Independent component analysis based on nonparametric density estimation
Independent component analysis based on nonparametric density estimation
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DOI：
10.1109/tnn.2003.820667
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发表时间：
2004-01-01
影响因子：
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通讯作者：
Roychowdhury, VP
中科院分区：
文献类型：
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作者：
Boscolo, R;Pan, H;Roychowdhury, VP
在本文中，我们介绍了一种新型的独立组件分析（ICA）算法，该算法确实对混合信号的特定潜在分布而盲目。使用非参数内核密度估计技术，该算法同时执行源信号的未知概率密度函数和Unmixing矩阵的估计。遵循提出的方法，可以将盲信号分离框架作为非线性优化问题提出，其中可用成本函数的封闭形式表达式，并且只有Unmixing矩阵的元素显示为未知数。我们进行了一系列蒙特卡洛模拟，涉及具有不同统计特征和样本量的各种源信号的线性混合物。新算法不仅始终超过所有最新的ICA方法，而且还证明了以下属性：1）仅一个能够学习源统计的灵活模型，才能始终如一地实现所有混合信号的准确分离。 2）采用适当设计的优化框架，可以得出与传统算法的稳定性和收敛性匹配的灵活ICA算法。 3）非参数方法不一定需要大型样本量，以优于具有固定或部分适应性对比功能的方法。
In this paper, we introduce a novel independent component analysis (ICA) algorithm, which is truly blind to the particular underlying distribution of the mixed signals. Using a nonparametric kernel density estimation technique, the algorithm performs simultaneously the estimation of the unknown probability density functions of the source signals and the estimation of the unmixing matrix. Following the proposed approach, the blind signal separation framework can be posed as a nonlinear optimization problem, where a closed form expression of the cost function is available, and only the elements of the unmixing matrix appear as unknowns. We conducted a series of Monte Carlo simulations, involving linear mixtures of various source signals with different statistical characteristics and sample sizes. The new algorithm not only consistently outperformed all state-of-the-art ICA methods, but also demonstrated the following properties: 1) Only a flexible model, capable of learning the source statistics, can consistently achieve an accurate separation of all the mixed signals. 2) Adopting a suitably designed optimization framework, it is possible to derive a flexible ICA algorithm that matches the stability and convergence properties of conventional algorithms. 3) A nonparametric approach does not necessarily require large sample sizes in order to outperform methods with fixed or partially adaptive contrast functions.