23,034 research outputs found
Bayesian estimation of linear mixtures using the normal compositional model. Application to hyperspectral imagery
This paper studies a new Bayesian unmixing algorithm for hyperspectral images. Each pixel of the image is modeled as a linear combination of so-called endmembers. These endmembers are supposed to be random in order to model uncertainties regarding their knowledge. More precisely, we model endmembers as Gaussian vectors whose means have been determined using an endmember extraction algorithm such as the famous N-finder (N-FINDR) or Vertex Component Analysis (VCA) algorithms. This paper proposes to estimate the mixture coefficients (referred to as abundances) using a Bayesian algorithm. Suitable priors are assigned to the abundances in order to satisfy positivity and additivity constraints whereas conjugate priors are chosen for the remaining parameters. A hybrid Gibbs sampler is then constructed to generate abundance and variance samples distributed according to the joint posterior of the abundances and noise variances. The performance of the proposed methodology is evaluated by comparison with other unmixing algorithms on synthetic and real images
Bayesian separation of spectral sources under non-negativity and full additivity constraints
This paper addresses the problem of separating spectral sources which are
linearly mixed with unknown proportions. The main difficulty of the problem is
to ensure the full additivity (sum-to-one) of the mixing coefficients and
non-negativity of sources and mixing coefficients. A Bayesian estimation
approach based on Gamma priors was recently proposed to handle the
non-negativity constraints in a linear mixture model. However, incorporating
the full additivity constraint requires further developments. This paper
studies a new hierarchical Bayesian model appropriate to the non-negativity and
sum-to-one constraints associated to the regressors and regression coefficients
of linear mixtures. The estimation of the unknown parameters of this model is
performed using samples generated using an appropriate Gibbs sampler. The
performance of the proposed algorithm is evaluated through simulation results
conducted on synthetic mixture models. The proposed approach is also applied to
the processing of multicomponent chemical mixtures resulting from Raman
spectroscopy.Comment: v4: minor grammatical changes; Signal Processing, 200
Combining Neuro-Fuzzy Classifiers for Improved Generalisation and Reliability
In this paper a combination of neuro-fuzzy
classifiers for improved classification performance and reliability
is considered. A general fuzzy min-max (GFMM) classifier with
agglomerative learning algorithm is used as a main building
block. An alternative approach to combining individual classifier
decisions involving the combination at the classifier model level is
proposed. The resulting classifier complexity and transparency is
comparable with classifiers generated during a single crossvalidation
procedure while the improved classification
performance and reduced variance is comparable to the ensemble
of classifiers with combined (averaged/voted) decisions. We also
illustrate how combining at the model level can be used for
speeding up the training of GFMM classifiers for large data sets
How good is the generalized Langevin equation to describe the dynamics of photo-induced electron transfer in fluid solution?
The dynamics of unimolecular photo-triggered reactions can be strongly
affected by the surrounding medium. An accurate description of these reactions
requires knowing the free energy surface (FES) and the friction felt by the
reactants. Most of theories start from the Langevin equation to derive the
dynamics, but there are few examples comparing it with experiments. Here we
explore the applicability of a Generalized Langevin Equation (GLE) with an
arbitrary potential and a non-markovian friction. To this end we have performed
broadband fluorescence measurements with sub-picosecond time resolution of a
covalently linked organic electron donor-acceptor system in solvents of
changing viscosity and dielectric permittivity. In order to establish the FES
of the reaction we resort to stationary electronic spectroscopy. On the other
hand, the dynamics of a non-reacting substance, Coumarin 153, provide the
calibrating tool for the friction over the FES, which is assumed to be solute
independent. A simpler and computationally faster approach uses the Generalized
Smoluchowski Equation (GSE), which can be derived from the GLE for pure
harmonic potentials. Both approaches reproduce the measurements in most of the
solvents reasonably well. At long times, some differences arise from the errors
inherited from the analysis of the stationary solvatochromism and at short
times from the excess excitation energy. However, whenever the dynamics become
slow the GSE shows larger deviations than the GLE, the results of which always
agree qualitatively with the measured dynamics, regardless of the solvent
viscosity or dielectric properties. The here applied method can be used to
predict the dynamics of any other reacting system, given the FES parameters and
solvent dynamics are provided. Thus no fitting parameters enter the GLE
simulations, within the applicability limits found for the model in this work.Comment: 30 pages, 22 figures, 5 tables, 97 reference
Deep clustering: Discriminative embeddings for segmentation and separation
We address the problem of acoustic source separation in a deep learning
framework we call "deep clustering." Rather than directly estimating signals or
masking functions, we train a deep network to produce spectrogram embeddings
that are discriminative for partition labels given in training data. Previous
deep network approaches provide great advantages in terms of learning power and
speed, but previously it has been unclear how to use them to separate signals
in a class-independent way. In contrast, spectral clustering approaches are
flexible with respect to the classes and number of items to be segmented, but
it has been unclear how to leverage the learning power and speed of deep
networks. To obtain the best of both worlds, we use an objective function that
to train embeddings that yield a low-rank approximation to an ideal pairwise
affinity matrix, in a class-independent way. This avoids the high cost of
spectral factorization and instead produces compact clusters that are amenable
to simple clustering methods. The segmentations are therefore implicitly
encoded in the embeddings, and can be "decoded" by clustering. Preliminary
experiments show that the proposed method can separate speech: when trained on
spectrogram features containing mixtures of two speakers, and tested on
mixtures of a held-out set of speakers, it can infer masking functions that
improve signal quality by around 6dB. We show that the model can generalize to
three-speaker mixtures despite training only on two-speaker mixtures. The
framework can be used without class labels, and therefore has the potential to
be trained on a diverse set of sound types, and to generalize to novel sources.
We hope that future work will lead to segmentation of arbitrary sounds, with
extensions to microphone array methods as well as image segmentation and other
domains.Comment: Originally submitted on June 5, 201
Mixtures of Regression Models for Time-Course Gene Expression Data: Evaluation of Initialization and Random Effects
Finite mixture models are routinely applied to time course microarray data.
Due to the complexity and size of this type of data the choice of good starting values plays
an important role. So far initialization strategies have only been investigated for data
from a mixture of multivariate normal distributions. In this work several initialization
procedures are evaluated for mixtures of regression models with and without random
effects in an extensive simulation study on different artificial datasets. Finally these
procedures are also applied to a real dataset from E. coli
Variational Bayesian Inference of Line Spectra
In this paper, we address the fundamental problem of line spectral estimation
in a Bayesian framework. We target model order and parameter estimation via
variational inference in a probabilistic model in which the frequencies are
continuous-valued, i.e., not restricted to a grid; and the coefficients are
governed by a Bernoulli-Gaussian prior model turning model order selection into
binary sequence detection. Unlike earlier works which retain only point
estimates of the frequencies, we undertake a more complete Bayesian treatment
by estimating the posterior probability density functions (pdfs) of the
frequencies and computing expectations over them. Thus, we additionally capture
and operate with the uncertainty of the frequency estimates. Aiming to maximize
the model evidence, variational optimization provides analytic approximations
of the posterior pdfs and also gives estimates of the additional parameters. We
propose an accurate representation of the pdfs of the frequencies by mixtures
of von Mises pdfs, which yields closed-form expectations. We define the
algorithm VALSE in which the estimates of the pdfs and parameters are
iteratively updated. VALSE is a gridless, convergent method, does not require
parameter tuning, can easily include prior knowledge about the frequencies and
provides approximate posterior pdfs based on which the uncertainty in line
spectral estimation can be quantified. Simulation results show that accounting
for the uncertainty of frequency estimates, rather than computing just point
estimates, significantly improves the performance. The performance of VALSE is
superior to that of state-of-the-art methods and closely approaches the
Cram\'er-Rao bound computed for the true model order.Comment: 15 pages, 8 figures, accepted for publication in IEEE Transactions on
Signal Processin
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