Nonlinear independent component analysis:: Existence and uniqueness results
Nonlinear independent component analysis:: Existence and uniqueness results
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DOI：
10.1016/s0893-6080(98)00140-3
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发表时间：
1999-04-01
期刊：
影响因子：
7.8
通讯作者：
Pajunen, P
中科院分区：
文献类型：
--
作者：
Hyvärinen, A;Pajunen, P
研究了非线性独立分量分析问题解的存在唯一性问题。证明了如果混合函数空间不受限制，则总是存在无穷多个解。特别是，它示出了如何构造参数化的家庭的解决方案。所涉及的不确定性并不像线性情形那样微不足道。其次，它是如何利用复分析的一些结果，以获得唯一的解决方案。我们表明，对于二维，解决方案是唯一的旋转，如果混合函数被约束为一个保角映射连同一些其他的假设。我们还推测，解决方案是严格唯一的，除了在一些退化的情况下，旋转所隐含的不确定性基本上类似于估计线性伊卡的模型。(C)1999 Elsevier Science Ltd.保留所有权利。
The question of existence and uniqueness of solutions for nonlinear independent component analysis is addressed. It is shown that if the space of mixing functions is not limited there exists always an infinity of solutions. In particular, it is shown how to construct parameterized families of solutions. The indeterminacies involved are not trivial, as in the linear case. Next, it is shown how to utilize some results of complex analysis to obtain uniqueness of solutions. We show that for two dimensions, the solution is unique up to a rotation, if the mixing function is constrained to be a conformal mapping together with some other assumptions. We also conjecture that the solution is strictly unique except in some degenerate cases, as the indeterminacy implied by the rotation is essentially similar to estimating the model of linear ICA. (C) 1999 Elsevier Science Ltd. All rights reserved.