  We investigate whether the standard dimensionality reduction technique of PCA
inadvertently produces data representations with different fidelity for two
different populations. We show on several real-world data sets, PCA has higher
reconstruction error on population A than on B (for example, women versus men
or lower- versus higher-educated individuals). This can happen even when the
data set has a similar number of samples from A and B. This motivates our study
of dimensionality reduction techniques which maintain similar fidelity for A
and B. We define the notion of Fair PCA and give a polynomial-time algorithm
for finding a low dimensional representation of the data which is
nearly-optimal with respect to this measure. Finally, we show on real-world
data sets that our algorithm can be used to efficiently generate a fair low
dimensional representation of the data.
