Evaluation of Parameter Choice Methods for Regularization of Ill-Posed Problems in Geomathematics

Bauer, Frank; Gutting, Martin; Lukas, Mark A.

doi:10.1007/978-3-642-27793-1_99-1

Cited by 42 publications

(87 citation statements)

References 138 publications

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“…Two specific merits to be evaluated with SRD in this study are generalized CV (GCV) [46], AIC [47], BIC [48], trace (X T X) + [21], and others [12,18,19]. These merits were not used in this paper, but their usages with SRD are also feasible.…”

Section: Rrmentioning

confidence: 99%

“…One of the data sets evaluated in this paper has such a difficulty. Other single model merits have been developed and compared for model selection [10][11][12][13][14][15][16][17][18][19].…”

mentioning

confidence: 99%

“…Variations are possible by combining respective R 2 values slopes, or intercepts from plotting model predicted values against reference values. While these most recent approaches have expanded beyond two the number of model merits simultaneously evaluated, there are many more model merits that can participate in the tuning parameter selection process [13][14][15][16][17][18][19].…”

mentioning

confidence: 99%

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Sum of ranking differences (SRD) to ensemble multivariate calibration model merits for tuning parameter selection and comparing calibration methods

Kalivas

Héberger

Andries

2015

Analytica Chimica Acta

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and variance ultimately decides the merits used in SRD and hence, the tuning parameter values ranked lowest by SRD for automatic selection. The SRD process is also shown to allow simultaneous comparison of different calibration methods for a particular data set in conjunction with tuning parameter selection. Because SRD evaluates consistency across multiple merits, decisions on how to combine and weight merits are avoided. To demonstrate the utility of SRD, a near infrared spectral data set and a quantitative structure activity relationship (QSAR) data set are evaluated using PLS and RR.

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Section: Rrmentioning

confidence: 99%

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confidence: 99%

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confidence: 99%

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Sum of ranking differences (SRD) to ensemble multivariate calibration model merits for tuning parameter selection and comparing calibration methods

Kalivas

Héberger

Andries

2015

Analytica Chimica Acta

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show abstract

“…A thorough comparison of many heuristic parameter choice rules is reported in [3]. All the linear discrete ill-posed problems in this comparison have a diagonal matrix.…”

Section: Introductionmentioning

confidence: 99%

“…The singular vectors for matrices obtained in this way typically are discretizations of oscillatory functions, with the frequency of the oscillations increasing with the index of the vector. We include several methods in our comparison that are not considered in [3]. Another recent comparison of heuristic parameter choice rules is reported in [29].…”

Section: Introductionmentioning

confidence: 99%

Old and new parameter choice rules for discrete ill-posed problems

2012

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Using the L₁norm to select basis set vectors for multivariate calibration and calibration updating

Shahbazikhah

Kalivas

Andries

et al. 2016

Journal of Chemometrics

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dWith projection based calibration approaches, such as partial least squares (PLS) and principal component regression (PCR), the calibration space is spanned by respective basis vectors (latent vectors). Up to rank k basis vectors are formed where k ≤ min(m,n) with m and n denoting the number of calibration samples and measured variables. The user needs to decide how many and which respective basis vectors (tuning parameters). To avoid the second issue, basis vectors are selected top-down starting with the first and sequentially adding until model criteria are satisfied. Ridge regression (RR) avoids the issues by using the full set of basis vectors. Another approach is to select a subset from the total available. The presented work develops a process based on the L 1 vector norm to select basis vectors. Specifically, the L 1 norm is used to select singular value decomposition (SVD) basis set vectors for PCR (LPCR). Because PCR, PLS, RR, and others can be expressed as linear combination of the SVD basis vectors, the focus is on selection and comparison using the SVD basis set. Results based on respective tuning parameter selections and weights applied to the SVD basis vectors for LPCR, top-down PCR, correlation PCR (CPCR), PLS, and RR are compared for calibration and calibration updating using spectroscopic data sets. The methods are found to predict equivalently. In particular, the L 1 norm produces similar results to those obtained by the well-studied CPCR process. Thus, the new method provides a different theoretical framework than CPCR for selecting basis vectors.

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Evaluation of Parameter Choice Methods for Regularization of Ill-Posed Problems in Geomathematics

Cited by 42 publications

References 138 publications

Sum of ranking differences (SRD) to ensemble multivariate calibration model merits for tuning parameter selection and comparing calibration methods

Sum of ranking differences (SRD) to ensemble multivariate calibration model merits for tuning parameter selection and comparing calibration methods

Old and new parameter choice rules for discrete ill-posed problems

Using the L₁norm to select basis set vectors for multivariate calibration and calibration updating

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Evaluation of Parameter Choice Methods for Regularization of Ill-Posed Problems in Geomathematics

Cited by 42 publications

References 138 publications

Sum of ranking differences (SRD) to ensemble multivariate calibration model merits for tuning parameter selection and comparing calibration methods

Sum of ranking differences (SRD) to ensemble multivariate calibration model merits for tuning parameter selection and comparing calibration methods

Old and new parameter choice rules for discrete ill-posed problems

Using the L1norm to select basis set vectors for multivariate calibration and calibration updating

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Product

Resources

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Using the L₁norm to select basis set vectors for multivariate calibration and calibration updating