Mathematical Morphology in Machine Learning
Quick Take
This article integrates mathematical morphology into machine learning, proposing a fast clustering algorithm that preserves cluster shapes and density. A novel distance metric, combining Minkowski and Chebyshev distances, outperforms traditional metrics, achieving above-average accuracy in 26 of 33 UCI datasets and the best accuracy in 9 cases.
Key Points
- Proposed a fast clustering algorithm based on morphological reconstruction.
- New distance metric is 1.3x faster than Manhattan and 329.5x faster than Euclidean.
- Achieved above-average accuracy in 26 out of 33 UCI datasets.
- Best overall accuracy in 9 cases using k-NN classifier.
- Introduced novel morphological classifiers modeling shape, density, and fractal information.
Article Content
From source RSS / original summaryarXiv:2605. 30700v1 Announce Type: new Abstract: 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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