775,522 research outputs found
Semi-Supervised Sparse Coding
Sparse coding approximates the data sample as a sparse linear combination of
some basic codewords and uses the sparse codes as new presentations. In this
paper, we investigate learning discriminative sparse codes by sparse coding in
a semi-supervised manner, where only a few training samples are labeled. By
using the manifold structure spanned by the data set of both labeled and
unlabeled samples and the constraints provided by the labels of the labeled
samples, we learn the variable class labels for all the samples. Furthermore,
to improve the discriminative ability of the learned sparse codes, we assume
that the class labels could be predicted from the sparse codes directly using a
linear classifier. By solving the codebook, sparse codes, class labels and
classifier parameters simultaneously in a unified objective function, we
develop a semi-supervised sparse coding algorithm. Experiments on two
real-world pattern recognition problems demonstrate the advantage of the
proposed methods over supervised sparse coding methods on partially labeled
data sets
Fast Parallel Randomized Algorithm for Nonnegative Matrix Factorization with KL Divergence for Large Sparse Datasets
Nonnegative Matrix Factorization (NMF) with Kullback-Leibler Divergence
(NMF-KL) is one of the most significant NMF problems and equivalent to
Probabilistic Latent Semantic Indexing (PLSI), which has been successfully
applied in many applications. For sparse count data, a Poisson distribution and
KL divergence provide sparse models and sparse representation, which describe
the random variation better than a normal distribution and Frobenius norm.
Specially, sparse models provide more concise understanding of the appearance
of attributes over latent components, while sparse representation provides
concise interpretability of the contribution of latent components over
instances. However, minimizing NMF with KL divergence is much more difficult
than minimizing NMF with Frobenius norm; and sparse models, sparse
representation and fast algorithms for large sparse datasets are still
challenges for NMF with KL divergence. In this paper, we propose a fast
parallel randomized coordinate descent algorithm having fast convergence for
large sparse datasets to archive sparse models and sparse representation. The
proposed algorithm's experimental results overperform the current studies' ones
in this problem
Sparse Recovery with Very Sparse Compressed Counting
Compressed sensing (sparse signal recovery) often encounters nonnegative data
(e.g., images). Recently we developed the methodology of using (dense)
Compressed Counting for recovering nonnegative K-sparse signals. In this paper,
we adopt very sparse Compressed Counting for nonnegative signal recovery. Our
design matrix is sampled from a maximally-skewed p-stable distribution (0<p<1),
and we sparsify the design matrix so that on average (1-g)-fraction of the
entries become zero. The idea is related to very sparse stable random
projections (Li et al 2006 and Li 2007), the prior work for estimating summary
statistics of the data.
In our theoretical analysis, we show that, when p->0, it suffices to use M=
K/(1-exp(-gK) log N measurements, so that all coordinates can be recovered in
one scan of the coordinates. If g = 1 (i.e., dense design), then M = K log N.
If g= 1/K or 2/K (i.e., very sparse design), then M = 1.58K log N or M = 1.16K
log N. This means the design matrix can be indeed very sparse at only a minor
inflation of the sample complexity.
Interestingly, as p->1, the required number of measurements is essentially M
= 2.7K log N, provided g= 1/K. It turns out that this result is a general
worst-case bound
Sparse phase retrieval via group-sparse optimization
This paper deals with sparse phase retrieval, i.e., the problem of estimating
a vector from quadratic measurements under the assumption that few components
are nonzero. In particular, we consider the problem of finding the sparsest
vector consistent with the measurements and reformulate it as a group-sparse
optimization problem with linear constraints. Then, we analyze the convex
relaxation of the latter based on the minimization of a block l1-norm and show
various exact recovery and stability results in the real and complex cases.
Invariance to circular shifts and reflections are also discussed for real
vectors measured via complex matrices
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