2,748 research outputs found
Collaborative Representation based Classification for Face Recognition
By coding a query sample as a sparse linear combination of all training
samples and then classifying it by evaluating which class leads to the minimal
coding residual, sparse representation based classification (SRC) leads to
interesting results for robust face recognition. It is widely believed that the
l1- norm sparsity constraint on coding coefficients plays a key role in the
success of SRC, while its use of all training samples to collaboratively
represent the query sample is rather ignored. In this paper we discuss how SRC
works, and show that the collaborative representation mechanism used in SRC is
much more crucial to its success of face classification. The SRC is a special
case of collaborative representation based classification (CRC), which has
various instantiations by applying different norms to the coding residual and
coding coefficient. More specifically, the l1 or l2 norm characterization of
coding residual is related to the robustness of CRC to outlier facial pixels,
while the l1 or l2 norm characterization of coding coefficient is related to
the degree of discrimination of facial features. Extensive experiments were
conducted to verify the face recognition accuracy and efficiency of CRC with
different instantiations.Comment: It is a substantial revision of a previous conference paper (L.
Zhang, M. Yang, et al. "Sparse Representation or Collaborative
Representation: Which Helps Face Recognition?" in ICCV 2011
On the Effective Measure of Dimension in the Analysis Cosparse Model
Many applications have benefited remarkably from low-dimensional models in
the recent decade. The fact that many signals, though high dimensional, are
intrinsically low dimensional has given the possibility to recover them stably
from a relatively small number of their measurements. For example, in
compressed sensing with the standard (synthesis) sparsity prior and in matrix
completion, the number of measurements needed is proportional (up to a
logarithmic factor) to the signal's manifold dimension.
Recently, a new natural low-dimensional signal model has been proposed: the
cosparse analysis prior. In the noiseless case, it is possible to recover
signals from this model, using a combinatorial search, from a number of
measurements proportional to the signal's manifold dimension. However, if we
ask for stability to noise or an efficient (polynomial complexity) solver, all
the existing results demand a number of measurements which is far removed from
the manifold dimension, sometimes far greater. Thus, it is natural to ask
whether this gap is a deficiency of the theory and the solvers, or if there
exists a real barrier in recovering the cosparse signals by relying only on
their manifold dimension. Is there an algorithm which, in the presence of
noise, can accurately recover a cosparse signal from a number of measurements
proportional to the manifold dimension? In this work, we prove that there is no
such algorithm. Further, we show through numerical simulations that even in the
noiseless case convex relaxations fail when the number of measurements is
comparable to the manifold dimension. This gives a practical counter-example to
the growing literature on compressed acquisition of signals based on manifold
dimension.Comment: 19 pages, 6 figure
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