4,314 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
Unsupervised Multi Class Segmentation of 3D Images with Intensity Inhomogeneities
Intensity inhomogeneities in images constitute a considerable challenge in
image segmentation. In this paper we propose a novel biconvex variational model
to tackle this task. We combine a total variation approach for multi class
segmentation with a multiplicative model to handle the inhomogeneities. Our
method assumes that the image intensity is the product of a smoothly varying
part and a component which resembles important image structures such as edges.
Therefore, we penalize in addition to the total variation of the label
assignment matrix a quadratic difference term to cope with the smoothly varying
factor. A critical point of our biconvex functional is computed by a modified
proximal alternating linearized minimization method (PALM). We show that the
assumptions for the convergence of the algorithm are fulfilled by our model.
Various numerical examples demonstrate the very good performance of our method.
Particular attention is paid to the segmentation of 3D FIB tomographical images
which was indeed the motivation of our work
Laplacian Mixture Modeling for Network Analysis and Unsupervised Learning on Graphs
Laplacian mixture models identify overlapping regions of influence in
unlabeled graph and network data in a scalable and computationally efficient
way, yielding useful low-dimensional representations. By combining Laplacian
eigenspace and finite mixture modeling methods, they provide probabilistic or
fuzzy dimensionality reductions or domain decompositions for a variety of input
data types, including mixture distributions, feature vectors, and graphs or
networks. Provable optimal recovery using the algorithm is analytically shown
for a nontrivial class of cluster graphs. Heuristic approximations for scalable
high-performance implementations are described and empirically tested.
Connections to PageRank and community detection in network analysis demonstrate
the wide applicability of this approach. The origins of fuzzy spectral methods,
beginning with generalized heat or diffusion equations in physics, are reviewed
and summarized. Comparisons to other dimensionality reduction and clustering
methods for challenging unsupervised machine learning problems are also
discussed.Comment: 13 figures, 35 reference
Efficient Semidefinite Spectral Clustering via Lagrange Duality
We propose an efficient approach to semidefinite spectral clustering (SSC),
which addresses the Frobenius normalization with the positive semidefinite
(p.s.d.) constraint for spectral clustering. Compared with the original
Frobenius norm approximation based algorithm, the proposed algorithm can more
accurately find the closest doubly stochastic approximation to the affinity
matrix by considering the p.s.d. constraint. In this paper, SSC is formulated
as a semidefinite programming (SDP) problem. In order to solve the high
computational complexity of SDP, we present a dual algorithm based on the
Lagrange dual formalization. Two versions of the proposed algorithm are
proffered: one with less memory usage and the other with faster convergence
rate. The proposed algorithm has much lower time complexity than that of the
standard interior-point based SDP solvers. Experimental results on both UCI
data sets and real-world image data sets demonstrate that 1) compared with the
state-of-the-art spectral clustering methods, the proposed algorithm achieves
better clustering performance; and 2) our algorithm is much more efficient and
can solve larger-scale SSC problems than those standard interior-point SDP
solvers.Comment: 13 page
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