Experimental results demonstrate that the proposed adaptive and efficient KNN approach via granular-ball computing outperforms existing KNN variants across multiple datasets in terms of both accuracy and efficiency.
Abstract
The $k$-Nearest Neighbor~(KNN) algorithm is widely used across various tasks. The selection of the $k$ value is a key issue because it significantly impacts performance. In this paper, an adaptive and efficient KNN approach via granular-ball computing is proposed. The method consists of two stages. \textcolor{black}{In the training stage, the dataset is first coarsely partitioned to reduce the complexity of data distributions within a granular ball, and then the Fisher criterion is introduced to control ball splitting and stopping, yielding a multi-granularity granular ball representation. In the prediction stage, the nearest granular ball is first located through a weighted distance mechanism, and an adaptive neighborhood is then constructed around the test sample. The effective $k$ value is dynamically determined by the actual number of samples contained in this neighborhood. The neighborhood induced by the nearest granular ball provides more stable local group information, thereby improving robustness against noise and local perturbations.} Experimental results demonstrate that the proposed method outperforms existing KNN variants across multiple datasets in terms of both accuracy and efficiency. The code has been open-sourced for reproducibility: https://github.com/lianxiaoyu724/Adaptive-GBKNN.
Curvature-Aware Radius Shrinkage for Adaptive Nearest Neighbor Classification (CARSANN) is introduced, a geometry-driven framework that adapts the spatial support of each neighborhood according to local geometric complexity and is competitive with adaptive nearest-neighbor methods.
Lloyd's $K$-means algorithm, also known as na\"{i}ve $K$-means, is a widely used ad hoc optimization heuristic, designed to minimize the sum of squared errors (SSE) across all $K$-partitions of a dataset via iterative cluster refinement. In this work, we establish a novel connection between Lloyd's algorithm and the Frank-Wolfe (FW) algorithm, a prominent first-order method for projection-free optimization. We demonstrate that Lloyd's algorithm is a special case of FW. Leveraging recent advances in FW methods for concave objectives, we derive a non-asymptotic $\mathcal{O}(1/t)$ convergence rate to a local minimum of the SSE objective. To account for empty clusters, an outcome possible under Lloyd's greedy assignment, we develop an FW variant for semismooth objectives while retaining the same convergence rate that is solely controlled by the initial SSE value. We illustrate our findings with a simulation study for spherical Gaussian mixtures and a real-world image segmentation dataset.
Michael Pokojovy, J. Jobe, Simon Lacoste-Julien· 0 citations
In the Big Data era, the scalability of clustering algorithms constitutes a key challenge. Traditional density-based methods (e.g., DBSCAN) offer robustness to noise and the ability to detect non-linear clusters, yet their quadratic time complexity $O(N^2)$ drastically limits their applicability. Conversely, partitional algorithms (e.g., K-Means), with their linear complexity $O(N)$, impose sphericity on the resulting groups and fail in the presence of outliers. This paper presents K-SCAN -- a novel hybrid algorithm that optimizes this trade-off. The method integrates preliminary vector quantization (stochastic Mini-Batch K-Means) to extract a reduced set of weighted micro-clusters, followed by a subsequent density-based structural analysis. Empirical evaluation on datasets of up to $10^6$ samples confirms the linear computational complexity of the proposed solution. K-SCAN achieves more than a 3-fold speed-up over the hierarchical BIRCH algorithm, avoiding the costly management of tree-based structures. The method precisely identifies non-linear manifolds while maintaining structural stability (Adjusted Rand Index>0.99), even with noise levels reaching 55\% of the data volume. The main limitation of the proposed algorithm, which could not be fully eliminated in the present study, remains its susceptibility to over-smoothing and its difficulty in separating clusters with highly heterogeneous local density. In complex visual spaces, this can lead to the loss of the finest topological details.
The theoretical results provide a principled non-cross-validated alternative to the classical n rule, and cross-validation remains the strongest k-selection strategy when computationally feasible.
Ahmad Hassanat, A. A. Alkasasbeh, Esra’a Alkafaween et al.· Mathematics· 1 citation
Experiments show that KNNG-CS achieves accuracy comparable to representative gradient-approximation coreset methods, while reducing selection time by $2.3\times$-$41.2\times$ and peak memory to $0.3\%$-$7.5\%$ of the baselines.
Yingfan Liu, Leiyu Zhang, Jiadong Xie et al.· 0 citations