  We map stock market interactions to spin models to recover their hierarchical
structure using a simulated annealing based Super-Paramagnetic Clustering (SPC)
algorithm. This is directly compared to a modified implementation of a maximum
likelihood approach we call Fast Super-Paramagnetic Clustering (f-SPC). The
methods are first applied standard toy test-case problems, and then to a
data-set of 447 stocks traded on the New York Stock Exchange (NYSE) over 1249
days. The signal to noise ratio of stock market correlation matrices is briefly
considered. Our result recover approximately clusters representative of
standard economic sectors and mixed ones whose dynamics shine light on the
adaptive nature of financial markets and raise concerns relating to the
effectiveness of industry based static financial market classification in the
world of real-time data analytics. A key result is that we show that f-SPC
maximum likelihood solutions converge to ones found within the
Super-Paramagnetic Phase where the entropy is maximum, and those solutions are
qualitatively better for high dimensionality data-sets.
