  Though there is a growing body of literature on fairness for supervised
learning, the problem of incorporating fairness into unsupervised learning has
been less well-studied. This paper studies fairness in the context of principal
component analysis (PCA). We first present a definition of fairness for
dimensionality reduction, and our definition can be interpreted as saying that
a reduction is fair if information about a protected class (e.g., race or
gender) cannot be inferred from the dimensionality-reduced data points. Next,
we develop convex optimization formulations that can improve the fairness (with
respect to our definition) of PCA and kernel PCA. These formulations are
semidefinite programs (SDP's), and we demonstrate the effectiveness of our
formulations using several datasets. We conclude by showing how our approach
can be used to perform a fair (with respect to age) clustering of health data
that may be used to set health insurance rates.
