A latent variable generative model with finite noise is used to describe several different algorithms for Independent Components Analysis (ICA). In particular, the Fixed Point ICA algorithm is shown to be equivalent to the ExpectationMaximization algorithm for maximum likelihood under certain constraints, allowing the conditions for global convergence to be elucidated. The algorithms can also b...

In order to achieve of PNL-ICA (Post-Nonlinear Independent Component Analysis) by using Dimensionality Reduction [1] the data set has to be embedded in a hyperplane, i.e. linear combination of the latent variables. This condition must be fulfilled in order to ensure that there is an unique solution to the problem. This article describes a new quality measure for Nonlinear Dimensionality Reducti...

We present a novel probabilistic framework for a hierarchical extension of independent component analysis (ICA), with a particular motivation in neuroscientific data analysis and modeling. The framework incorporates a general subspace pooling with linear ICA-like layers stacked recursively. Unlike related previous models, our generative model is fully tractable: both the likelihood and the post...

Ensemble independent component analysis (ICA) is a Bayesian multivariate data analysis method which allows various prior distributions for parameters and latent variables, leading to flexible data fitting. In this paper we apply ensemble ICA with a rectified Gaussian prior to dynamic H 2 O positron emission tomography (PET) image data, emphasizing its clinical usefulness by showing that major c...

Independent Variable Group Analysis (IVGA) is a principle for grouping dependent variables together while keeping mutually independent or weakly dependent variables in separate groups. In this paper an agglomerative method for learning a hierarchy of IVGA groupings is presented. The method resembles hierarchical clustering, but the distance measure is based on a model-based approximation of mut...