Mathematical Morphology in Machine Learning
This work offers a new approach to clustering and classification for machine learning practitioners by leveraging shape and density information, potentially improving performance and efficiency.
This paper introduces mathematical morphology into machine learning, proposing a fast clustering algorithm that preserves cluster shapes and density, and a novel distance metric. The new distance metric is 1.3 times faster than Manhattan and 329.5 times faster than Euclidean distances in $Z^2$ discrete neighborhood iterations, and achieved above-average accuracies in 26 of 33 UCI datasets when used with a k-NN classifier.
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.