  In the presence of mass anisotropy, anisotropic interaction, or in-plane
magnetic field, quantum Hall droplets can exhibit shape deformation and
internal geometrical degree of freedom. We characterize the geometry of quantum
Hall states by principal component analysis, which is a statistical technique
that emphasizes variation in a dataset. We first test the method in an integer
quantum Hall droplet with dipole-dipole interaction in disk geometry. In the
subsequent application to fractional quantum Hall systems with anisotropic
Coulomb interaction in torus geometry, we demonstrate that the principal
component analysis can quantify the metric degree of freedom and predict the
collapse of a $\nu= 1/3$ state. We also calculate the metric response to
interaction anisotropy at filling fractions $\nu= 1/5$ and $2/5$ and show that
the response is roughly the same within the same Jain sequence, but can differ
at large anisotropy for different sequences.
