1. Independent component analysis (ICA)
Independent component analysis (ICA) is a computationa method for separating a multivariate signal into additive sub-components supposing the mutual statistical independence of the non-Gaussian source signals. The regular ICA usually assumes linear combinations of independent sources over the field of real valued number.
ICA was firstemployed in the context of neural network modeling. In 1990s, some highly successful new algorithms were developed by several research groups, particularly on problems like the cocktail party effect, where the individual speech waveforms are found from their mixtures. ICA became a topic of interest for the field of neural networks. Applications of ICA can be found in signal processing, audio signal separation, telecommunications, fault diagnosis, feature extraction, financial time series analysis, and data mining.
2. Binary (BICA)
Regular ICA methods assume linear mixing of continuous signals. A special variant of ICA, called Binary ICA (BICA), considers boolean mixing (e.g., OR, XOR etc...) of binary signals. Existing solutions to BICA mainly differ in their assumptions of the binary operator (e.g., OR or XOR), the prior distribution of the mixing matrix, noise model, and/or hidden causes. in 2007, Yeredor considered BICA in XOR mixtures and investigated the identifiability problem. A deflation algorithm is employed for source separation based on entropy minimization. BICA in XOR mixtures can be viewed as the binary counterpart of classical linear ICA problems. In 2006, Singliar and Hauskrecht employed a noise OR model to model dependencyamong observable random variables using K known latent factors. A variational inference algorithm is developed. In the noise OR model, the probabilistic dependency between observable vectors and latent vectors is modeled via the noise OR conditional distribution. The dimension of the latent vector is assumed to be known and less than that of the observable. In 2011, Nguyen and Zheng used a OR Mixtures noise model.