6,518 research outputs found
High-order regularized regression in Electrical Impedance Tomography
We present a novel approach for the inverse problem in electrical impedance
tomography based on regularized quadratic regression. Our contribution
introduces a new formulation for the forward model in the form of a nonlinear
integral transform, that maps changes in the electrical properties of a domain
to their respective variations in boundary data. Using perturbation theory the
transform is approximated to yield a high-order misfit unction which is then
used to derive a regularized inverse problem. In particular, we consider the
nonlinear problem to second-order accuracy, hence our approximation method
improves upon the local linearization of the forward mapping. The inverse
problem is approached using Newton's iterative algorithm and results from
simulated experiments are presented. With a moderate increase in computational
complexity, the method yields superior results compared to those of regularized
linear regression and can be implemented to address the nonlinear inverse
problem
Elite Bases Regression: A Real-time Algorithm for Symbolic Regression
Symbolic regression is an important but challenging research topic in data
mining. It can detect the underlying mathematical models. Genetic programming
(GP) is one of the most popular methods for symbolic regression. However, its
convergence speed might be too slow for large scale problems with a large
number of variables. This drawback has become a bottleneck in practical
applications. In this paper, a new non-evolutionary real-time algorithm for
symbolic regression, Elite Bases Regression (EBR), is proposed. EBR generates a
set of candidate basis functions coded with parse-matrix in specific mapping
rules. Meanwhile, a certain number of elite bases are preserved and updated
iteratively according to the correlation coefficients with respect to the
target model. The regression model is then spanned by the elite bases. A
comparative study between EBR and a recent proposed machine learning method for
symbolic regression, Fast Function eXtraction (FFX), are conducted. Numerical
results indicate that EBR can solve symbolic regression problems more
effectively.Comment: The 2017 13th International Conference on Natural Computation, Fuzzy
Systems and Knowledge Discovery (ICNC-FSKD 2017
Towards Efficient Maximum Likelihood Estimation of LPV-SS Models
How to efficiently identify multiple-input multiple-output (MIMO) linear
parameter-varying (LPV) discrete-time state-space (SS) models with affine
dependence on the scheduling variable still remains an open question, as
identification methods proposed in the literature suffer heavily from the curse
of dimensionality and/or depend on over-restrictive approximations of the
measured signal behaviors. However, obtaining an SS model of the targeted
system is crucial for many LPV control synthesis methods, as these synthesis
tools are almost exclusively formulated for the aforementioned representation
of the system dynamics. Therefore, in this paper, we tackle the problem by
combining state-of-the-art LPV input-output (IO) identification methods with an
LPV-IO to LPV-SS realization scheme and a maximum likelihood refinement step.
The resulting modular LPV-SS identification approach achieves statical
efficiency with a relatively low computational load. The method contains the
following three steps: 1) estimation of the Markov coefficient sequence of the
underlying system using correlation analysis or Bayesian impulse response
estimation, then 2) LPV-SS realization of the estimated coefficients by using a
basis reduced Ho-Kalman method, and 3) refinement of the LPV-SS model estimate
from a maximum-likelihood point of view by a gradient-based or an
expectation-maximization optimization methodology. The effectiveness of the
full identification scheme is demonstrated by a Monte Carlo study where our
proposed method is compared to existing schemes for identifying a MIMO LPV
system
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