Reddy Chandan K, Chiang Hsiao-Dong, Rajaratnam Bala
Department of Computer Science, Wayne State University, Detroit, MI 48202, USA.
IEEE Trans Pattern Anal Mach Intell. 2008 Jul;30(7):1146-57. doi: 10.1109/TPAMI.2007.70775.
In spite of the initialization problem, the Expectation-Maximization (EM) algorithm is widely used for estimating the parameters of finite mixture models. Most popular model-based clustering techniques might yield poor clusters if the parameters are not initialized properly. To reduce the sensitivity of initial points, a novel algorithm for learning mixture models from multivariate data is introduced in this paper. The proposed algorithm takes advantage of TRUST-TECH (TRansformation Under STability-reTaining Equilibra CHaracterization) to compute neighborhood local maxima on likelihood surface using stability regions. Basically, our method coalesces the advantages of the traditional EM with that of the dynamic and geometric characteristics of the stability regions of the corresponding nonlinear dynamical system of the log-likelihood function. Two phases namely, the EM phase and the stability region phase, are repeated alternatively in the parameter space to achieve improvements in the maximum likelihood. The EM phase obtains the local maximum of the likelihood function and the stability region phase helps to escape out of the local maximum by moving towards the neighboring stability regions. The algorithm has been tested on both synthetic and real datasets and the improvements in the performance compared to other approaches are demonstrated. The robustness with respect to initialization is also illustrated experimentally.
尽管存在初始化问题，但期望最大化（EM）算法仍被广泛用于估计有限混合模型的参数。如果参数初始化不当，大多数流行的基于模型的聚类技术可能会产生较差的聚类结果。为了降低初始点的敏感性，本文介绍了一种从多变量数据中学习混合模型的新算法。所提出的算法利用TRUST-TECH（稳定性保持平衡特征下的变换），通过稳定区域在似然表面上计算邻域局部最大值。基本上，我们的方法结合了传统EM算法的优点以及对数似然函数相应非线性动力系统稳定区域的动态和几何特征。在参数空间中交替重复两个阶段，即EM阶段和稳定区域阶段，以实现最大似然的改进。EM阶段获得似然函数的局部最大值，稳定区域阶段通过向相邻稳定区域移动来帮助逃离局部最大值。该算法已在合成数据集和真实数据集上进行了测试，并展示了与其他方法相比在性能上的改进。实验还说明了该算法在初始化方面的鲁棒性。
