1,335 research outputs found
Hyperspectral Unmixing Overview: Geometrical, Statistical, and Sparse Regression-Based Approaches
Imaging spectrometers measure electromagnetic energy scattered in their
instantaneous field view in hundreds or thousands of spectral channels with
higher spectral resolution than multispectral cameras. Imaging spectrometers
are therefore often referred to as hyperspectral cameras (HSCs). Higher
spectral resolution enables material identification via spectroscopic analysis,
which facilitates countless applications that require identifying materials in
scenarios unsuitable for classical spectroscopic analysis. Due to low spatial
resolution of HSCs, microscopic material mixing, and multiple scattering,
spectra measured by HSCs are mixtures of spectra of materials in a scene. Thus,
accurate estimation requires unmixing. Pixels are assumed to be mixtures of a
few materials, called endmembers. Unmixing involves estimating all or some of:
the number of endmembers, their spectral signatures, and their abundances at
each pixel. Unmixing is a challenging, ill-posed inverse problem because of
model inaccuracies, observation noise, environmental conditions, endmember
variability, and data set size. Researchers have devised and investigated many
models searching for robust, stable, tractable, and accurate unmixing
algorithms. This paper presents an overview of unmixing methods from the time
of Keshava and Mustard's unmixing tutorial [1] to the present. Mixing models
are first discussed. Signal-subspace, geometrical, statistical, sparsity-based,
and spatial-contextual unmixing algorithms are described. Mathematical problems
and potential solutions are described. Algorithm characteristics are
illustrated experimentally.Comment: This work has been accepted for publication in IEEE Journal of
Selected Topics in Applied Earth Observations and Remote Sensin
Non-negative mixtures
This is the author's accepted pre-print of the article, first published as M. D. Plumbley, A. Cichocki and R. Bro. Non-negative mixtures. In P. Comon and C. Jutten (Ed), Handbook of Blind Source Separation: Independent Component Analysis and Applications. Chapter 13, pp. 515-547. Academic Press, Feb 2010. ISBN 978-0-12-374726-6 DOI: 10.1016/B978-0-12-374726-6.00018-7file: Proof:p\PlumbleyCichockiBro10-non-negative.pdf:PDF owner: markp timestamp: 2011.04.26file: Proof:p\PlumbleyCichockiBro10-non-negative.pdf:PDF owner: markp timestamp: 2011.04.2
Is Simple Better? Revisiting Non-linear Matrix Factorization for Learning Incomplete Ratings
Matrix factorization techniques have been widely used as a method for
collaborative filtering for recommender systems. In recent times, different
variants of deep learning algorithms have been explored in this setting to
improve the task of making a personalized recommendation with user-item
interaction data. The idea that the mapping between the latent user or item
factors and the original features is highly nonlinear suggest that classical
matrix factorization techniques are no longer sufficient. In this paper, we
propose a multilayer nonlinear semi-nonnegative matrix factorization method,
with the motivation that user-item interactions can be modeled more accurately
using a linear combination of non-linear item features. Firstly, we learn
latent factors for representations of users and items from the designed
multilayer nonlinear Semi-NMF approach using explicit ratings. Secondly, the
architecture built is compared with deep-learning algorithms like Restricted
Boltzmann Machine and state-of-the-art Deep Matrix factorization techniques. By
using both supervised rate prediction task and unsupervised clustering in
latent item space, we demonstrate that our proposed approach achieves better
generalization ability in prediction as well as comparable representation
ability as deep matrix factorization in the clustering task.Comment: version
HyperNTF: A Hypergraph Regularized Nonnegative Tensor Factorization for Dimensionality Reduction
Most methods for dimensionality reduction are based on either tensor
representation or local geometry learning. However, the tensor-based methods
severely rely on the assumption of global and multilinear structures in
high-dimensional data; and the manifold learning methods suffer from the
out-of-sample problem. In this paper, bridging the tensor decomposition and
manifold learning, we propose a novel method, called Hypergraph Regularized
Nonnegative Tensor Factorization (HyperNTF). HyperNTF can preserve
nonnegativity in tensor factorization, and uncover the higher-order
relationship among the nearest neighborhoods. Clustering analysis with HyperNTF
has low computation and storage costs. The experiments on four synthetic data
show a desirable property of hypergraph in uncovering the high-order
correlation to unfold the curved manifolds. Moreover, the numerical experiments
on six real datasets suggest that HyperNTF robustly outperforms
state-of-the-art algorithms in clustering analysis.Comment: 12 pages, 6 figures, 9 table
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