This letter studies a new expectation maximization (EM) algorithm to solve the problem of circle, sphere and more generally hypersphere fitting. This algorithm relies on the introduction of random latent vectors having a priori independent von Mises-Fisher distributions defined on the hypersphere. This statistical model leads to a complete data likelihood whose expected value, conditioned on the observed data, has a Von Mises-Fisher distribution. As a result, the inference problem can be solved with a simple EM algorithm. The performance of the resulting hypersphere fitting algorithm is evaluated for circle and sphere fitting.

中文翻译：

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使用EM算法根据噪声数据进行超球面拟合

这封信研究了一种新的期望最大化（EM）算法，以解决圆，球以及更一般的超球体拟合问题。该算法依赖于在超球面上定义的具有先验独立的冯·米塞斯-费舍尔分布的随机潜矢量的引入。该统计模型导致了完整的数据似然性，其似然值以观察到的数据为条件，具有冯·米塞斯·费舍尔分布。结果，可以用简单的EM算法解决推理问题。评估所得超球面拟合算法的性能，以进行圆形和球面拟合。