2,075 research outputs found
Multiclass Semi-Supervised Learning on Graphs using Ginzburg-Landau Functional Minimization
We present a graph-based variational algorithm for classification of
high-dimensional data, generalizing the binary diffuse interface model to the
case of multiple classes. Motivated by total variation techniques, the method
involves minimizing an energy functional made up of three terms. The first two
terms promote a stepwise continuous classification function with sharp
transitions between classes, while preserving symmetry among the class labels.
The third term is a data fidelity term, allowing us to incorporate prior
information into the model in a semi-supervised framework. The performance of
the algorithm on synthetic data, as well as on the COIL and MNIST benchmark
datasets, is competitive with state-of-the-art graph-based multiclass
segmentation methods.Comment: 16 pages, to appear in Springer's Lecture Notes in Computer Science
volume "Pattern Recognition Applications and Methods 2013", part of series on
Advances in Intelligent and Soft Computin
Error Bounds for Piecewise Smooth and Switching Regression
The paper deals with regression problems, in which the nonsmooth target is
assumed to switch between different operating modes. Specifically, piecewise
smooth (PWS) regression considers target functions switching deterministically
via a partition of the input space, while switching regression considers
arbitrary switching laws. The paper derives generalization error bounds in
these two settings by following the approach based on Rademacher complexities.
For PWS regression, our derivation involves a chaining argument and a
decomposition of the covering numbers of PWS classes in terms of the ones of
their component functions and the capacity of the classifier partitioning the
input space. This yields error bounds with a radical dependency on the number
of modes. For switching regression, the decomposition can be performed directly
at the level of the Rademacher complexities, which yields bounds with a linear
dependency on the number of modes. By using once more chaining and a
decomposition at the level of covering numbers, we show how to recover a
radical dependency. Examples of applications are given in particular for PWS
and swichting regression with linear and kernel-based component functions.Comment: This work has been submitted to the IEEE for possible publication.
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Detecting Semantic Parts on Partially Occluded Objects
In this paper, we address the task of detecting semantic parts on partially
occluded objects. We consider a scenario where the model is trained using
non-occluded images but tested on occluded images. The motivation is that there
are infinite number of occlusion patterns in real world, which cannot be fully
covered in the training data. So the models should be inherently robust and
adaptive to occlusions instead of fitting / learning the occlusion patterns in
the training data. Our approach detects semantic parts by accumulating the
confidence of local visual cues. Specifically, the method uses a simple voting
method, based on log-likelihood ratio tests and spatial constraints, to combine
the evidence of local cues. These cues are called visual concepts, which are
derived by clustering the internal states of deep networks. We evaluate our
voting scheme on the VehicleSemanticPart dataset with dense part annotations.
We randomly place two, three or four irrelevant objects onto the target object
to generate testing images with various occlusions. Experiments show that our
algorithm outperforms several competitors in semantic part detection when
occlusions are present.Comment: Accepted to BMVC 2017 (13 pages, 3 figures
Extrinsic Methods for Coding and Dictionary Learning on Grassmann Manifolds
Sparsity-based representations have recently led to notable results in
various visual recognition tasks. In a separate line of research, Riemannian
manifolds have been shown useful for dealing with features and models that do
not lie in Euclidean spaces. With the aim of building a bridge between the two
realms, we address the problem of sparse coding and dictionary learning over
the space of linear subspaces, which form Riemannian structures known as
Grassmann manifolds. To this end, we propose to embed Grassmann manifolds into
the space of symmetric matrices by an isometric mapping. This in turn enables
us to extend two sparse coding schemes to Grassmann manifolds. Furthermore, we
propose closed-form solutions for learning a Grassmann dictionary, atom by
atom. Lastly, to handle non-linearity in data, we extend the proposed Grassmann
sparse coding and dictionary learning algorithms through embedding into Hilbert
spaces.
Experiments on several classification tasks (gender recognition, gesture
classification, scene analysis, face recognition, action recognition and
dynamic texture classification) show that the proposed approaches achieve
considerable improvements in discrimination accuracy, in comparison to
state-of-the-art methods such as kernelized Affine Hull Method and
graph-embedding Grassmann discriminant analysis.Comment: Appearing in International Journal of Computer Visio
Deep Divergence-Based Approach to Clustering
A promising direction in deep learning research consists in learning
representations and simultaneously discovering cluster structure in unlabeled
data by optimizing a discriminative loss function. As opposed to supervised
deep learning, this line of research is in its infancy, and how to design and
optimize suitable loss functions to train deep neural networks for clustering
is still an open question. Our contribution to this emerging field is a new
deep clustering network that leverages the discriminative power of
information-theoretic divergence measures, which have been shown to be
effective in traditional clustering. We propose a novel loss function that
incorporates geometric regularization constraints, thus avoiding degenerate
structures of the resulting clustering partition. Experiments on synthetic
benchmarks and real datasets show that the proposed network achieves
competitive performance with respect to other state-of-the-art methods, scales
well to large datasets, and does not require pre-training steps
Convolutional Color Constancy
Color constancy is the problem of inferring the color of the light that
illuminated a scene, usually so that the illumination color can be removed.
Because this problem is underconstrained, it is often solved by modeling the
statistical regularities of the colors of natural objects and illumination. In
contrast, in this paper we reformulate the problem of color constancy as a 2D
spatial localization task in a log-chrominance space, thereby allowing us to
apply techniques from object detection and structured prediction to the color
constancy problem. By directly learning how to discriminate between correctly
white-balanced images and poorly white-balanced images, our model is able to
improve performance on standard benchmarks by nearly 40%
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