ICA (independent component analysis) is a new, simple and powerful idea for analyzing multi-variant data. One of the successful applications is neurobiological data analysis such as EEG (electroencephalography), MRI (magnetic resonance imaging), and MEG (magnetoencephalography). But there remain a lot of problems. In most cases, neurobiological data contain a lot of sensory noise, and the number of independent components is unknown. In this article, we discuss an approach to separate noise-contaminated data without knowing the number of independent components. A well-known two stage approach to ICA is to pre-process the data by PCA (principal component analysis), and then the necessary rotation matrix is estimated. Since PCA does not work well for noisy data, we implement a factor analysis model for pre-processing. In the new pre-processing, the number of the sources and the amount of the sensory noise are estimated. After the pre-processing, the rotation matrix is estimated using an ...