Adaptive Lagrange constraints neural network under multisensing

The traditional BSAO solution on independent component analysis (ICA) needs the ensemble a posteriori information averaging, but in reality, the probability distribution of a posteriori information is unknown, so the premise of equal probability is imprecise, and the geometrical information is discarded. Lagrange constraints neural network (LCNN) solution, which was based on a Lyapunov function------Helmholtz freedom energy equation, was designed to overcome these issues. However, LCNN cannot break out of ill-conditioned matrixand its inversion, the computing complexity was up to O(n²) and even the worst no solution. In this paper, we proposed a new solution to improve LCNN, which is called adaptive LCNN (ALCNN). ALCNN tried to solve not only ill-conditioned matrix, but also the computing complexities of learning matrix and the time to get independent components were all down to O(n). In the end, we present a watermarking application using ALCNN and multiscale wavelet.