<p>Nowadays, fingerprint Presentation Attack Detection systems (PADs) are primarily based on deep learning architectures subjected to massive training. However, their performance decreases to never-seen-before attacks. With the goal of contributing to explaining this issue, we hypothesized that this limited ability to generalize is due to the lack of "representativeness" of the samples available for the PAD training. "Representativeness" is treated here from a geometrical perspective: the spread of samples into the feature space, especially near the decision boundaries. In particular, we explored the possibility of adopting three-dimensionality reduction methods to make the problem affordable through visual inspection. These methods enable visual inspection and interpretation by projecting data into two-dimensional spaces, facilitating the identification of weak areas in the decision regions estimated after the training phase. Our analysis delineates the benefits and drawbacks of each dimensionality reduction method and leads us to make substantial recommendations in the crucial phase of the training design.</p>