168,484 research outputs found
Privileged Communications-Attorney and Client
A high-dimensional regression space usually causes problems in nonlinear system identification.However, if the regression data are contained in (or spread tightly around) some manifold, thedimensionality can be reduced. This paper presents a use of dimension reduction techniques tocompose a two-step identification scheme suitable for high-dimensional identification problems withmanifold-valued regression data. Illustrating examples are also given
Isometric Sliced Inverse Regression for Nonlinear Manifolds Learning
[[abstract]]Sliced inverse regression (SIR) was developed to find effective linear dimension-reduction directions for exploring the intrinsic structure of the high-dimensional data. In this study, we present isometric SIR for nonlinear dimension reduction, which is a hybrid of the SIR method using the geodesic distance approximation. First, the proposed method computes the isometric distance between data points; the resulting distance matrix is then sliced according to K-means clustering results, and the classical SIR algorithm is applied. We show that the isometric SIR (ISOSIR) can reveal the geometric structure of a nonlinear manifold dataset (e.g., the Swiss roll). We report and discuss this novel method in comparison to several existing dimension-reduction techniques for data visualization and classification problems. The results show that ISOSIR is a promising nonlinear feature extractor for classification applications.[[incitationindex]]SCI[[booktype]]紙本[[booktype]]電子
Matrix factorisation and the interpretation of geodesic distance
Given a graph or similarity matrix, we consider the problem of recovering a
notion of true distance between the nodes, and so their true positions. We show
that this can be accomplished in two steps: matrix factorisation, followed by
nonlinear dimension reduction. This combination is effective because the point
cloud obtained in the first step lives close to a manifold in which latent
distance is encoded as geodesic distance. Hence, a nonlinear dimension
reduction tool, approximating geodesic distance, can recover the latent
positions, up to a simple transformation. We give a detailed account of the
case where spectral embedding is used, followed by Isomap, and provide
encouraging experimental evidence for other combinations of techniques
Order Reduction of the Radiative Heat Transfer Model for the Simulation of Plasma Arcs
An approach to derive low-complexity models describing thermal radiation for
the sake of simulating the behavior of electric arcs in switchgear systems is
presented. The idea is to approximate the (high dimensional) full-order
equations, modeling the propagation of the radiated intensity in space, with a
model of much lower dimension, whose parameters are identified by means of
nonlinear system identification techniques. The low-order model preserves the
main structural aspects of the full-order one, and its parameters can be
straightforwardly used in arc simulation tools based on computational fluid
dynamics. In particular, the model parameters can be used together with the
common approaches to resolve radiation in magnetohydrodynamic simulations,
including the discrete-ordinate method, the P-N methods and photohydrodynamics.
The proposed order reduction approach is able to systematically compute the
partitioning of the electromagnetic spectrum in frequency bands, and the
related absorption coefficients, that yield the best matching with respect to
the finely resolved absorption spectrum of the considered gaseous medium. It is
shown how the problem's structure can be exploited to improve the computational
efficiency when solving the resulting nonlinear optimization problem. In
addition to the order reduction approach and the related computational aspects,
an analysis by means of Laplace transform is presented, providing a
justification to the use of very low orders in the reduction procedure as
compared with the full-order model. Finally, comparisons between the full-order
model and the reduced-order ones are presented
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