via Sparsity-based Representation
In this paper, we propose a general collaborative sparse representation
framework for multi-sensor classification, which takes into account the
correlations as well as complementary information between heterogeneous sensors
simultaneously while considering joint sparsity within each sensor's
observations. We also robustify our models to deal with the presence of sparse
noise and low-rank interference signals. Specifically, we demonstrate that
incorporating the noise or interference signal as a low-rank component in our
models is essential in a multi-sensor classification problem when multiple
co-located sources/sensors simultaneously record the same physical event. We
further extend our frameworks to kernelized models which rely on sparsely
representing a test sample in terms of all the training samples in a feature
space induced by a kernel function. A fast and efficient algorithm based on
alternative direction method is proposed where its convergence to an optimal
solution is guaranteed. Extensive experiments are conducted on several real
multi-sensor data sets and results are compared with the conventional
classifiers to verify the effectiveness of the proposed methods
Manifold-Based Signal Recovery and Parameter Estimation from Compressive Measurements
A field known as Compressive Sensing (CS) has recently emerged to help
address the growing challenges of capturing and processing high-dimensional
signals and data sets. CS exploits the surprising fact that the information
contained in a sparse signal can be preserved in a small number of compressive
(or random) linear measurements of that signal. Strong theoretical guarantees
have been established on the accuracy to which sparse or near-sparse signals
can be recovered from noisy compressive measurements. In this paper, we address
similar questions in the context of a different modeling framework. Instead of
sparse models, we focus on the broad class of manifold models, which can arise
in both parametric and non-parametric signal families. Building upon recent
results concerning the stable embeddings of manifolds within the measurement
space, we establish both deterministic and probabilistic instance-optimal
bounds in for manifold-based signal recovery and parameter estimation
from noisy compressive measurements. In line with analogous results for
sparsity-based CS, we conclude that much stronger bounds are possible in the
probabilistic setting. Our work supports the growing empirical evidence that
manifold-based models can be used with high accuracy in compressive signal
processing
Sparse Deep Nonnegative Matrix Factorization
Nonnegative matrix factorization is a powerful technique to realize dimension
reduction and pattern recognition through single-layer data representation
learning. Deep learning, however, with its carefully designed hierarchical
structure, is able to combine hidden features to form more representative
features for pattern recognition. In this paper, we proposed sparse deep
nonnegative matrix factorization models to analyze complex data for more
accurate classification and better feature interpretation. Such models are
designed to learn localized features or generate more discriminative
representations for samples in distinct classes by imposing -norm penalty
on the columns of certain factors. By extending one-layer model into
multi-layer one with sparsity, we provided a hierarchical way to analyze big
data and extract hidden features intuitively due to nonnegativity. We adopted
the Nesterov's accelerated gradient algorithm to accelerate the computing
process with the convergence rate of after steps iteration. We
also analyzed the computing complexity of our framework to demonstrate their
efficiency. To improve the performance of dealing with linearly inseparable
data, we also considered to incorporate popular nonlinear functions into this
framework and explored their performance. We applied our models onto two
benchmarking image datasets, demonstrating our models can achieve competitive
or better classification performance and produce intuitive interpretations
compared with the typical NMF and competing multi-layer models.Comment: 13 pages, 8 figure
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