  To extract useful information about quantum effects in cold atom experiments,
one central task is to identify the intrinsic quantum fluctuation from
extrinsic system noises of various kinds. As a data processing method,
principal component analysis can decompose fluctuations in experimental data
into eigen modes, and give a chance to separate noises originated from
different physical sources. In this paper, we demonstrate for Bose-Einstein
condensates in one-dimensional optical lattices that the principal component
analysis can be applied to time-of-flight images to successfully separate and
identify noises from different origins of leading contribution, and can help to
reduce or even eliminate noises via corresponding data processing procedures.
The attribution of noise modes to their physical origins is also confirmed by
numerical analysis within a mean-field theory.
