819,181 research outputs found
Residual Component Analysis
Probabilistic principal component analysis (PPCA) seeks a low dimensional
representation of a data set in the presence of independent spherical Gaussian
noise, Sigma = (sigma^2)*I. The maximum likelihood solution for the model is an
eigenvalue problem on the sample covariance matrix. In this paper we consider
the situation where the data variance is already partially explained by other
factors, e.g. covariates of interest, or temporal correlations leaving some
residual variance. We decompose the residual variance into its components
through a generalized eigenvalue problem, which we call residual component
analysis (RCA). We show that canonical covariates analysis (CCA) is a special
case of our algorithm and explore a range of new algorithms that arise from the
framework. We illustrate the ideas on a gene expression time series data set
and the recovery of human pose from silhouette
Fault detection and diagnosis based on extensions of PCA
The paper presents two approaches for fault detection and discrimination based on principal component analysis (PCA). The first approach proposes the concept of y-indices through a transposed formulation of the data matrices utilized in traditional PCA. Residual errors (REs) and faulty sensor identification indices (FSIIs) are introduced in the second approach, where REs are generated from the residual sub-space of PCA, and FSIIs are introduced to classify sensor- or component-faults. Through field data from gas turbines during commissioning, it is shown that in-operation sensor faults can be detected, and sensor- and component-faults can be discriminated through the proposed methods. The techniques are generic, and will find use in many military systems with complex, safety critical control and sensor arrangements
Principal Component Analysis for Functional Data on Riemannian Manifolds and Spheres
Functional data analysis on nonlinear manifolds has drawn recent interest.
Sphere-valued functional data, which are encountered for example as movement
trajectories on the surface of the earth, are an important special case. We
consider an intrinsic principal component analysis for smooth Riemannian
manifold-valued functional data and study its asymptotic properties. Riemannian
functional principal component analysis (RFPCA) is carried out by first mapping
the manifold-valued data through Riemannian logarithm maps to tangent spaces
around the time-varying Fr\'echet mean function, and then performing a
classical multivariate functional principal component analysis on the linear
tangent spaces. Representations of the Riemannian manifold-valued functions and
the eigenfunctions on the original manifold are then obtained with exponential
maps. The tangent-space approximation through functional principal component
analysis is shown to be well-behaved in terms of controlling the residual
variation if the Riemannian manifold has nonnegative curvature. Specifically,
we derive a central limit theorem for the mean function, as well as root-
uniform convergence rates for other model components, including the covariance
function, eigenfunctions, and functional principal component scores. Our
applications include a novel framework for the analysis of longitudinal
compositional data, achieved by mapping longitudinal compositional data to
trajectories on the sphere, illustrated with longitudinal fruit fly behavior
patterns. RFPCA is shown to be superior in terms of trajectory recovery in
comparison to an unrestricted functional principal component analysis in
applications and simulations and is also found to produce principal component
scores that are better predictors for classification compared to traditional
functional functional principal component scores
Bayesian nonlinear hyperspectral unmixing with spatial residual component analysis
This paper presents a new Bayesian model and algorithm for nonlinear unmixing
of hyperspectral images. The model proposed represents the pixel reflectances
as linear combinations of the endmembers, corrupted by nonlinear (with respect
to the endmembers) terms and additive Gaussian noise. Prior knowledge about the
problem is embedded in a hierarchical model that describes the dependence
structure between the model parameters and their constraints. In particular, a
gamma Markov random field is used to model the joint distribution of the
nonlinear terms, which are expected to exhibit significant spatial
correlations. An adaptive Markov chain Monte Carlo algorithm is then proposed
to compute the Bayesian estimates of interest and perform Bayesian inference.
This algorithm is equipped with a stochastic optimisation adaptation mechanism
that automatically adjusts the parameters of the gamma Markov random field by
maximum marginal likelihood estimation. Finally, the proposed methodology is
demonstrated through a series of experiments with comparisons using synthetic
and real data and with competing state-of-the-art approaches
Least Dependent Component Analysis Based on Mutual Information
We propose to use precise estimators of mutual information (MI) to find least
dependent components in a linearly mixed signal. On the one hand this seems to
lead to better blind source separation than with any other presently available
algorithm. On the other hand it has the advantage, compared to other
implementations of `independent' component analysis (ICA) some of which are
based on crude approximations for MI, that the numerical values of the MI can
be used for:
(i) estimating residual dependencies between the output components;
(ii) estimating the reliability of the output, by comparing the pairwise MIs
with those of re-mixed components;
(iii) clustering the output according to the residual interdependencies.
For the MI estimator we use a recently proposed k-nearest neighbor based
algorithm. For time sequences we combine this with delay embedding, in order to
take into account non-trivial time correlations. After several tests with
artificial data, we apply the resulting MILCA (Mutual Information based Least
dependent Component Analysis) algorithm to a real-world dataset, the ECG of a
pregnant woman.
The software implementation of the MILCA algorithm is freely available at
http://www.fz-juelich.de/nic/cs/softwareComment: 18 pages, 20 figures, Phys. Rev. E (in press
Using Happiness Surveys to Value Intangibles: The Case of Airport Noise
Inhabitants of houses near Amsterdam Airport are complaining of noise nuisance, caused by aircraft traffic. The usual assumption is that the effect of the externality will be perfectly reflected by house price differentials. This is based on the implicit assumption that there is a well-functioning housing market. If that is not true, we need a correction method in order to assess the intangible damage. We assess the monetary value of the noise damage, caused by aircraft noise nuisance around Amsterdam Airport as the sum of hedonic price differentials and a residual cost component. The residual costs are assessed from a survey, including an ordinal life satisfaction scale, on which individual respondents have scored. The derived compensation scheme depends on, among other things, the objective noise level, income, the degree to which prices account for noise differences, and the presence of noise insulation.cost-benefit analysis, externalities, airport noise, satisfaction analysis, residual shadow costs
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