  In this paper with study phase transitions of the $q$-state Potts model,
through a number of unsupervised machine learning techniques, namely Principal
Component Analysis (PCA), $k$-means clustering, Uniform Manifold Approximation
and Projection (UMAP), and Topological Data Analysis (TDA). Even though in all
cases we are able to retrieve the correct critical temperatures $T_c(q)$, for
$q = 3, 4$ and $5$, results show that non-linear methods as UMAP and TDA are
less dependent on finite size effects, while still being able to distinguish
between first and second order phase transitions. This study may be considered
as a benchmark for the use of different unsupervised machine learning
algorithms in the investigation of phase transitions.
