Over the last decade, the Dip-test of unimodality has gained increasing
interest in the data mining community as it is a parameter-free statistical
test that reliably rates the modality in one-dimensional samples. It returns a
so called Dip-value and a corresponding probability for the sample's
unimodality (Dip-p-value). These two values share a sigmoidal relationship.
However, the specific transformation is dependent on the sample size. Many
Dip-based clustering algorithms use bootstrapped look-up tables translating
Dip- to Dip-p-values for a certain limited amount of sample sizes. We propose a
specifically designed sigmoid function as a substitute for these
state-of-the-art look-up tables. This accelerates computation and provides an
approximation of the Dip- to Dip-p-value transformation for every single sample
size. Further, it is differentiable and can therefore easily be integrated in
learning schemes using gradient descent. We showcase this by exploiting our
function in a novel subspace clustering algorithm called Dip'n'Sub. We
highlight in extensive experiments the various benefits of our proposal.

过去十年中，Dip-test 在数据挖掘领域引起越来越多的关注，它是一种无参数统计检验方法，可可靠地评估一维样本的单峰性，并返回 Dip 值和相应的单峰性概率 (Dip-p-value)。我们提出了一种专门设计的 sigmoid 函数，用作现有查找表的替代方案，加速计算，并为每个样本大小提供 Dip - 到 Dip-p-value 的转换近似值，并且易于在梯度下降中集成进学习方案。我们在名为 Dip'n'Sub 的新型子空间聚类算法中利用该函数，通过广泛的实验展示了我们提出的方法的各种优点。