用数学形态学提升聚类与分类，更好捕捉数据形状和密度特征。
Mathematical Morphology in Machine Learning
- 基于形态学重建的快速聚类，能保持簇形貌与密度分布。
- 新距离度量在33个数据集上26次表现优于平均，9次最优。
- 首次融合形状、密度与分形信息构建分类器，适合复杂结构数据。
本文将成熟的视觉计算理论——数学形态学引入机器学习，以挖掘标准方法常忽略的形状与密度信息。提出一种基于形态学重建的快速聚类算法，能准确保持簇的形状与密度分布，具备内在最大簇识别能力、无需额外代价的噪声清除功能，以及由结构元素调控的多样生长模式。此外，设计了一种结合Minkowski与Chebyshev距离的新度量，在$Z^2$离散邻域迭代中速度约为曼哈顿距离的1.3倍，比欧几里得距离快329.5倍。在33个UCI数据集上的k-NN分类实验中，该度量在26次中超过平均性能，9次取得最佳准确率。最后，提出新型形态学分类器，首次同时建模数据集的形状、密度与分形特性。
原文摘要 · Abstract (English)
This work introduces mathematical morphology-an established visual computing theory-into machine learning to exploit shape and density aspects often overlooked by standard techniques. We propose a fast clustering algorithm based on morphological reconstruction that accurately preserves cluster shapes and density. This scheme offers unique features: an intrinsic sense of maximal clusters, cost-free noise removal, and diverse growth patterns controlled by structuring elements.Additionally, we propose a novel distance metric combining Minkowski and Chebyshev distances, highly efficient for morphological dilations. In $Z^2$ discrete neighbourhood iterations, it is roughly 1.3 times faster than Manhattan and 329.5 times faster than Euclidean distances. When evaluated using a k-Nearest Neighbours (k-NN) classifier across 33 UCI datasets against 14 other distances, our metric achieved above-average accuracies most frequently (26 of 33 cases) and the best overall accuracy in 9 cases.Finally, we introduce novel morphological classifiers. Unlike current literature, this proposal uniquely models shape, density, and fractal information in datasets.
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