مقایسهٔ روش‌ها

	تحلیل مؤلفه‌های اصلی مقاوم (RPCA)	Factor Analysis	تحلیل مؤلفه‌های اصلی	رگرسیون مقاوم
حوزه	آمار	آمار پژوهش	یادگیری ماشین	آمار
خانواده	Regression model	Process / pipeline	Machine learning	Regression model
سال پیدایش	2011	1931	2002	1964
پدیدآور	Candès, Li, Ma & Wright (2011); Hubert, Rousseeuw & Vanden Branden (2005)	Louis Leon Thurstone	Jolliffe, I.T. (textbook); Pearson & Hotelling (origins)	Peter J. Huber (M-estimation, 1964); Frank Hampel (influence function, 1974)
نوع	Robust dimensionality reduction / matrix decomposition	Method	Unsupervised dimensionality reduction	Regression with outlier resistance
منبع بنیادین	Candès, E. J., Li, X., Ma, Y., & Wright, J. (2011). Robust Principal Component Analysis? Journal of the ACM, 58(3), 1-37.	Thurstone, L. L. (1947). Multiple Factor Analysis. University of Chicago Press.	Jolliffe, I.T. (2002). Principal Component Analysis (2nd ed.). Springer.	Huber, P. J. (1964). Robust estimation of a location parameter. The Annals of Mathematical Statistics, 35(1), 73–101.
نام‌های دیگر	RPCA, robust principal component analysis, low-rank plus sparse decomposition, Robust Temel Bileşen Analizi (RPCA)	EFA, CFA, latent variable modeling	Temel Bileşenler Analizi (PCA), PCA, principal components analysis, Karhunen-Loève transform	M-estimation regression, robust linear regression, outlier-resistant regression, MM-estimation
مرتبط	3	3	3	6
خلاصه	Robust Principal Component Analysis is a dimensionality-reduction method that extracts reliable components when the data are contaminated by outliers and noise. Introduced by Candès, Li, Ma and Wright (2011), and developed in the ROBPCA approach of Hubert, Rousseeuw and Vanden Branden (2005), it separates a data matrix into a clean low-rank part and a sparse outlier part.	Factor analysis is a statistical technique for identifying latent (unobserved) dimensions underlying observed variables, developed by Louis Leon Thurstone in the 1930s and formalized by Jöreskog (1969). Exploratory factor analysis (EFA) discovers unknown factor structure from data; confirmatory factor analysis (CFA) tests hypothesized relationships between observed and latent variables. Essential in psychometrics (test development), organizational research (measuring constructs like leadership style), and biomedicine (identifying disease subtypes), factor analysis reduces dimensionality while revealing conceptual organization in multivariate data.	Principal Component Analysis (PCA) is an unsupervised dimensionality-reduction method — given its modern textbook treatment by Ian Jolliffe (2002) — that compresses high-dimensional data into fewer dimensions while preserving the maximum possible variance. It re-expresses correlated variables as a small set of uncorrelated principal components ordered by how much of the data's variation each one captures.	Robust regression estimates the linear relationship between a continuous outcome and predictors while sharply reducing the influence of outliers and leverage points. Unlike OLS, which is highly sensitive to extreme observations, robust methods assign down-weighted influence to atypical data points, producing coefficient estimates that remain stable even when a fraction of the data is contaminated or non-normally distributed.