We consider the problem of clustering with $K$-means and Gaussian mixture models with a constraint on the separation between the centers in the context of real-valued data. We first propose a dynamic programming approach to solving the $K$-means problem with a separation constraint on the centers, building on (Wang and Song, 2011). In the context of fitting a Gaussian mixture model, we then propose an EM algorithm that incorporates such a constraint. A separation constraint can help regularize the output of a clustering algorithm, and we provide both simulated and real data examples to illustrate this point.

翻译：我们考虑了以K$和Gaussian混合模型组合的问题,限制在实际价值数据的背景下将中心分开。我们首先提出一种动态的方案编制方法,在中心分开的限制下解决K$问题,并以(Wang和Song,2011年)为基础(Wang和Song,2011年)。在设计高斯混合模型时,我们然后提出一种包含这种限制的EM算法。分离限制可以帮助组合算法的输出规范化,我们提供模拟和真实的数据例子来说明这一点。