How many principal components? stopping rules for determining the number of non-trivial axes revisited

By P. Peres‐Neto, Donald A. Jackson, Keith M. Somers. Computational Statistics & Data Analysis, 2005

850 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/6dc3aa26b2cd3591e2b78bfa9ae8cfe54ee71ab2

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In Artificial Intelligence

In Statistics and Probability

Citations in the corpus

Bi-cross-validation for factor analysis (2015, background): “, [50]) and recommendations among them are based largely on simulation studies [13, 58].”
Bootstrap based confidence limits in principal component analysis: a case study (2013, methodology): “The practical rank is determined beforehand based on the stability of the PCA subspace [17–21], by using techniques such as cross-validation [41], some reported alternative methods [40,42,43], or knowledge of the user about the data; this rank will be fixed from here on.”
The Hull Method for Selecting the Number of Common Factors (2011, methodology): “We considered a variant of PA that appeared to be highly efficient in Peres-Neto et al. (2005) and which they refer to as Rnd-Lambda.”
Dimensionality assessment of ordered polytomous items with parallel analysis. (2011, background): “Horn’s PA has been extensively studied, both on the basis of empirical data sets (Cota, Longman, Holden, & Fekken, 1993; Hubbard & Allen, 1987) and Monte Carlo simulation (Glorfeld, 1995; Peres-Neto et al., 2005; Turner, 1998; Velicer, Eaton, & Fava, 2000; Zwick & Velicer, 1986).”
Dimensionality of object representations in monkey inferotemporal cortex (2014, methodology): “A variety of procedures in this genre are reviewed by Peres-Neto et al. (2005).”
Multiple linear regression and artificial neural networks based on principal components to predict ozone concentrations (2007, methodology): “…the eigenvalue for the kjth component, n is the number of observations in the sample and l is obtained by the following equation: l¼ Xp j¼kþ1 lj p k ð4Þ The null hypothesis considered was that all variables were uncorrelated and when accepted, PCA could be applied (Peres-Neto et al., 2005).”