K-期望聚类
K-expectiles clustering
摘要：
$K$ -均值聚类算法是聚类分析中应用最广泛的划分算法之一，具有简单、计算效率高等优点。然而，$K$ -均值在应用于具有非球形形状的聚类的数据时不提供适当的聚类结果。提出了一种新的基于期望值的划分聚类算法。聚类中心被定义为多变量期望值，并且通过最小化聚类内“$τ$ -方差”的贪婪算法来搜索聚类。我们提出了两种方案：固定的$τ$聚类和自适应的$τ$聚类。仿真结果表明，该方法在具有非对称形状的聚类或具有复杂结构的聚类（包括非对称正态、β、偏态$t$和$F$分布的聚类）上优于$K$ -均值聚类和谱聚类.提供了自适应$τ$集群在加密货币（CC）市场数据上的应用。研究发现，CC市场的预期集群表现出机构投资者主导市场的现象。第二个应用是图像分割。与其他基于中心的聚类方法相比，像素数据的自适应$τ$聚类中心可以更好地捕获和描述图像的特征。固定的$τ$聚类带来了更大的灵活性，分割精度相当高。
英文摘要：
$K$-means clustering is one of the most widely-used partitioning algorithm in cluster analysis due to its simplicity and computational efficiency. However, $K$-means does not provide an appropriate clustering result when applying to data with non-spherically shaped clusters. We propose a novel partitioning clustering algorithm based on expectiles. The cluster centers are defined as multivariate expectiles and clusters are searched via a greedy algorithm by minimizing the within cluster '$τ$ -variance'. We suggest two schemes: fixed $τ$ clustering, and adaptive $τ$ clustering. Validated by simulation results, this method beats both $K$-means and spectral clustering on data with asymmetric shaped clusters, or clusters with a complicated structure, including asymmetric normal, beta, skewed $t$ and $F$ distributed clusters. Applications of adaptive $τ$ clustering on crypto-currency (CC) market data are provided. One finds that the expectiles clusters of CC markets show the phenomena of an institutional investors dominated market. The second application is on image segmentation. compared to other center based clustering methods, the adaptive $τ$ cluster centers of pixel data can better capture and describe the features of an image. The fixed $τ$ clustering brings more flexibility on segmentation with a decent accuracy.
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