203 research outputs found
Robustness analysis of a Maximum Correntropy framework for linear regression
In this paper we formulate a solution of the robust linear regression problem
in a general framework of correntropy maximization. Our formulation yields a
unified class of estimators which includes the Gaussian and Laplacian
kernel-based correntropy estimators as special cases. An analysis of the
robustness properties is then provided. The analysis includes a quantitative
characterization of the informativity degree of the regression which is
appropriate for studying the stability of the estimator. Using this tool, a
sufficient condition is expressed under which the parametric estimation error
is shown to be bounded. Explicit expression of the bound is given and
discussion on its numerical computation is supplied. For illustration purpose,
two special cases are numerically studied.Comment: 10 pages, 5 figures, To appear in Automatic
Correntropy Maximization via ADMM - Application to Robust Hyperspectral Unmixing
In hyperspectral images, some spectral bands suffer from low signal-to-noise
ratio due to noisy acquisition and atmospheric effects, thus requiring robust
techniques for the unmixing problem. This paper presents a robust supervised
spectral unmixing approach for hyperspectral images. The robustness is achieved
by writing the unmixing problem as the maximization of the correntropy
criterion subject to the most commonly used constraints. Two unmixing problems
are derived: the first problem considers the fully-constrained unmixing, with
both the non-negativity and sum-to-one constraints, while the second one deals
with the non-negativity and the sparsity-promoting of the abundances. The
corresponding optimization problems are solved efficiently using an alternating
direction method of multipliers (ADMM) approach. Experiments on synthetic and
real hyperspectral images validate the performance of the proposed algorithms
for different scenarios, demonstrating that the correntropy-based unmixing is
robust to outlier bands.Comment: 23 page
Multi-kernel Correntropy Regression: Robustness, Optimality, and Application on Magnetometer Calibration
This paper investigates the robustness and optimality of the multi-kernel
correntropy (MKC) on linear regression. We first derive an upper error bound
for a scalar regression problem in the presence of arbitrarily large outliers
and reveal that the kernel bandwidth should be neither too small nor too big in
the sense of the lowest upper error bound. Meanwhile, we find that the proposed
MKC is related to a specific heavy-tail distribution, and the level of the
heavy tail is controlled by the kernel bandwidth solely. Interestingly, this
distribution becomes the Gaussian distribution when the bandwidth is set to be
infinite, which allows one to tackle both Gaussian and non-Gaussian problems.
We propose an expectation-maximization (EM) algorithm to estimate the parameter
vectors and explore the kernel bandwidths alternatively. The results show that
our algorithm is equivalent to the traditional linear regression under Gaussian
noise and outperforms the conventional method under heavy-tailed noise. Both
numerical simulations and experiments on a magnetometer calibration application
verify the effectiveness of the proposed method
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