Various information-theoretic divergences have been proposed for the cost function in tasks such as matrix factorization and clustering. One class of divergence is called the Beta divergence. By varying a real-valued parameter $\beta ,$ the Beta divergence connects several well-known divergences, such as the Euclidean distance, Kullback-Leibler divergence, and Itakura-Saito divergence. Unfortunately, the Beta divergence is properly defined only for positive real values, hindering its use for measuring distances between complex-valued data points. We define a new divergence, the Complex Beta divergence, that operates on complex values, and show that it coincides with the standard Beta divergence when the data is restricted to be in phase. Moreover, we show that different values of $\beta$ place different penalties on errors in magnitude and phase.

对于诸如矩阵分解和聚类的任务中的成本函数，已经提出了各种信息理论上的分歧。一类背离称为Beta背离。通过更改实值参数$\beta ，$Beta散度连接了几个著名的散度，例如欧几里得距离，Kullback-Leibler散度和Itakura-Saito散度。不幸的是，仅对正实数值正确定义了Beta散度，这妨碍了它用于测量复数值数据点之间的距离。我们定义了一个新的散度，即复杂Beta散度，该散度适用于复杂值，并显示了当数据被限制为同相时，它与标准Beta散度一致。此外，我们证明了$\beta$ 对幅度和相位误差施加不同的惩罚。