  Advanced data analysis techniques have proved to be crucial for extracting
information from noisy images. Here we show that principal component analysis
can be successfully applied to ultracold gases to unveil their collective
excitations. By analyzing the correlations in a series of images we are able to
identify the collective modes which are excited, determine their population,
image their eigenfunction, and measure their frequency. Our method allows to
discriminate the relevant modes from other noise components and is robust with
respect to the data sampling procedure. It can be extended to other dynamical
systems including cavity polariton quantum gases or trapped ions.
