Nonlinear principal components analysis is shown to generate some of the most common criteria for solving the linear independent components analysis problem. These include minimum kurtosis, maximum likelihood and the contrast score functions. In this paper, a topology that can separate the independent sources from a linear mixture by specifically utilizing a Gaussianizing nonlinearity is demons...

In 2002, Császár [1] introduced the notions of generalized topology and generalized continuity. In 2008, Császár [3] defined an enlargement and construct the generalized topology induced by an enlargement; introduced the concept of (κ, λ)-continuity and (κμ, λμ)continuity on enlargements. In 2008, Császár [4] defined and studied the notions of product of generalized topologies. In 2010, S. Mara...

Generalized metric spaces are a common generalization of preorders and ordinary metric spaces (Lawvere, 1973). Combining Lawvere’s (1973) enriched-categorical and Smyth’s (1988, 1991) topological view on generalized metric spaces, it is shown how to construct (1) completion, (2) two topologies, and (3) powerdomains for generalized metric spaces. Restricted to the special cases of preorders and ...