基于概率生成邻域的线数据聚类，可处理缺失信息的高维数据。
Density based Spatial Clustering of Lines via Probabilistic Generation of Neighbourhood
- 为每条线生成固定体积的定制邻域，用概率密度函数定义邻近关系。
- 能有效识别噪声且对异常值不敏感，适用于含至少(n-1)维信息的数据。
- 适合处理缺失值的高维数据聚类，如道路/铁路网络等实际场景。
在ℝⁿ中基于密度的点聚类已有广泛应用。本文将该问题推广至高维空间中线的密度聚类，考虑到线之间不存在满足三角不等式的有效距离度量。我们设计了一种聚类算法，基于可选的连续概率密度函数，为每条线生成固定体积（作为参数给定）的定制邻域。该算法对异常值不敏感，并可通过基数参数有效识别噪声。其关键应用之一是利用领域知识聚类含缺失条目的ℝⁿ数据点，尤其适用于至少保留(n−1)维信息的n维数据。我们展示了标准概率分布下的邻域生成效果，并在多种合成及真实世界数据集（如铁路与公路网络）上验证了算法有效性。实验结果还凸显了其在不完整数据聚类中的应用潜力。
原文摘要 · Abstract (English)
Density based spatial clustering of points in $\mathbb{R}^n$ has a myriad of applications in a variety of industries. We generalise this problem to the density based clustering of lines in high-dimensional spaces, keeping in mind there exists no valid distance measure that follows the triangle inequality for lines. In this paper, we design a clustering algorithm that generates a customised neighbourhood for a line of a fixed volume (given as a parameter), based on an optional parameter as a continuous probability density function. This algorithm is not sensitive to the outliers and can effectively identify the noise in the data using a cardinality parameter. One of the pivotal applications of this algorithm is clustering data points in $\mathbb{R}^n$ with missing entries, while utilising the domain knowledge of the respective data. In particular, the proposed algorithm is able to cluster $n$-dimensional data points that contain at least $(n-1)$-dimensional information. We illustrate the neighbourhoods for the standard probability distributions with continuous probability density functions and demonstrate the effectiveness of our algorithm on various synthetic and real-world datasets (e.g., rail and road networks). The experimental results also highlight its application in clustering incomplete data.
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