Density estimation is a fundamental technique employed in various fields to model and to understand the underlying distribution of data. The primary objective of density estimation is to estimate the probability density function of a random variable. This process is particularly valuable when dealing with univariate or multivariate data and is essential for tasks such as clustering, anomaly detection, and generative modeling. In this paper we propose the mono-variate approximation of the density using spline quasi interpolation and we applied it in the context of clustering modeling. The clustering technique used is based on the construction of suitable multivariate distributions which rely on the estimation of the monovariate empirical densities (marginals). Such an approximation is achieved by using the proposed spline quasi-interpolation, while the joint distributions to model the sought clustering partition is constructed with the use of copulas functions. In particular, since copulas can capture the dependence between the features of the data independently from the marginal distributions, a finite mixture copula model is proposed. The presented algorithm is validated on artificial and real datasets.

使用样条准插值方法对密度进行单变量逼近，并将其应用于聚类建模；通过构建适当的多变量分布来实现聚类分区模型，并使用copula函数来捕捉数据特征间的依赖关系，提出了有限混合copula模型；在人工数据集和实际数据集上验证了提出的算法。

基于样条拟合的经验密度估计及其在Copulas聚类建模中的应用