Nonlinear and Noisy Extension of Independent Component Analysis: Theory and Its Application to a Pitch Sensation Model
Nonlinear and Noisy Extension of Independent Component Analysis: Theory and Its Application to a Pitch Sensation Model
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DOI：
10.1162/0899766052530866
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发表时间：
2005
影响因子：
2.9
通讯作者：
S. Maeda;Wen-Jie Song;S. Ishii
中科院分区：
文献类型：
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作者：
S. Maeda;Wen-Jie Song;S. Ishii
在这封信中，我们提出了独立分量分析（ICA）的噪声非线性版本。假设源的概率密度函数 (p.d.f.) 已知，则基于最大似然估计 (MLE) 导出学习规则。我们的模型涉及一些有噪声线性 ICA 算法（例如，Bermond & Cardoso，1999）或无噪声非线性 ICA（例如，Lee，Koehler，& Orglmeister，1997）作为特殊情况。特别是当非线性函数是线性时，作为广义期望最大化算法导出的学习规则与 Douglas、Cichocki 和 Amari (1998) 先前提出的噪声 ICA 算法具有相似的形式。此外，我们的学习规则在无噪声限制下变得与标准无噪声线性 ICA 算法相同，而现有的基于 MLE 的噪声 ICA 算法并不严格包括无噪声 ICA。我们使用语音和音乐等声学信号来训练噪声非线性 ICA。学习后的模型成功模拟了虚拟音高现象，并且虚拟音高的存在区域与心理声学实验中观察到的存在区域在质量上相似。尽管中枢听觉系统中假设的线性变换可以解释音调感觉，但我们的模型表明可以通过学习实际声学信号来获得线性变换。由于我们的模型在特殊情况下包括倒谱分析，因此期望提供倒谱分析经常给出的有用的特征提取方法。
In this letter, we propose a noisy nonlinear version of independent component analysis (ICA). Assuming that the probability density function (p.d.f.) of sources is known, a learning rule is derived based on maximum likelihood estimation (MLE). Our model involves some algorithms of noisy linear ICA (e.g., Bermond & Cardoso, 1999) or noise-free nonlinear ICA (e.g., Lee, Koehler, & Orglmeister, 1997) as special cases. Especially when the nonlinear function is linear, the learning rule derived as a generalized expectation-maximization algorithm has a similar form to the noisy ICA algorithm previously presented by Douglas, Cichocki, and Amari (1998). Moreover, our learning rule becomes identical to the standard noise-free linear ICA algorithm in the noiseless limit, while existing MLE-based noisy ICA algorithms do not rigorously include the noise-free ICA. We trained our noisy nonlinear ICA by using acoustic signals such as speech and music. The model after learning successfully simulates virtual pitch phenomena, and the existence region of virtual pitch is qualitatively similar to that observed in a psychoacoustic experiment. Although a linear transformation hypothesized in the central auditory system can account for the pitch sensation, our model suggests that the linear transformation can be acquired through learning from actual acoustic signals. Since our model includes a cepstrum analysis in a special case, it is expected to provide a useful feature extraction method that has often been given by the cepstrum analysis.