5,051 research outputs found
Geometry-Aware Neighborhood Search for Learning Local Models for Image Reconstruction
Local learning of sparse image models has proven to be very effective to
solve inverse problems in many computer vision applications. To learn such
models, the data samples are often clustered using the K-means algorithm with
the Euclidean distance as a dissimilarity metric. However, the Euclidean
distance may not always be a good dissimilarity measure for comparing data
samples lying on a manifold. In this paper, we propose two algorithms for
determining a local subset of training samples from which a good local model
can be computed for reconstructing a given input test sample, where we take
into account the underlying geometry of the data. The first algorithm, called
Adaptive Geometry-driven Nearest Neighbor search (AGNN), is an adaptive scheme
which can be seen as an out-of-sample extension of the replicator graph
clustering method for local model learning. The second method, called
Geometry-driven Overlapping Clusters (GOC), is a less complex nonadaptive
alternative for training subset selection. The proposed AGNN and GOC methods
are evaluated in image super-resolution, deblurring and denoising applications
and shown to outperform spectral clustering, soft clustering, and geodesic
distance based subset selection in most settings.Comment: 15 pages, 10 figures and 5 table
Geometric robustness of deep networks: analysis and improvement
Deep convolutional neural networks have been shown to be vulnerable to
arbitrary geometric transformations. However, there is no systematic method to
measure the invariance properties of deep networks to such transformations. We
propose ManiFool as a simple yet scalable algorithm to measure the invariance
of deep networks. In particular, our algorithm measures the robustness of deep
networks to geometric transformations in a worst-case regime as they can be
problematic for sensitive applications. Our extensive experimental results show
that ManiFool can be used to measure the invariance of fairly complex networks
on high dimensional datasets and these values can be used for analyzing the
reasons for it. Furthermore, we build on Manifool to propose a new adversarial
training scheme and we show its effectiveness on improving the invariance
properties of deep neural networks
Manitest: Are classifiers really invariant?
Invariance to geometric transformations is a highly desirable property of
automatic classifiers in many image recognition tasks. Nevertheless, it is
unclear to which extent state-of-the-art classifiers are invariant to basic
transformations such as rotations and translations. This is mainly due to the
lack of general methods that properly measure such an invariance. In this
paper, we propose a rigorous and systematic approach for quantifying the
invariance to geometric transformations of any classifier. Our key idea is to
cast the problem of assessing a classifier's invariance as the computation of
geodesics along the manifold of transformed images. We propose the Manitest
method, built on the efficient Fast Marching algorithm to compute the
invariance of classifiers. Our new method quantifies in particular the
importance of data augmentation for learning invariance from data, and the
increased invariance of convolutional neural networks with depth. We foresee
that the proposed generic tool for measuring invariance to a large class of
geometric transformations and arbitrary classifiers will have many applications
for evaluating and comparing classifiers based on their invariance, and help
improving the invariance of existing classifiers.Comment: BMVC 201
Bayesian Inference on Matrix Manifolds for Linear Dimensionality Reduction
We reframe linear dimensionality reduction as a problem of Bayesian inference
on matrix manifolds. This natural paradigm extends the Bayesian framework to
dimensionality reduction tasks in higher dimensions with simpler models at
greater speeds. Here an orthogonal basis is treated as a single point on a
manifold and is associated with a linear subspace on which observations vary
maximally. Throughout this paper, we employ the Grassmann and Stiefel manifolds
for various dimensionality reduction problems, explore the connection between
the two manifolds, and use Hybrid Monte Carlo for posterior sampling on the
Grassmannian for the first time. We delineate in which situations either
manifold should be considered. Further, matrix manifold models are used to
yield scientific insight in the context of cognitive neuroscience, and we
conclude that our methods are suitable for basic inference as well as accurate
prediction.Comment: All datasets and computer programs are publicly available at
http://www.ics.uci.edu/~babaks/Site/Codes.htm
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