  We study the photospheric magnetic field of ~2000 active regions in solar
cycle 23 to search for parameters indicative of energy build-up and subsequent
release as a solar flare. We extract three sets of parameters: snapshots in
space and time- total flux, magnetic gradients, and neutral lines; evolution in
time- flux evolution; structures at multiple size scales- wavelet analysis.
This combines pattern recognition and classification techniques via a relevance
vector machine to determine whether a region will flare. We consider
classification performance using all 38 extracted features and several feature
subsets. Classification performance is quantified using both the true positive
rate and the true negative rate. Additionally, we compute the true skill score
which provides an equal weighting to true positive rate and true negative rate
and the Heidke skill score to allow comparison to other flare forecasting work.
  We obtain a true skill score of ~0.5 for any predictive time window in the
range 2-24hr, with a TPR of ~0.8 and a TNR of ~0.7. These values do not appear
to depend on the time window, although the Heidke skill score (<0.5) does.
Features relating to snapshots of the distribution of magnetic gradients show
the best predictive ability over all predictive time windows. Other
gradient-related features and the instantaneous power at various wavelet scales
also feature in the top five ranked features in predictive power. While the
photospheric magnetic field governs the coronal non-potentiality (and
likelihood of flaring), photospheric magnetic field alone is not sufficient to
determine this uniquely. Furthermore we are only measuring proxies of the
magnetic energy build up. We still lack observational details on why energy is
released at any particular point in time. We may have discovered the natural
limit of the accuracy of flare predictions from these large scale studies.
