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memgonzales authored Apr 30, 2023
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## Description

**ABSTRACT:** The choice of distance metric impacts the clustering quality of centroid-based algorithms, such as $k$-means. Theoretical attempts to select the optimal metric entail deep domain knowledge, while experimental approaches are resourceintensive. This paper presents a meta-learning approach to automatically recommend a distance metric for $k$-means clustering that optimizes the Davies-Bouldin score. Three distance measures were considered: Chebyshev, Euclidean, and Manhattan. General, statistical, information-theoretic, structural, and complexity meta-features were extracted, and random forest was used to construct the meta-learning model; borderline SMOTE was applied to address class imbalance. The model registered an accuracy of 70.59%. Employing Shapley additive explanations, it was found that the mean of the sparsity of the attributes has the highest meta-feature importance. Feeding only the top 25 most important meta-features increased the accuracy to 71.57%. The main contribution of this paper is twofold: the construction of a meta-learning model for distance metric recommendation and a fine-grained analysis of the importance and effects of the meta-features on the model’s output.
**ABSTRACT:** The choice of distance metric impacts the clustering quality of centroid-based algorithms, such as $k$-means. Theoretical attempts to select the optimal metric entail deep domain knowledge, while experimental approaches are resource-intensive. This paper presents a meta-learning approach to automatically recommend a distance metric for $k$-means clustering that optimizes the Davies-Bouldin score. Three distance measures were considered: Chebyshev, Euclidean, and Manhattan. General, statistical, information-theoretic, structural, and complexity meta-features were extracted, and random forest was used to construct the meta-learning model; borderline SMOTE was applied to address class imbalance. The model registered an accuracy of 70.59%. Employing Shapley additive explanations, it was found that the mean of the sparsity of the attributes has the highest meta-feature importance. Feeding only the top 25 most important meta-features increased the accuracy to 71.57%. The main contribution of this paper is twofold: the construction of a meta-learning model for distance metric recommendation and a fine-grained analysis of the importance and effects of the meta-features on the model’s output.

**INDEX TERMS:** meta-learning, meta-features, $k$-means, clustering, distance metric, random forest

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