🤖 AI Summary
This work addresses the limitations of traditional clustering algorithms—specifically, the high computational complexity (O(N²)) of density-based methods like DBSCAN and the inability of partitioning approaches such as K-Means to capture nonlinear structures or handle noise effectively. To overcome these challenges, the authors propose K-SCAN, a novel algorithm that synergistically integrates vector quantization with density-based analysis. K-SCAN first employs stochastic mini-batch K-Means to generate weighted micro-clusters and then performs density connectivity analysis on these micro-clusters. This approach achieves linear time complexity while accurately identifying nonlinear manifold structures and exhibiting robustness to noise. Experimental results demonstrate that K-SCAN runs over three times faster than BIRCH on million-scale datasets, attains an Adjusted Rand Index exceeding 0.99, and remains effective even with noise levels as high as 55%.
📝 Abstract
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.