381 research outputs found
Sparse Modeling for Image and Vision Processing
In recent years, a large amount of multi-disciplinary research has been
conducted on sparse models and their applications. In statistics and machine
learning, the sparsity principle is used to perform model selection---that is,
automatically selecting a simple model among a large collection of them. In
signal processing, sparse coding consists of representing data with linear
combinations of a few dictionary elements. Subsequently, the corresponding
tools have been widely adopted by several scientific communities such as
neuroscience, bioinformatics, or computer vision. The goal of this monograph is
to offer a self-contained view of sparse modeling for visual recognition and
image processing. More specifically, we focus on applications where the
dictionary is learned and adapted to data, yielding a compact representation
that has been successful in various contexts.Comment: 205 pages, to appear in Foundations and Trends in Computer Graphics
and Visio
Linear dimensionality reduction: Survey, insights, and generalizations
Linear dimensionality reduction methods are a cornerstone of analyzing high
dimensional data, due to their simple geometric interpretations and typically
attractive computational properties. These methods capture many data features
of interest, such as covariance, dynamical structure, correlation between data
sets, input-output relationships, and margin between data classes. Methods have
been developed with a variety of names and motivations in many fields, and
perhaps as a result the connections between all these methods have not been
highlighted. Here we survey methods from this disparate literature as
optimization programs over matrix manifolds. We discuss principal component
analysis, factor analysis, linear multidimensional scaling, Fisher's linear
discriminant analysis, canonical correlations analysis, maximum autocorrelation
factors, slow feature analysis, sufficient dimensionality reduction,
undercomplete independent component analysis, linear regression, distance
metric learning, and more. This optimization framework gives insight to some
rarely discussed shortcomings of well-known methods, such as the suboptimality
of certain eigenvector solutions. Modern techniques for optimization over
matrix manifolds enable a generic linear dimensionality reduction solver, which
accepts as input data and an objective to be optimized, and returns, as output,
an optimal low-dimensional projection of the data. This simple optimization
framework further allows straightforward generalizations and novel variants of
classical methods, which we demonstrate here by creating an
orthogonal-projection canonical correlations analysis. More broadly, this
survey and generic solver suggest that linear dimensionality reduction can move
toward becoming a blackbox, objective-agnostic numerical technology.JPC and ZG received funding from the UK Engineering and Physical Sciences Research Council (EPSRC EP/H019472/1). JPC received funding from a Sloan Research Fellowship, the Simons Foundation (SCGB#325171 and SCGB#325233), the Grossman Center at Columbia University, and the Gatsby Charitable Trust.This is the author accepted manuscript. The final version is available from MIT Press via http://jmlr.org/papers/v16/cunningham15a.htm
A Personalized Zero-Shot ECG Arrhythmia Monitoring System: From Sparse Representation Based Domain Adaption to Energy Efficient Abnormal Beat Detection for Practical ECG Surveillance
This paper proposes a low-cost and highly accurate ECG-monitoring system
intended for personalized early arrhythmia detection for wearable mobile
sensors. Earlier supervised approaches for personalized ECG monitoring require
both abnormal and normal heartbeats for the training of the dedicated
classifier. However, in a real-world scenario where the personalized algorithm
is embedded in a wearable device, such training data is not available for
healthy people with no cardiac disorder history. In this study, (i) we propose
a null space analysis on the healthy signal space obtained via sparse
dictionary learning, and investigate how a simple null space projection or
alternatively regularized least squares-based classification methods can reduce
the computational complexity, without sacrificing the detection accuracy, when
compared to sparse representation-based classification. (ii) Then we introduce
a sparse representation-based domain adaptation technique in order to project
other existing users' abnormal and normal signals onto the new user's signal
space, enabling us to train the dedicated classifier without having any
abnormal heartbeat of the new user. Therefore, zero-shot learning can be
achieved without the need for synthetic abnormal heartbeat generation. An
extensive set of experiments performed on the benchmark MIT-BIH ECG dataset
shows that when this domain adaptation-based training data generator is used
with a simple 1-D CNN classifier, the method outperforms the prior work by a
significant margin. (iii) Then, by combining (i) and (ii), we propose an
ensemble classifier that further improves the performance. This approach for
zero-shot arrhythmia detection achieves an average accuracy level of 98.2% and
an F1-Score of 92.8%. Finally, a personalized energy-efficient ECG monitoring
scheme is proposed using the above-mentioned innovations.Comment: Software implementation: https://github.com/MertDuman/Zero-Shot-EC
Automatic Music Transcription using Structure and Sparsity
PhdAutomatic Music Transcription seeks a machine understanding of a musical signal in terms of
pitch-time activations. One popular approach to this problem is the use of spectrogram decompositions,
whereby a signal matrix is decomposed over a dictionary of spectral templates, each
representing a note. Typically the decomposition is performed using gradient descent based
methods, performed using multiplicative updates based on Non-negative Matrix Factorisation
(NMF). The final representation may be expected to be sparse, as the musical signal itself is considered
to consist of few active notes. In this thesis some concepts that are familiar in the sparse
representations literature are introduced to the AMT problem. Structured sparsity assumes that
certain atoms tend to be active together. In the context of AMT this affords the use of subspace
modelling of notes, and non-negative group sparse algorithms are proposed in order to exploit
the greater modelling capability introduced. Stepwise methods are often used for decomposing
sparse signals and their use for AMT has previously been limited. Some new approaches to
AMT are proposed by incorporation of stepwise optimal approaches with promising results seen.
Dictionary coherence is used to provide recovery conditions for sparse algorithms. While such
guarantees are not possible in the context of AMT, it is found that coherence is a useful parameter
to consider, affording improved performance in spectrogram decompositions
Tensor Regression
Regression analysis is a key area of interest in the field of data analysis
and machine learning which is devoted to exploring the dependencies between
variables, often using vectors. The emergence of high dimensional data in
technologies such as neuroimaging, computer vision, climatology and social
networks, has brought challenges to traditional data representation methods.
Tensors, as high dimensional extensions of vectors, are considered as natural
representations of high dimensional data. In this book, the authors provide a
systematic study and analysis of tensor-based regression models and their
applications in recent years. It groups and illustrates the existing
tensor-based regression methods and covers the basics, core ideas, and
theoretical characteristics of most tensor-based regression methods. In
addition, readers can learn how to use existing tensor-based regression methods
to solve specific regression tasks with multiway data, what datasets can be
selected, and what software packages are available to start related work as
soon as possible. Tensor Regression is the first thorough overview of the
fundamentals, motivations, popular algorithms, strategies for efficient
implementation, related applications, available datasets, and software
resources for tensor-based regression analysis. It is essential reading for all
students, researchers and practitioners of working on high dimensional data.Comment: 187 pages, 32 figures, 10 table
- …