Search results for "Dimension reduction"
showing 10 items of 15 documents
Efficient unsupervised clustering for spatial bird population analysis along the Loire river
2015
International audience; This paper focuses on application and comparison of Non Linear Dimensionality Reduction (NLDR) methods on natural high dimensional bird communities dataset along the Loire River (France). In this context, biologists usually use the well-known PCA in order to explain the upstream-downstream gradient.Unfortunately this method was unsuccessful on this kind of nonlinear dataset.The goal of this paper is to compare recent NLDR methods coupled with different data transformations in order to find out the best approach. Results show that Multiscale Jensen-Shannon Embedding (Ms JSE) outperform all over methods in this context.
Approximation of functions over manifolds : A Moving Least-Squares approach
2021
We present an algorithm for approximating a function defined over a $d$-dimensional manifold utilizing only noisy function values at locations sampled from the manifold with noise. To produce the approximation we do not require any knowledge regarding the manifold other than its dimension $d$. We use the Manifold Moving Least-Squares approach of (Sober and Levin 2016) to reconstruct the atlas of charts and the approximation is built on-top of those charts. The resulting approximant is shown to be a function defined over a neighborhood of a manifold, approximating the originally sampled manifold. In other words, given a new point, located near the manifold, the approximation can be evaluated…
Dimension Estimation in Two-Dimensional PCA
2021
We propose an automated way of determining the optimal number of low-rank components in dimension reduction of image data. The method is based on the combination of two-dimensional principal component analysis and an augmentation estimator proposed recently in the literature. Intuitively, the main idea is to combine a scree plot with information extracted from the eigenvectors of a variation matrix. Simulation studies show that the method provides accurate estimates and a demonstration with a finger data set showcases its performance in practice. peerReviewed
Dimensional reduction for energies with linear growth involving the bending moment
2008
A $\Gamma$-convergence analysis is used to perform a 3D-2D dimension reduction of variational problems with linear growth. The adopted scaling gives rise to a nonlinear membrane model which, because of the presence of higher order external loadings inducing a bending moment, may depend on the average in the transverse direction of a Cosserat vector field, as well as on the deformation of the mid-plane. The assumption of linear growth on the energy leads to an asymptotic analysis in the spaces of measures and of functions with bounded variation.
3D-2D dimensional reduction for a nonlinear optimal design problem with perimeter penalization
2012
A 3D-2D dimension reduction for a nonlinear optimal design problem with a perimeter penalization is performed in the realm of $\Gamma$-convergence, providing an integral representation for the limit functional.
Data-driven analysis for fMRI during naturalistic music listening
2017
Interest towards higher ecological validity in functional magnetic resonance imaging (fMRI) experiments has been steadily growing since the turn of millennium. The trend is reflected in increasing amount of naturalistic experiments, where participants are exposed to the real-world complex stimulus and/or cognitive tasks such as watching movie, playing video games, or listening to music. Multifaceted stimuli forming parallel streams of input information, combined with reduced control over experimental variables introduces number of methodological challenges associated with isolating brain responses to individual events. This exploratory work demonstrated some of those methodological challeng…
Snowball ICA: A Model Order Free Independent Component Analysis Strategy for Functional Magnetic Resonance Imaging Data
2020
In independent component analysis (ICA), the selection of model order (i.e., number of components to be extracted) has crucial effects on functional magnetic resonance imaging (fMRI) brain network analysis. Model order selection (MOS) algorithms have been used to determine the number of estimated components. However, simulations show that even when the model order equals the number of simulated signal sources, traditional ICA algorithms may misestimate the spatial maps of the signal sources. In principle, increasing model order will consider more potential information in the estimation, and should therefore produce more accurate results. However, this strategy may not work for fMRI because …
Exploring regression structure with graphics
1993
We investigate the extent to which it may be possible to carry out a regression analysis using graphics alone, an idea that we refer to asgraphical regression. The limitations of this idea are explored. It is shown that graphical regression is theoretically possible with essentially no constraints on the conditional distribution of the response given the predictors, but with some conditions on marginal distribution of the predictors. Dimension reduction subspaces and added variable plots play a central role in the development. The possibility of useful methodology is explored through two examples.
On the usage of joint diagonalization in multivariate statistics
2022
Scatter matrices generalize the covariance matrix and are useful in many multivariate data analysis methods, including well-known principal component analysis (PCA), which is based on the diagonalization of the covariance matrix. The simultaneous diagonalization of two or more scatter matrices goes beyond PCA and is used more and more often. In this paper, we offer an overview of many methods that are based on a joint diagonalization. These methods range from the unsupervised context with invariant coordinate selection and blind source separation, which includes independent component analysis, to the supervised context with discriminant analysis and sliced inverse regression. They also enco…
Dimension reduction for time series in a blind source separation context using r
2021
Funding Information: The work of KN was supported by the CRoNoS COST Action IC1408 and the Austrian Science Fund P31881-N32. The work of ST was supported by the CRoNoS COST Action IC1408. The work of JV was supported by Academy of Finland (grant 321883). We would like to thank the anonymous reviewers for their comments which improved the paper and package considerably. Publisher Copyright: © 2021, American Statistical Association. All rights reserved. Multivariate time series observations are increasingly common in multiple fields of science but the complex dependencies of such data often translate into intractable models with large number of parameters. An alternative is given by first red…