Determining The Correct Number Of Components To Extract From A Principal Components Analysis: A Monte Carlo Study Of The Accuracy Of The Scree Plot

Kanyongo, Gibbs Y.

doi:10.22237/jmasm/1114906380

Cited by 49 publications

(25 citation statements)

References 13 publications

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“…The PC values can be visualized in a Scree plot, in which the explained variance is plotted versus PC index in order of decreasing explained variance . Often, the number of components retained for further analysis is determined through the identification of a change in slope in the Scree plot, with the lowest order PCs, corresponding to the largest slope value, used for further analysis; however, this method is often criticized for its subjectivity . Alternately, the number of retained PCs can be chosen using a parallel analysis, in which the eigenvalues of the covariance matrix C are compared to those of a random, uncorrelated matrix of the same size .…”

Section: Experimental Procedures and Data Analysis Methodologiesmentioning

confidence: 99%

“…Often, the number of components retained for further analysis is determined through the identification of a change in slope in the Scree plot, with the lowest order PCs, corresponding to the largest slope value, used for further analysis; however, this method is often criticized for its subjectivity . Alternately, the number of retained PCs can be chosen using a parallel analysis, in which the eigenvalues of the covariance matrix C are compared to those of a random, uncorrelated matrix of the same size . In parallel analysis, an eigenvalue of C , which is greater than the corresponding parallel random eigenvalue is said to correspond to a significant component, whereas those eigenvalues of C that are smaller than their parallel random eigenvalues are said to correspond to random noise .…”

Section: Experimental Procedures and Data Analysis Methodologiesmentioning

confidence: 99%

“…The results of PCA can be used for outlier detection, variable selection, and predictive modeling . Furthermore, analysis of the linear combinations that define each PC can be used to accurately and concisely summarize relationships between the original variables …”

Section: Introductionmentioning

confidence: 99%

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Classifying formulations of crosslinked polyethylene pipe by applying machine‐learning concepts to infrared spectra

Hiles

Grossutti

Dutcher

2019

J Polym Sci B Polym Phys

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Crosslinked polyethylene (PEX-a) pipes are emerging as promising replacements for traditional metal or concrete pipes used for water, gas, and sewage transport. Understanding the relationship between pipe formulation and performance is critical to their proper design and implementation. We have developed a methodology using principal component analysis (PCA) and the machine learning techniques of k-means clustering and support vector machines (SVM) to compare and classify different PEX-a pipe formulations based on characteristic infrared (IR) spectroscopy absorbance peaks. The application of PCA revealed that a large percentage (89%) of the total variance could be explained by the first three principal components (PC1-PC3), with distinct clustering of the data for each formulation. By examining the contribution of the individual IR

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Section: Experimental Procedures and Data Analysis Methodologiesmentioning

confidence: 99%

Section: Experimental Procedures and Data Analysis Methodologiesmentioning

confidence: 99%

See 1 more Smart Citation

Classifying formulations of crosslinked polyethylene pipe by applying machine‐learning concepts to infrared spectra

Hiles

Grossutti

Dutcher

2019

J Polym Sci B Polym Phys

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“…Deciding how many clusters to retain from a cluster analysis requires an element of visual subjectivity, but this remains a common method for determining the number of components to extract from a dataset (Cattell and Vogelmann 1977). Statistical simulation studies have shown that when component or cluster loading is higher, identification of the "correct" number of components is more accurate (Kanyongo 2005). These methods provide a more objective and assemblage specific approach to identifying data clusters than arbitrary universal size cut-offs.…”

Section: Sample and Methodsmentioning

confidence: 99%

Lithic miniaturization in Late Pleistocene southern Africa

Pargeter

2016

Journal of Archaeological Science: Reports

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versus accidental small tool production. This can be achieved by showing purposeful raw material selection for small core production, systematic technological intent to miniaturize production, and by conduction use-trace analyses on the resulting flakes. A fourth factor involves the use of middle range theoretical models derived from experimental and/or ethnographic research to demonstrate the use of small tools and cores. These middle range models guide discussions about why humans choose to miniaturize lithic production.Lithic miniaturization is a truly global phenomenon increasing during the Late Pleistocene in many regions of the Old World from Africa to East Asia (Elston and Kuhn 2002). By the Holocene, small stone tools were regular components of hunter-gatherer toolkits in Australia, Northern Asia and North America. Because lithic miniaturization (also sometimes called "microlithization") proliferated during the Late Pleistocene and the Later Stone Age (LSA), archaeologists associate it with "modern human behavior" (e.g. McBrearty and Brooks, 2000).However, lithic miniaturization is no more consistent a feature of Late Pleistocene assemblages than pointed bone production, rock art or engraved ochre. Lithic miniaturization was one of our Pleistocene ancestor"s many strategic options for making stone tools. Lithic miniaturization remains one of the most economically consequential developments inPleistocene lithic technology (Hiscock 2015b). Small tool technologies enabled humans to extract usable cutting edges from raw materials more effectively and efficiently and to do so on a wide range of rock types (Bamforth and Bleed 1997). Humans used multiple technological strategies for lithic miniaturization in various parts of the world, ranging from specialized pressure-based techniques to simpler bipolar techniques (Elston and Brantingham 2002; Desrosiers 2012; de la Peña 2015a). These strategies provided a range of flexible technological solutions to the problems posed by migration and diffusion into new territories (e.g. North America) and to the maintenance of these territories once established (e.g. East Africa) (Madsen

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“…Traditional ways of selecting the principal components from the projected space would rely on a simple threshold that filters out the dimensions with relatively small eigenvalues. The threshold is normally determined by visual or statistical analysis on the scree-plot [4], matrix properties [5], or information gain [6]. However, as one of the special properties of Bayes classifier, the estimation of the conditional likelihood, especially the sensitivity of the estimation, are not normally considered as a critical factor when deciding the threshold for selecting the principal components.…”

Section: Introductionmentioning

confidence: 99%

Controlling Sensitivity of Gaussian Bayes Predictions based on Eigenvalue Thresholding

Han¹,

Du²,

Jassim³

2018

EAI Endorsed Transactions on Industrial Networks and Intelligen

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Gaussian Bayes classifiers are widely used in machine learning for various purposes. Its special characteristic has provided a great capacity for estimating the likelihood and reliability of individual classification decision made, which has been used in many areas such as decision support assessments and risk analysis. However, Gaussian Bayes models tend to perform poorly when processing feature vectors of high dimensionality. This limitation is often resolved using dimension reduction techniques such as Principal Component Analysis. Conventional approaches on reducing dimensionalities usually rely on using a simple threshold based on accuracy measurements or sampling characteristics but rarely consider the sensitivity aspect of the prediction model created. In this paper, we have investigated the influence of eigenvalue selections on Gaussian Bayes classifiers in the context of sensitivity adjustment. Experiments based on real-life data have shown indicative and intriguing results.

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Determining The Correct Number Of Components To Extract From A Principal Components Analysis: A Monte Carlo Study Of The Accuracy Of The Scree Plot

Cited by 49 publications

References 13 publications

Classifying formulations of crosslinked polyethylene pipe by applying machine‐learning concepts to infrared spectra

Classifying formulations of crosslinked polyethylene pipe by applying machine‐learning concepts to infrared spectra

Lithic miniaturization in Late Pleistocene southern Africa

Controlling Sensitivity of Gaussian Bayes Predictions based on Eigenvalue Thresholding

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