Directional data is ubiquitious in science. Due to its circular nature such data cannot be analyzed with commonly used statistical techniques. Despite the rapid development of specialized methods for directional statistics over the last fty years, there is only little software available that makes such methods easy to use for practioners. Most importantly, one of the most commonly used programming languages in biosciences, MATLAB, is currently not supporting directional statistics. To remedy this situation, we have implemented the CircStat toolbox for MATLAB which provides methods for the descriptive and inferential statistical analysis of directional data. We cover the statistical background of the available methods and describe how to apply them to data. Finally, we analyze a dataset from neurophysiology to demonstrate the capabilities of the CircStat toolbox

在scikit-learn中的单元超球面上聚类 演算法 此软件包实现了scikit-learn的Banerjee等人在JMLR 2005 概述的三种算法。 球形K均值（spkmeans） 球形K均值与常规K均值的不同之处在于，它在每个最大化步骤结束时（即归一化质心）将估计的聚类质心投影到单位球体上。 冯·米塞斯·费舍尔分布（movMF）的混合 就像通过均值和方差来参数化高斯分布一样，具有均值方向$\mu$和浓度参数$\kappa$ 。 从vMF分布得出的每个点$x_i$和平均方向$\|\mu\|_2 = 1$生活在单位超球面$\S^{N-1}$ （即$\|x_i\|_2 = 1$ ）的表面上$\|\mu\|_2 = 1$ 。 较大的$\kappa$会导致点集中度更高。 如果我们的数据作为一种模式米塞斯费舍尔分布的，我们有一个额外的重量参数$\alpha$在混合物中各分布。 movMF算法通过期望最大化（EM）估计混合参数，使我们能够相应地对数据进行聚类。 软运动MF 估计每个类别的每个示例的实值后验。 从某种意义上说，这使我们可以进行软聚类，因为每个数据点都有聚类的可能性。