Application of modified alternating least squares regression to spectroscopic image analysis

Wang, Jihong; Hopke, Philip K.; Hancewicz, Thomas M.; Zhang, Shuliang L.

doi:10.1016/s0003-2670(02)01369-7

Cited by 117 publications

(85 citation statements)

References 7 publications

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“…Assume that all the components a (n) j n are ℓ 2 -norm unit length vectors: a (n) T j n a (n) j n = 1, the entry g¯j can be updated using the learning rule (38) …”

Section: Local Update Rule For Gmentioning

confidence: 99%

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Extended HALS algorithm for nonnegative Tucker decomposition and its applications for multiway analysis and classification

Phan

Cichocki

2011

Neurocomputing

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“…Assume that all the components a (n) j n are ℓ 2 -norm unit length vectors: a (n) T j n a (n) j n = 1, the entry g¯j can be updated using the learning rule (38) …”

Section: Local Update Rule For Gmentioning

confidence: 99%

“…Moreover, they are quite sensitive with respect to noise, and can be relatively slow when the data are nearly collinear [1,[35][36][37][38].…”

Section: Introductionmentioning

confidence: 99%

Extended HALS algorithm for nonnegative Tucker decomposition and its applications for multiway analysis and classification

Phan

Cichocki

2011

Neurocomputing

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“…to minimize the off-diagonal elements of the covariance matrix. In a class of algorithms known as MCR-ALS, prewhitening and the interdependence minimization are done as in standard ICA, but non-negativity is then enforced in a postprocessing step using the alternating least squares (ALS) technique [7,29,30]. In general, this gives better results than the algorithms without ALS.…”

Section: Introductionmentioning

confidence: 99%

Monte Carlo Algorithm for Least Dependent Non-Negative Mixture Decomposition

et al. 2006

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We propose a simulated annealing algorithm (called SNICA for "stochastic non-negative independent component analysis") for blind decomposition of linear mixtures of non-negative sources with non-negative coefficients. The de-mixing is based on a Metropolis type Monte Carlo search for least dependent components, with the mutual information between recovered components as a cost function and their non-negativity as a hard constraint. Elementary moves are shears in two-dimensional subspaces and rotations in three-dimensional subspaces. The algorithm is geared at decomposing signals whose probability densities peak at zero, the case typical in analytical spectroscopy and multivariate curve resolution. The decomposition performance on large samples of synthetic mixtures and experimental data is much better than that of traditional blind source separation methods based on principal component analysis (MILCA, FastICA, RADICAL) and chemometrics techniques (SIMPLISMA, ALS, BTEM).

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“…Similar problems occur, e.g., in factor analysis, chemometrics, psychometrics (Leardi et al 2000;Leurgans and Ross 1992;Lopes and Menezes 2003;Paatero 1997;Wang et al 2003). Our approach may be extended to solving such problems.…”

Section: Discussionmentioning

confidence: 83%

Sparsity optimization in design of multidimensional filter networks

et al. 2015

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Filter networks are used as a powerful tool used for reducing the image processing time and maintaining high image quality. They are composed of sparse sub-filters whose high sparsity ensures fast image processing. The filter network design is related to solving a sparse optimization problem where a cardinality constraint bounds above the sparsity level. In the case of sequentially connected sub-filters, which is the simplest network structure of those considered in this paper, a cardinalityconstrained multilinear least-squares (MLLS) problem is to be solved.Even when disregarding the cardinality constraint, the MLLS is typically a large-scale problem characterized by a large number of local minimizers, each of which is singular and non-isolated. The cardinality constraint makes the problem even more difficult to solve.An approach for approximately solving the cardinality-constrained MLLS problem is presented. It is then applied to solving a bi-criteria optimization problem in which both the time and quality of image processing are optimized. The developed approach is extended to designing filter networks of a more general structure. Its efficiency is demonstrated by designing certain 2D and 3D filter networks. It is also compared with the existing approaches.

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Application of modified alternating least squares regression to spectroscopic image analysis

Cited by 117 publications

References 7 publications

Extended HALS algorithm for nonnegative Tucker decomposition and its applications for multiway analysis and classification

Extended HALS algorithm for nonnegative Tucker decomposition and its applications for multiway analysis and classification

Monte Carlo Algorithm for Least Dependent Non-Negative Mixture Decomposition

Sparsity optimization in design of multidimensional filter networks

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