Singular Value Decomposition and factor analysis in Social Science and Humanities
DOI:
https://doi.org/10.46661/rev.metodoscuant.econ.empresa.8004Keywords:
Singular Value Decomposition, Factor Analysis, Humanities and Social SciencesAbstract
The objects of study of the humanities and social sciences are intrinsically complex. Because it is philosophically attractive, and because it helps in practice to manage
such complexity, one of the most influential central ideas throughout the history and present of these disciplines is the notion that the large number of empirical manifestations that characterize their objects of study are actually expressions of a few factors that influence all other variables. The corresponding statistical methodology to implement these ideas has different names and differs in detail in different disciplines, but one name that can be recognized in many of them is “factor analysis”. The first objective of this work is to present a classical method of
linear algebra, known as “Singular Value Decomposition” (SVD), in an intuitive and at the same time rigorous way to the community of human and social sciences.
SVD systematizes and generalizes the factorization of any data matrix. In addition, the method is of enormous importance in the era of big data and machine learning,
which are increasingly influencing research in all areas of study. The second objective is to invite questioning of certain hypotheses in traditional factor analysis. The SVD
reveals that factors are inherent in any matrix-structured data set; what is crucial is how singular values decay. Data will determine this decay, with potentially profoundly
transformative theoretical repercussions.
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