In this study, we utilize Gaussian Mixture Model (GMM) and propose a novel learn algorithm to approximate any density in a fast and simple way. In our previous study, we proposed a idea called GMM expansion which inspired by Fourier expansion. Similar to the base of frequencies in Fourier expansion, GMM expansion assume that normal distributions can be placed evenly along the support as a set of bases to approximate a large set of distribution in good accuracy. In this work, a new algorithm is proposed base on the idea of GMM expansion. A theoretical analysis also given to verify the convergence. Various experiments are carried out to exam the efficacy of proposed method. Experiment result demonstrate the advantages of proposed method and support that this new algorithm perform faster, is more accurate, has better stability, and is easier to use than the Expectation Maximization (EM) algorithm. Furthermore, the benefits of this proposed method helps improve the integration of GMM in neural network. The experiment results show that the neural network with our proposed method significantly improves ability to handle the inverse problem and data uncertainty. Finally, another application, a GMM-based neural network generator, is built. This application shows the potential to utilize distribution random sampling for feature variation control in generative mode.

中文翻译：

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一种基于密度高斯混合展开的有效一次迭代学习算法


在这项研究中，我们利用高斯混合模型 （GMM） 并提出了一种新的学习算法，以快速简单的方式近似任何密度。在我们之前的研究中，我们提出了一个叫做 GMM 扩展的想法，它受到傅里叶扩展的启发。与傅里叶展开中的频率底数类似，GMM 展开假设正态分布可以作为一组底面沿着支撑均匀放置，以良好的精度近似一大组分布。在这项工作中，基于 GMM 扩展的思想提出了一种新的算法。还给出了理论分析以验证收敛性。进行了各种实验以检验所提方法的有效性。实验结果表明了所提方法的优势，并支持这种新算法比期望最大化 （EM） 算法执行更快、更准确、稳定性更好、更易于使用。此外，这种提出的方法的好处有助于改善 GMM 在神经网络中的集成。实验结果表明，采用我们提出的方法的神经网络显著提高了处理逆问题和数据不确定性的能力。最后，构建了另一个应用程序，即基于 GMM 的神经网络生成器。此 App 显示了在生成模式下利用分布随机采样进行特征变化控制的潜力。