L-ASCRA: A Linearithmic Time Approximate Spectral Clustering Algorithm Using Topologically-Preserved Representatives

Approximate spectral clustering (ASC) algorithms work on the representative points of the data for discovering intrinsic groups. The existing ASC methods identify fewer representatives as compared to the number of data points to reduce the cubic computational overhead of the spectral clustering technique. However, identifying such representative points without any domain knowledge to capture the shapes and topology of the clusters remains a challenge. This work proposes an ASC method that suitably computes enough well-scattered representatives to efficiently capture the topology of the data, making the ASC faster without the requirement of tuning any external parameters. The proposed ASC algorithm first applies two-level partitioning using both boundary points and centroids-based partitioning to identify quality representatives in less time. In the next step, we calculate the proximity between the neighboring representatives using <inline-formula><tex-math notation="LaTeX">$k$</tex-math></inline-formula>-rounds of minimum spanning tree (MST) by considering the distribution of edge weights in each round to find <inline-formula><tex-math notation="LaTeX">$k$</tex-math></inline-formula>. The proposed method effectively utilizes the number of representatives in a way that the overall computational time is bounded by <inline-formula><tex-math notation="LaTeX">$O(N\lg N)$</tex-math></inline-formula>. The experimental results suggest that the proposed ASC method outperforms the competing ASC methods in terms of both running time and clustering quality.