IEEE Trans Cybern. 2014 Jun;44(6):857-69. doi: 10.1109/TCYB.2013.2273714. Epub 2013 Jul 24.
The finite mixture model based on the Student's-t distribution, which is heavily tailed and more robust than the Gaussian mixture model (GMM), is a flexible and powerful tool to address many computer vision and pattern recognition problems. However, the Student's-t distribution is unbounded and symmetrical around its mean. In many applications, the observed data are digitalized and have bounded support. The distribution of the observed data usually has an asymmetric form. A new finite bounded asymmetrical Student's-t mixture model (BASMM), which includes the GMM and the Student's-t mixture model (SMM) as special cases, is presented in this paper. We propose an extension of the Student's-t distribution in this paper. This new distribution is sufficiently flexible to fit different shapes of observed data, such as non-Gaussian, nonsymmetric, and bounded support data. Another advantage of the proposed model is that each of its components can model the observed data with different bounded support regions. In order to estimate the model parameters, previous models represent the Student's-t distributions as an infinite mixture of scaled Gaussians. We propose an alternate approach in order to minimize the higher bound on the data negative log-likelihood function, and directly deal with the Student's-t distribution. As an application, our method has been applied to image segmentation with promising results.
基于学生 t 分布的有限混合模型比高斯混合模型（GMM）具有更重尾和更强鲁棒性，是解决许多计算机视觉和模式识别问题的灵活而强大的工具。然而，学生 t 分布在其均值周围是无界和对称的。在许多应用中，观测数据是数字化的，并且具有有界的支持。观测数据的分布通常具有不对称的形式。本文提出了一种新的有限有界不对称学生 t 混合模型（BASMM），它包括 GMM 和学生 t 混合模型（SMM）作为特例。我们在本文中提出了学生 t 分布的扩展。这种新的分布具有足够的灵活性，可以拟合不同形状的观测数据，例如非高斯、非对称和有界支持的数据。该模型的另一个优点是，其每个分量都可以用不同的有界支持区域来对观测数据进行建模。为了估计模型参数，以前的模型将学生 t 分布表示为缩放高斯的无限混合。我们提出了一种替代方法，以便最小化数据负对数似然函数的上限，并直接处理学生 t 分布。作为一种应用，我们的方法已应用于图像分割，并取得了良好的效果。
