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UBC Theses and Dissertations

On the statistical properties of Entromin as an orthogonal rotation criterion Chiu, Kenny


The primary goal of factor analysis is to uncover a set of latent factors that can explain the variation in the data. Principal Component Analysis is one approach that estimates the factors by a set of orthogonal vectors. However, it may be difficult to interpret the factors as-is, and so it is common to rotate the estimated factors to make their coefficients as sparse as possible to improve interpretability. Varimax is the most popular method for factor rotations, and its statistical properties have been studied in recent literature. Entromin is another factor rotation method that is less commonly used and not as well-studied, but there exists conventional wisdom that Entromin generally finds sparser rotations compared to Varimax. In this thesis, we aim to explain the sparsity claim for Entromin by studying its statistical properties. Our main contributions include several theoretical results that take steps towards this aim. We show that Varimax is a first-order approximation of Entromin, and that generalizing this connection leads to a family of Entromin approximations. We derive the conditions under which the second-order approximation can be viewed as performing statistical inference in a latent factor model. We then make the connection between optimizing the Entromin criterion and recovering sparsity in the factors. Other contributions of this thesis include novel connections to statistical concepts that have not been made in the literature to our knowledge, and an empirical study of Entromin on a dataset of New York Times articles.

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