Towards Tight Robust Coresets for k-Medians Clustering

Parameterized and Streaming Algorithms for Euclidean Fair k -Center Clustering

Online Differentially Private Consistent Clustering

We study differentially private (DP) $k$-means and $k$-median clustering in the online streaming setting. In this model, points arrive sequentially, and at each time step, we need to output a set of $k$ centers that optimizes the clustering objective for all points seen so far. We give a generic reduction that transforms the (sensitive) input stream into a private stream, which is a semi-coreset of the input stream. This implies that any (non-private) online clustering algorithm, run as a post-processing step, can achieve good utility for the original clustering objective. Our algorithm matches or improves upon the approximation ratio, space usage, and running time of existing algorithms [Epasto et al., 2026, Dupr\'e la Tour et al., 2024]. A key aspect of our reduction is that it inherits desirable properties of the underlying non-private clustering algorithm, such as consistency [Lattanzi and Vassilvitskii, 2017]--a property not satisfied by previous DP algorithms.

Efficient Coreset Selection via K-Nearest Neighbor Graphs

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.

Incremental ( 𝒌, 𝒛 ) -Clustering on Graphs

KNN-maximum dispersion balanced K-means algorithm

Clustering analysis is an essential task in data mining and machine learning, and the classical K-means algorithm is widely used due to its efficiency. However, its random initialization often leads to unstable results, especially on complex or nonuniform datasets, where it easily falls into local optima. Moreover, its objective function focuses solely on intra-cluster compactness while overlooking inter-cluster separability, thus limiting global clustering performance. To address these issues, this paper proposes an improved K-means method (MD-Kmeans). The algorithm integrates K-nearest-neighbor– based density estimation with a maximum-dispersion strategy to ensure representative and well-distributed initial centers, and employs a balanced objective that jointly enhances intra-cluster compactness and inter-cluster separability. Experimental results show that MD-Kmeans achieves notable improvements in Adjusted Rand Index (ARI), Silhouette Coefficient (SC), and Davies–Bouldin Index (DBI), outperforming traditional K-means and recent variants, particularly on non-uniform datasets.

The K-SCAN Clustering Algorithm

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.