544 research outputs found
Generalized visual information analysis via tensorial algebra
High order data is modeled using matrices whose entries are numerical arrays of a fixed size. These arrays, called t-scalars, form a commutative ring under the convolution product. Matrices with elements in the ring of t-scalars are referred to as t-matrices. The t-matrices can be scaled, added and multiplied in the usual way. There are t-matrix generalizations of positive matrices, orthogonal matrices and Hermitian symmetric matrices. With the t-matrix model, it is possible to generalize many well known matrix algorithms. In particular, the t-matrices are used to generalize the SVD (Singular Value Decomposition), HOSVD (High Order SVD), PCA (Principal Component Analysis), 2DPCA (two Dimensional PCA) and GCA (Grassmannian Component Analysis). The generalized t-matrix algorithms, namely TSVD, THOSVD, TPCA, T2DPCA and TGCA, are applied to low-rank approximation, reconstruction and supervised classification of images. Experiments show that the t-matrix algorithms compare favourably with standard matrix algorithms
Hyperspectral image spectral-spatial feature extraction via tensor principal component analysis
We consider the tensor-based spectral-spatial feature\ud
extraction problem for hyperspectral image classification.\ud
First, a tensor framework based on circular convolution is proposed.\ud
Based on this framework, we extend the traditional PCA to\ud
its tensorial version TPCA, which is applied to the spectral-spatial\ud
features of hyperspectral image data. The experiments show\ud
that the classification accuracy obtained using TPCA features\ud
is significantly higher than the accuracies obtained by its rivals
A group model for stable multi-subject ICA on fMRI datasets
Spatial Independent Component Analysis (ICA) is an increasingly used
data-driven method to analyze functional Magnetic Resonance Imaging (fMRI)
data. To date, it has been used to extract sets of mutually correlated brain
regions without prior information on the time course of these regions. Some of
these sets of regions, interpreted as functional networks, have recently been
used to provide markers of brain diseases and open the road to paradigm-free
population comparisons. Such group studies raise the question of modeling
subject variability within ICA: how can the patterns representative of a group
be modeled and estimated via ICA for reliable inter-group comparisons? In this
paper, we propose a hierarchical model for patterns in multi-subject fMRI
datasets, akin to mixed-effect group models used in linear-model-based
analysis. We introduce an estimation procedure, CanICA (Canonical ICA), based
on i) probabilistic dimension reduction of the individual data, ii) canonical
correlation analysis to identify a data subspace common to the group iii)
ICA-based pattern extraction. In addition, we introduce a procedure based on
cross-validation to quantify the stability of ICA patterns at the level of the
group. We compare our method with state-of-the-art multi-subject fMRI ICA
methods and show that the features extracted using our procedure are more
reproducible at the group level on two datasets of 12 healthy controls: a
resting-state and a functional localizer study
Properties of the general NHDM. I. The orbit space
We study the scalar sector of the general N-Higgs-doublet model via geometric
constructions in the space of gauge orbits. We give a detailed description of
the shape of the orbit space both for general N and, in more detail, for N=3.
We also comment on remarkable analogies between NHDM and quantum information
theory.Comment: 27 pages, 2 figure
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