Statistical <i>F</i>‐tests for abstract factor analysis and target testing

Malinowski, Edmund R.

doi:10.1002/cem.1180030107

Cited by 184 publications

(73 citation statements)

References 22 publications

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“…PCA was performed on X to determine the chemical rank and to further visualize the relationships between the samples. Six principal components (PCs) were found to be optimal according to a Malinowski F-test [15], and the score plot for PC1 versus PC2 (Figure 3) separated the samples into the different classes (i.e., the different LDHs). It can also be seen that the amino acid sequence similarity between LDH rabbit and hog muscle is reflected by a short distance between these two classes in the score plot.…”

Section: Resultsmentioning

confidence: 99%

Classification of lactate dehydrogenase of different origin by liquid chromatography-mass spectrometry and multivariate analysis

Bylund

Samskog

Markides

et al. 2003

J. Am. Soc. Mass Spectrom.

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A method intended to serve as a multivariate quality control tool in the production of pharmaceutical proteins is presented. The method is based on multivariate analysis of peptide maps generated with liquid chromatography-mass spectrometry (LC-MS). Lactate dehydrogenase (LDH) from different species and tissues were used as model compounds in the study. The proteins were digested with Endoproteinase Lys-C before the LC-MS analysis. After data pretreatment of the peptide maps, successful classification of the LDHs were obtained by discriminant analysis with partial least squares regression and artificial neural networks. Further, principal component analysis was applied to visualize the relationships between the samples. (J Am Soc Mass Spectrom 2003, 14, 236 -240)

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Section: Resultsmentioning

confidence: 99%

Classification of lactate dehydrogenase of different origin by liquid chromatography-mass spectrometry and multivariate analysis

Bylund

Samskog

Markides

et al. 2003

J. Am. Soc. Mass Spectrom.

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“…Typically the fraction chosen is at least 90%; we use ε = 0.01 in the results shown below. The Malinowski's F-test [18] was introduced in the chemometrics literature to differentiate between significant and noise eigenvectors in PCA. The sum of the eigenvalues p j=1 λ j can be decomposed into pieces representing significant and noise eigenvalues, with the number of significant eigenvalues providing an estimate of the number of pure components.…”

Section: Current Methods For Estimating the Number Of Pure Componentsmentioning

confidence: 99%

Estimating the number of pure chemical components in a mixture by maximum likelihood

Levina

Wagaman

Callender

et al. 2007

Journal of Chemometrics

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This paper addresses the problem of determining the number of pure chemical components in a mixture by applying the maximum likelihood estimator (MLE) of intrinsic dimension. The application here is to Raman spectroscopy data, although the method is general and can be applied to any type of data from a chemical mixture. We show that the MLE produces superior results compared to other methods on both simulated and real chemical mixtures, and is accurate even when minor components are present. Even if the signal-to-noise (SN) ratio is very low, accurate estimates can still be obtained by smoothing the data before applying the estimator, this approach is illustrated on two real datasets with high noise levels. Since the MLE is computed locally at every data point, we also show how the local estimates can be used for other applications, such as segmenting the specimen into homogeneous regions.

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“…The optimum number of PCs was chosen as the minimum PC number where adding an additional PC did not yield a statistically significant decrease in the standard error of the model predictions. This was determined by Malinowski's Ftest [20]. Malinowski's F-test assumes that the sum of the eigenvalues can be decomposed into either parts which are significant or noise, and that the significant eigenvalues provide an estimate of the true number of principal components needed.…”

Section: E Image Registrationmentioning

confidence: 99%

Wavelet Compressed PCA Models for Real-Time Image Registration in Augmented Reality Applications

Cooper¹,

Wise²,

Cooper³

et al. 2015

ijarai

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Abstract-The use of augmented reality (AR) has shown great promise in enhancing medical training and diagnostics via interactive simulations. This paper presents a novel method to perform accurate and inexpensive image registration (IR) utilizing a pre-constructed database of reference objects in conjunction with a principal component analysis (PCA) model. In addition, a wavelet compression algorithm is utilized to enhance the speed of the registration process. The proposed method is used to perform registration of a virtual 3D heart model based on tracking of an asymmetric reference object. The results indicate that the accuracy of the method is dependent upon the extent of asymmetry of the reference object which required inclusion of higher order principal components in the model. A key advantage of the presented IR technique is the absence of a restart mechanism required by the existing approaches while allowing up to six orders of magnitude compression of the modeled image space. The results demonstrate that the method is computationally inexpensive and thus suitable for real-time augmented reality implementation.

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Statistical F‐tests for abstract factor analysis and target testing

Cited by 184 publications

References 22 publications

Classification of lactate dehydrogenase of different origin by liquid chromatography-mass spectrometry and multivariate analysis

Classification of lactate dehydrogenase of different origin by liquid chromatography-mass spectrometry and multivariate analysis

Estimating the number of pure chemical components in a mixture by maximum likelihood

Wavelet Compressed PCA Models for Real-Time Image Registration in Augmented Reality Applications

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