2,365 research outputs found
Manifold Constrained Low-Rank Decomposition
Low-rank decomposition (LRD) is a state-of-the-art method for visual data
reconstruction and modelling. However, it is a very challenging problem when
the image data contains significant occlusion, noise, illumination variation,
and misalignment from rotation or viewpoint changes. We leverage the specific
structure of data in order to improve the performance of LRD when the data are
not ideal. To this end, we propose a new framework that embeds manifold priors
into LRD. To implement the framework, we design an alternating direction method
of multipliers (ADMM) method which efficiently integrates the manifold
constraints during the optimization process. The proposed approach is
successfully used to calculate low-rank models from face images, hand-written
digits and planar surface images. The results show a consistent increase of
performance when compared to the state-of-the-art over a wide range of
realistic image misalignments and corruptions
OL\'E: Orthogonal Low-rank Embedding, A Plug and Play Geometric Loss for Deep Learning
Deep neural networks trained using a softmax layer at the top and the
cross-entropy loss are ubiquitous tools for image classification. Yet, this
does not naturally enforce intra-class similarity nor inter-class margin of the
learned deep representations. To simultaneously achieve these two goals,
different solutions have been proposed in the literature, such as the pairwise
or triplet losses. However, such solutions carry the extra task of selecting
pairs or triplets, and the extra computational burden of computing and learning
for many combinations of them. In this paper, we propose a plug-and-play loss
term for deep networks that explicitly reduces intra-class variance and
enforces inter-class margin simultaneously, in a simple and elegant geometric
manner. For each class, the deep features are collapsed into a learned linear
subspace, or union of them, and inter-class subspaces are pushed to be as
orthogonal as possible. Our proposed Orthogonal Low-rank Embedding (OL\'E) does
not require carefully crafting pairs or triplets of samples for training, and
works standalone as a classification loss, being the first reported deep metric
learning framework of its kind. Because of the improved margin between features
of different classes, the resulting deep networks generalize better, are more
discriminative, and more robust. We demonstrate improved classification
performance in general object recognition, plugging the proposed loss term into
existing off-the-shelf architectures. In particular, we show the advantage of
the proposed loss in the small data/model scenario, and we significantly
advance the state-of-the-art on the Stanford STL-10 benchmark
Masking Strategies for Image Manifolds
We consider the problem of selecting an optimal mask for an image manifold,
i.e., choosing a subset of the pixels of the image that preserves the
manifold's geometric structure present in the original data. Such masking
implements a form of compressive sensing through emerging imaging sensor
platforms for which the power expense grows with the number of pixels acquired.
Our goal is for the manifold learned from masked images to resemble its full
image counterpart as closely as possible. More precisely, we show that one can
indeed accurately learn an image manifold without having to consider a large
majority of the image pixels. In doing so, we consider two masking methods that
preserve the local and global geometric structure of the manifold,
respectively. In each case, the process of finding the optimal masking pattern
can be cast as a binary integer program, which is computationally expensive but
can be approximated by a fast greedy algorithm. Numerical experiments show that
the relevant manifold structure is preserved through the data-dependent masking
process, even for modest mask sizes
Adaptive Locality Preserving Regression
This paper proposes a novel discriminative regression method, called adaptive
locality preserving regression (ALPR) for classification. In particular, ALPR
aims to learn a more flexible and discriminative projection that not only
preserves the intrinsic structure of data, but also possesses the properties of
feature selection and interpretability. To this end, we introduce a target
learning technique to adaptively learn a more discriminative and flexible
target matrix rather than the pre-defined strict zero-one label matrix for
regression. Then a locality preserving constraint regularized by the adaptive
learned weights is further introduced to guide the projection learning, which
is beneficial to learn a more discriminative projection and avoid overfitting.
Moreover, we replace the conventional `Frobenius norm' with the special l21
norm to constrain the projection, which enables the method to adaptively select
the most important features from the original high-dimensional data for feature
extraction. In this way, the negative influence of the redundant features and
noises residing in the original data can be greatly eliminated. Besides, the
proposed method has good interpretability for features owing to the
row-sparsity property of the l21 norm. Extensive experiments conducted on the
synthetic database with manifold structure and many real-world databases prove
the effectiveness of the proposed method.Comment: The paper has been accepted by IEEE Transactions on Circuits and
Systems for Video Technology (TCSVT), and the code can be available at
https://drive.google.com/file/d/1iNzONkRByIaUhXwdEhOkkh_0d2AAXNE8/vie
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