1,712 research outputs found
Interpretable Low-Rank Document Representations with Label-Dependent Sparsity Patterns
In context of document classification, where in a corpus of documents their
label tags are readily known, an opportunity lies in utilizing label
information to learn document representation spaces with better discriminative
properties. To this end, in this paper application of a Variational Bayesian
Supervised Nonnegative Matrix Factorization (supervised vbNMF) with
label-driven sparsity structure of coefficients is proposed for learning of
discriminative nonsubtractive latent semantic components occuring in TF-IDF
document representations. Constraints are such that the components pursued are
made to be frequently occuring in a small set of labels only, making it
possible to yield document representations with distinctive label-specific
sparse activation patterns. A simple measure of quality of this kind of
sparsity structure, dubbed inter-label sparsity, is introduced and
experimentally brought into tight connection with classification performance.
Representing a great practical convenience, inter-label sparsity is shown to be
easily controlled in supervised vbNMF by a single parameter
A Unified Framework for Sparse Non-Negative Least Squares using Multiplicative Updates and the Non-Negative Matrix Factorization Problem
We study the sparse non-negative least squares (S-NNLS) problem. S-NNLS
occurs naturally in a wide variety of applications where an unknown,
non-negative quantity must be recovered from linear measurements. We present a
unified framework for S-NNLS based on a rectified power exponential scale
mixture prior on the sparse codes. We show that the proposed framework
encompasses a large class of S-NNLS algorithms and provide a computationally
efficient inference procedure based on multiplicative update rules. Such update
rules are convenient for solving large sets of S-NNLS problems simultaneously,
which is required in contexts like sparse non-negative matrix factorization
(S-NMF). We provide theoretical justification for the proposed approach by
showing that the local minima of the objective function being optimized are
sparse and the S-NNLS algorithms presented are guaranteed to converge to a set
of stationary points of the objective function. We then extend our framework to
S-NMF, showing that our framework leads to many well known S-NMF algorithms
under specific choices of prior and providing a guarantee that a popular
subclass of the proposed algorithms converges to a set of stationary points of
the objective function. Finally, we study the performance of the proposed
approaches on synthetic and real-world data.Comment: To appear in Signal Processin
Hyperspectral Unmixing Overview: Geometrical, Statistical, and Sparse Regression-Based Approaches
Imaging spectrometers measure electromagnetic energy scattered in their
instantaneous field view in hundreds or thousands of spectral channels with
higher spectral resolution than multispectral cameras. Imaging spectrometers
are therefore often referred to as hyperspectral cameras (HSCs). Higher
spectral resolution enables material identification via spectroscopic analysis,
which facilitates countless applications that require identifying materials in
scenarios unsuitable for classical spectroscopic analysis. Due to low spatial
resolution of HSCs, microscopic material mixing, and multiple scattering,
spectra measured by HSCs are mixtures of spectra of materials in a scene. Thus,
accurate estimation requires unmixing. Pixels are assumed to be mixtures of a
few materials, called endmembers. Unmixing involves estimating all or some of:
the number of endmembers, their spectral signatures, and their abundances at
each pixel. Unmixing is a challenging, ill-posed inverse problem because of
model inaccuracies, observation noise, environmental conditions, endmember
variability, and data set size. Researchers have devised and investigated many
models searching for robust, stable, tractable, and accurate unmixing
algorithms. This paper presents an overview of unmixing methods from the time
of Keshava and Mustard's unmixing tutorial [1] to the present. Mixing models
are first discussed. Signal-subspace, geometrical, statistical, sparsity-based,
and spatial-contextual unmixing algorithms are described. Mathematical problems
and potential solutions are described. Algorithm characteristics are
illustrated experimentally.Comment: This work has been accepted for publication in IEEE Journal of
Selected Topics in Applied Earth Observations and Remote Sensin
Rectified Gaussian Scale Mixtures and the Sparse Non-Negative Least Squares Problem
In this paper, we develop a Bayesian evidence maximization framework to solve
the sparse non-negative least squares (S-NNLS) problem. We introduce a family
of probability densities referred to as the Rectified Gaussian Scale Mixture
(R- GSM) to model the sparsity enforcing prior distribution for the solution.
The R-GSM prior encompasses a variety of heavy-tailed densities such as the
rectified Laplacian and rectified Student- t distributions with a proper choice
of the mixing density. We utilize the hierarchical representation induced by
the R-GSM prior and develop an evidence maximization framework based on the
Expectation-Maximization (EM) algorithm. Using the EM based method, we estimate
the hyper-parameters and obtain a point estimate for the solution. We refer to
the proposed method as rectified sparse Bayesian learning (R-SBL). We provide
four R- SBL variants that offer a range of options for computational complexity
and the quality of the E-step computation. These methods include the Markov
chain Monte Carlo EM, linear minimum mean-square-error estimation, approximate
message passing and a diagonal approximation. Using numerical experiments, we
show that the proposed R-SBL method outperforms existing S-NNLS solvers in
terms of both signal and support recovery performance, and is also very robust
against the structure of the design matrix.Comment: Under Review by IEEE Transactions on Signal Processin
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