1,301 research outputs found
PADDLE: Proximal Algorithm for Dual Dictionaries LEarning
Recently, considerable research efforts have been devoted to the design of
methods to learn from data overcomplete dictionaries for sparse coding.
However, learned dictionaries require the solution of an optimization problem
for coding new data. In order to overcome this drawback, we propose an
algorithm aimed at learning both a dictionary and its dual: a linear mapping
directly performing the coding. By leveraging on proximal methods, our
algorithm jointly minimizes the reconstruction error of the dictionary and the
coding error of its dual; the sparsity of the representation is induced by an
-based penalty on its coefficients. The results obtained on synthetic
data and real images show that the algorithm is capable of recovering the
expected dictionaries. Furthermore, on a benchmark dataset, we show that the
image features obtained from the dual matrix yield state-of-the-art
classification performance while being much less computational intensive
Entropy of Overcomplete Kernel Dictionaries
In signal analysis and synthesis, linear approximation theory considers a
linear decomposition of any given signal in a set of atoms, collected into a
so-called dictionary. Relevant sparse representations are obtained by relaxing
the orthogonality condition of the atoms, yielding overcomplete dictionaries
with an extended number of atoms. More generally than the linear decomposition,
overcomplete kernel dictionaries provide an elegant nonlinear extension by
defining the atoms through a mapping kernel function (e.g., the gaussian
kernel). Models based on such kernel dictionaries are used in neural networks,
gaussian processes and online learning with kernels.
The quality of an overcomplete dictionary is evaluated with a diversity
measure the distance, the approximation, the coherence and the Babel measures.
In this paper, we develop a framework to examine overcomplete kernel
dictionaries with the entropy from information theory. Indeed, a higher value
of the entropy is associated to a further uniform spread of the atoms over the
space. For each of the aforementioned diversity measures, we derive lower
bounds on the entropy. Several definitions of the entropy are examined, with an
extensive analysis in both the input space and the mapped feature space.Comment: 10 page
Score Function Features for Discriminative Learning: Matrix and Tensor Framework
Feature learning forms the cornerstone for tackling challenging learning
problems in domains such as speech, computer vision and natural language
processing. In this paper, we consider a novel class of matrix and
tensor-valued features, which can be pre-trained using unlabeled samples. We
present efficient algorithms for extracting discriminative information, given
these pre-trained features and labeled samples for any related task. Our class
of features are based on higher-order score functions, which capture local
variations in the probability density function of the input. We establish a
theoretical framework to characterize the nature of discriminative information
that can be extracted from score-function features, when used in conjunction
with labeled samples. We employ efficient spectral decomposition algorithms (on
matrices and tensors) for extracting discriminative components. The advantage
of employing tensor-valued features is that we can extract richer
discriminative information in the form of an overcomplete representations.
Thus, we present a novel framework for employing generative models of the input
for discriminative learning.Comment: 29 page
Parametric dictionary design for sparse coding
Abstract—This paper introduces a new dictionary design method for sparse coding of a class of signals. It has been shown that one can sparsely approximate some natural signals using an overcomplete set of parametric functions, e.g. [1], [2]. A problem in using these parametric dictionaries is how to choose the parameters. In practice these parameters have been chosen by an expert or through a set of experiments. In the sparse approximation context, it has been shown that an incoherent dictionary is appropriate for the sparse approximation methods. In this paper we first characterize the dictionary design problem, subject to a constraint on the dictionary. Then we briefly explain that equiangular tight frames have minimum coherence. The complexity of the problem does not allow it to be solved exactly. We introduce a practical method to approximately solve it. Some experiments show the advantages one gets by using these dictionaries
Learning sparse representations of depth
This paper introduces a new method for learning and inferring sparse
representations of depth (disparity) maps. The proposed algorithm relaxes the
usual assumption of the stationary noise model in sparse coding. This enables
learning from data corrupted with spatially varying noise or uncertainty,
typically obtained by laser range scanners or structured light depth cameras.
Sparse representations are learned from the Middlebury database disparity maps
and then exploited in a two-layer graphical model for inferring depth from
stereo, by including a sparsity prior on the learned features. Since they
capture higher-order dependencies in the depth structure, these priors can
complement smoothness priors commonly used in depth inference based on Markov
Random Field (MRF) models. Inference on the proposed graph is achieved using an
alternating iterative optimization technique, where the first layer is solved
using an existing MRF-based stereo matching algorithm, then held fixed as the
second layer is solved using the proposed non-stationary sparse coding
algorithm. This leads to a general method for improving solutions of state of
the art MRF-based depth estimation algorithms. Our experimental results first
show that depth inference using learned representations leads to state of the
art denoising of depth maps obtained from laser range scanners and a time of
flight camera. Furthermore, we show that adding sparse priors improves the
results of two depth estimation methods: the classical graph cut algorithm by
Boykov et al. and the more recent algorithm of Woodford et al.Comment: 12 page
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