[论文解读] Nearest Descent, In-Tree, and Clustering

Teng Qiu, Kai-Fu Yang+2 more|arXiv (Cornell University)|Dec 7, 2014

Advanced Clustering Algorithms Research被引用 3

一句话总结

本文提出了一种基于物理启发规则——最近下降（Nearest Descent, ND）的新型图论聚类方法，通过迭代地在势能下降最陡方向选择父节点来构建入树（In-Tree）。该方法将聚类问题转化为从入树中移除少数可区分边，从而在各种数据形状和高维数据集上实现高精度的自动或交互式聚类检测。

ABSTRACT

In this paper, we propose a physically inspired graph-theoretical clustering method, which first makes the data points organized into an attractive graph, called In-Tree, via a physically inspired rule, called Nearest Descent (ND). In particular, the rule of ND works to select the nearest node in the descending direction of potential as the parent node of each node, which is in essence different from the classical Gradient Descent or Steepest Descent. The constructed In-Tree proves a very good candidate for clustering due to its particular features and properties. In the In-Tree, the original clustering problem is reduced to a problem of removing a very few of undesired edges from this graph. Pleasingly, the undesired edges in In-Tree are so distinguishable that they can be easily determined in either automatic or interactive way, which is in stark contrast to the cases in the widely used Minimal Spanning Tree and k-nearest-neighbor graph. The cluster number in the proposed method can be easily determined based on some intermediate plots, and the cluster assignment for each node is easily made by quickly searching its root node in each sub-graph (also an In-Tree). The proposed method is extensively evaluated on both synthetic and real-world datasets. Overall, the proposed clustering method is a density-based one, but shows significant differences and advantages in comparison to the traditional ones. The proposed method is simple yet efficient and reliable, and is applicable to various datasets with diverse shapes, attributes and any high dimensionality

研究动机与目标

• 开发一种对任意数据形状和高维性均具有鲁棒性的聚类方法。
• 解决传统聚类方法（如k-means和DBSCAN）在处理复杂非球形聚类时的局限性。
• 提供一种可通过中间可视化结果轻松确定聚类数量的方法。
• 通过在子树中进行根查找，实现高效可靠的聚类分配。
• 通过将聚类边界检测问题转化为在结构化图上稀疏边移除问题，降低其复杂度。

提出的方法

• 应用最近下降（ND）规则构建入树，其中每个节点选择在势能下降最陡方向上最近的节点作为其父节点。
• 利用基于数据点密度的势函数引导下降过程，确保层次化组织结构。
• 将入树构建为有向无环图，每个连通分量仅有一个根节点，同时保留拓扑结构。
• 基于其结构和拓扑可区分性，识别并移除连接不同聚类的少量“不希望的”边。
• 通过在入树中追踪每个节点至其根节点完成聚类分配，每个根节点代表一个独立聚类。
• 利用中间可视化图（如边权重分布或树深分布图）指导自动或交互式确定最优聚类数量。

实验结果

研究问题

• RQ1 像最近下降这样的物理启发图构建规则是否能生成适合聚类的层次结构？
• RQ2 与传统的最小生成树（MST）或k-NN图相比，入树中用于分隔聚类的不希望的边是否能被可靠且明显地区分？
• RQ3 该方法是否能无需先验知识即自动且准确地确定聚类数量？
• RQ4 该方法在具有复杂、非球形或高维聚类结构的数据集上的表现如何？
• RQ5 是否能通过在入树结构中进行简单的根查找操作，高效计算聚类分配过程？

主要发现

• 入树结构能有效捕捉数据的内在聚类层次结构，实现准确且高效的聚类分配。
• 在入树中，分隔聚类的不希望的边具有高度可区分性，可实现低人工或算法干预下的可靠移除。
• 该方法通过分析中间结构图（如边权重或深度分布图）自动确定聚类数量。
• 该方法在包括不规则形状和高维性在内的多样化数据集上均实现了高聚类准确率。
• 与传统基于密度的聚类技术相比，该方法在复杂数据分布上的鲁棒性和一致性表现更优。
• 由于入树的稀疏性以及树结构中根查找操作的高效性，计算成本较低。