Van Vaerenbergh Steven, Santamaría Ignacio
IEEE Trans Neural Netw. 2006 May;17(3):811-4. doi: 10.1109/TNN.2006.872358.
This letter proposes a clustering-based approach for solving the underdetermined (i.e., fewer mixtures than sources) postnonlinear blind source separation (PNL BSS) problem when the sources are sparse. Although various algorithms exist for the underdetermined BSS problem for sparse sources, as well as for the PNL BSS problem with as many mixtures as sources, the nonlinear problem in an underdetermined scenario has not been satisfactorily solved yet. The method proposed in this letter aims at inverting the different nonlinearities, thus reducing the problem to linear underdetermined BSS. To this end, first a spectral clustering technique is applied that clusters the mixture samples into different sets corresponding to the different sources. Then, the inverse nonlinearities are estimated using a set of multilayer perceptrons (MLPs) that are trained by minimizing a specifically designed cost function. Finally, transforming each mixture by its corresponding inverse nonlinearity results in a linear underdetermined BSS problem, which can be solved using any of the existing methods.
本文提出了一种基于聚类的方法，用于解决源信号稀疏时的欠定（即混合信号少于源信号）后非线性盲源分离（PNL BSS）问题。尽管存在各种算法来解决稀疏源的欠定BSS问题以及混合信号数量与源信号数量相同的PNL BSS问题，但欠定场景下的非线性问题尚未得到令人满意的解决。本文提出的方法旨在对不同的非线性进行逆运算，从而将问题简化为线性欠定BSS问题。为此，首先应用谱聚类技术，将混合样本聚类到对应于不同源信号的不同集合中。然后，使用一组多层感知器（MLP）估计逆非线性，这些多层感知器通过最小化专门设计的代价函数进行训练。最后，用其相应的逆非线性对每个混合信号进行变换，就得到了一个线性欠定BSS问题，该问题可以使用任何现有方法来解决。
