  We describe techniques to characterise the light-curves of regular variable
stars by applying principal component analysis (PCA) to a training set of high
quality data, and to fit the resulting light-curve templates to sparse and
noisy photometry to obtain parameters such as periods, mean magnitudes etc. The
PCA approach allows us to efficiently represent the multi-band light-curve
shapes of each variable, and hence quantitatively describe the average
behaviour of the sample as a smoothly varying function of period, and also the
range of variation around this average.
  In this paper we focus particularly on the utility of such methods for
analysing HST Cepheid photometry, and present simulations which illustrate the
advantages of our PCA template-fitting approach. These are: accurate parameter
determination, including light-curve shape information; simultaneous fitting to
multiple passbands; quantitative error analysis; objective rejection of
variables with non Cepheid-like light-curves or those with potential period
aliases.
  We also use PCA to confirm that Cepheid light-curve shapes are systematically
different (at the same period) between the Milky Way (MW) and the Large and
Small Magellanic Clouds (LMC, SMC), and consider whether light-curve shape
might therefore be used to estimate the mean metallicities of Cepheid samples,
thus allowing metallicity corrections to be applied to derived distance
estimates.
