We propose an Gaussian Mixture Model (GMM) learning algorithm, based on our
previous work of GMM expansion idea. The new algorithm brings more robustness
and simplicity than classic Expectation Maximization (EM) algorithm. It also
improves the accuracy and only take 1 iteration for learning. We theoretically
proof that this new algorithm is guarantee to converge regardless the
parameters initialisation. We compare our GMM expansion method with classic
probability layers in neural network leads to demonstrably better capability to
overcome data uncertainty and inverse problem. Finally, we test GMM based
generator which shows a potential to build further application that able to
utilized distribution random sampling for stochastic variation as well as
variation control.

本文提出了一种基于高斯混合模型（Gaussian Mixture Model，GMM）的学习算法，相比经典的期望最大化（Expectation Maximization，EM）算法，该算法具有更高的鲁棒性和简易性，提高了准确性，仅需 1 次迭代进行学习。我们在理论上证明了该新算法无论参数初始化如何，都能保证收敛。与神经网络中的经典概率层相比，我们比较了 GMM 扩展方法，证明其更好地克服了数据不确定性和逆问题。最后，我们测试了基于 GMM 的生成器，展示了进一步应用的潜力，能够利用分布随机抽样进行随机变异和变异控制。