10 research outputs found
Separable Cosparse Analysis Operator Learning
The ability of having a sparse representation for a certain class of signals
has many applications in data analysis, image processing, and other research
fields. Among sparse representations, the cosparse analysis model has recently
gained increasing interest. Many signals exhibit a multidimensional structure,
e.g. images or three-dimensional MRI scans. Most data analysis and learning
algorithms use vectorized signals and thereby do not account for this
underlying structure. The drawback of not taking the inherent structure into
account is a dramatic increase in computational cost. We propose an algorithm
for learning a cosparse Analysis Operator that adheres to the preexisting
structure of the data, and thus allows for a very efficient implementation.
This is achieved by enforcing a separable structure on the learned operator.
Our learning algorithm is able to deal with multidimensional data of arbitrary
order. We evaluate our method on volumetric data at the example of
three-dimensional MRI scans.Comment: 5 pages, 3 figures, accepted at EUSIPCO 201
Learning Co-Sparse Analysis Operators with Separable Structures
In the co-sparse analysis model a set of filters is applied to a signal out
of the signal class of interest yielding sparse filter responses. As such, it
may serve as a prior in inverse problems, or for structural analysis of signals
that are known to belong to the signal class. The more the model is adapted to
the class, the more reliable it is for these purposes. The task of learning
such operators for a given class is therefore a crucial problem. In many
applications, it is also required that the filter responses are obtained in a
timely manner, which can be achieved by filters with a separable structure. Not
only can operators of this sort be efficiently used for computing the filter
responses, but they also have the advantage that less training samples are
required to obtain a reliable estimate of the operator. The first contribution
of this work is to give theoretical evidence for this claim by providing an
upper bound for the sample complexity of the learning process. The second is a
stochastic gradient descent (SGD) method designed to learn an analysis operator
with separable structures, which includes a novel and efficient step size
selection rule. Numerical experiments are provided that link the sample
complexity to the convergence speed of the SGD algorithm.Comment: 11 pages double column, 4 figures, 3 table
Knowledge Augmented Machine Learning with Applications in Autonomous Driving: A Survey
The existence of representative datasets is a prerequisite of many successful artificial intelligence and machine learning models. However, the subsequent application of these models often involves scenarios that are inadequately represented in the data used for training. The reasons for this are manifold and range from time and cost constraints to ethical considerations. As a consequence, the reliable use of these models, especially in safety-critical applications, is a huge challenge. Leveraging additional, already existing sources of knowledge is key to overcome the limitations of purely data-driven approaches, and eventually to increase the generalization capability of these models. Furthermore, predictions that conform with knowledge are crucial for making trustworthy and safe decisions even in underrepresented scenarios. This work provides an overview of existing techniques and methods in the literature that combine data-based models with existing knowledge. The identified approaches are structured according to the categories integration, extraction and conformity. Special attention is given to applications in the field of autonomous driving
Knowledge Augmented Machine Learning with Applications in Autonomous Driving: A Survey
The existence of representative datasets is a prerequisite of many successful
artificial intelligence and machine learning models. However, the subsequent
application of these models often involves scenarios that are inadequately
represented in the data used for training. The reasons for this are manifold
and range from time and cost constraints to ethical considerations. As a
consequence, the reliable use of these models, especially in safety-critical
applications, is a huge challenge. Leveraging additional, already existing
sources of knowledge is key to overcome the limitations of purely data-driven
approaches, and eventually to increase the generalization capability of these
models. Furthermore, predictions that conform with knowledge are crucial for
making trustworthy and safe decisions even in underrepresented scenarios. This
work provides an overview of existing techniques and methods in the literature
that combine data-based models with existing knowledge. The identified
approaches are structured according to the categories integration, extraction
and conformity. Special attention is given to applications in the field of
autonomous driving.Comment: 93 page