Generalized binary independent component analysis

Independent component analysis (ICA) is a statistical method for transforming an observed multidimensional random vector into components that are as statistically independent as possible from each other. Usually the ICA framework assumes a model according to which the observations are generated (generative function, additive noise). Binary ICA (BICA) is a special case of ICA in which both the observations and the independent components are over the binary field GF(2). In this work we introduce a generalized BICA framework in which an observation vector is decomposed to its independent components (as much as possible) with no prior assumption on the way it was generated. We propose several theorems and show that this NP hard problem can be accurately solved with a branch and bound search tree algorithm, or tightly approximated with a series of linear programs. BICA was shown to have applications in many domains including medical diagnosis, multi-cluster assignment, network tomography and internet resource management. We suggest that BICA also applies in source coding; we argue that instead of generating statistically independent prediction errors, as in predictive coding, an improved encoder shall assemble a vector of observations and apply the generalized BICA on it. This is shown to achieve improved performance at the cost of introducing some time delay (working in batch).