基于样条拟插补的经验密度估计及其在 Copulas 聚类建模中的应用
Empirical Density Estimation based on Spline Quasi-Interpolation with applications to Copulas clustering modeling
AI总结：
本文提出基于样条拟插补的单变量密度估计方法，结合 copulas 函数构建多变量联合分布，提出有限混合 copula 模型用于聚类建模，并在人工和真实数据集上验证了算法有效性。
摘要：
密度估计是各个领域中用于建模和理解数据潜在分布的基本技术。密度估计的主要目标是估计随机变量的概率密度函数。在处理单变量或多变量数据时，此过程尤为有价值，且对于聚类、异常检测和生成建模等任务至关重要。本文提出使用样条拟插补进行密度的单变量近似，并将其应用于聚类建模。所使用的聚类技术基于构建合适的多变量分布，这些分布依赖于单变量经验密度（边缘分布）的估计。这种近似是通过使用所提出的样条拟插补实现的，而用于建模所需聚类划分的联合分布则是利用 copulas 函数构建的。特别是，由于 copulas 能够独立于边缘分布捕获数据特征之间的依赖关系，因此提出了一种有限混合 copula 模型。所提出的算法在人工和真实数据集上进行了验证。
英文摘要：
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.
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