地理参考数据K-means聚类初始种子选择算法提高聚类算法的可复制性
An Initial Seed Selection Algorithm for K-means Clustering of Georeferenced Data to Improve Replicability of Cluster Assignments for Mapping Application
摘要：
K-means是各种学科中使用最广泛的聚类算法之一，特别是对于大型数据集。然而，已知该方法对聚类中心的初始种子选择高度敏感。K-means++已经被提出来克服这个问题，并且已经被证明比k-means具有更好的准确性和计算效率。然而，在许多聚类问题中，例如当对地图应用的地理参考数据进行分类时，聚类方法的标准化，具体地说，对于方法的每次运行达到相同聚类分配的能力，即方法的可复制性，可能比任何感知的准确性度量更重要，特别是当解决方案已知为非唯一时，如在k均值聚类的情况下。在这里，我们提出了一个简单的初始种子选择算法的k-均值聚类沿着一个属性，绘制初始聚类边界沿“最深的山谷”或最大的差距数据集。因此，它采用了一种措施，以最大限度地提高连续的聚类中心之间的距离，这增强了传统的k-均值优化聚类中心和聚类成员之间的最小距离。不同于现有的初始化方法，没有额外的参数或自由度被引入到聚类算法。与k-means和k-means++相比，这将聚类分配的可复制性提高了100%，实际上将不同运行的方差降低到零，而无需向聚类过程引入任何额外的参数。此外，所提出的方法比k-means++计算效率更高，在某些情况下更准确。
英文摘要：
K-means is one of the most widely used clustering algorithms in various disciplines, especially for large datasets. However the method is known to be highly sensitive to initial seed selection of cluster centers. K-means++ has been proposed to overcome this problem and has been shown to have better accuracy and computational efficiency than k-means. In many clustering problems though -such as when classifying georeferenced data for mapping applications- standardization of clustering methodology, specifically, the ability to arrive at the same cluster assignment for every run of the method i.e. replicability of the methodology, may be of greater significance than any perceived measure of accuracy, especially when the solution is known to be non-unique, as in the case of k-means clustering. Here we propose a simple initial seed selection algorithm for k-means clustering along one attribute that draws initial cluster boundaries along the 'deepest valleys' or greatest gaps in dataset. Thus, it incorporates a measure to maximize distance between consecutive cluster centers which augments the conventional k-means optimization for minimum distance between cluster center and cluster members. Unlike existing initialization methods, no additional parameters or degrees of freedom are introduced to the clustering algorithm. This improves the replicability of cluster assignments by as much as 100% over k-means and k-means++, virtually reducing the variance over different runs to zero, without introducing any additional parameters to the clustering process. Further, the proposed method is more computationally efficient than k-means++ and in some cases, more accurate.
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