Ultra-Scalable Spectral Clustering and Ensemble Clustering (1903.01057v2)

Abstract: This paper focuses on scalability and robustness of spectral clustering for extremely large-scale datasets with limited resources. Two novel algorithms are proposed, namely, ultra-scalable spectral clustering (U-SPEC) and ultra-scalable ensemble clustering (U-SENC). In U-SPEC, a hybrid representative selection strategy and a fast approximation method for K-nearest representatives are proposed for the construction of a sparse affinity sub-matrix. By interpreting the sparse sub-matrix as a bipartite graph, the transfer cut is then utilized to efficiently partition the graph and obtain the clustering result. In U-SENC, multiple U-SPEC clusterers are further integrated into an ensemble clustering framework to enhance the robustness of U-SPEC while maintaining high efficiency. Based on the ensemble generation via multiple U-SEPC's, a new bipartite graph is constructed between objects and base clusters and then efficiently partitioned to achieve the consensus clustering result. It is noteworthy that both U-SPEC and U-SENC have nearly linear time and space complexity, and are capable of robustly and efficiently partitioning ten-million-level nonlinearly-separable datasets on a PC with 64GB memory. Experiments on various large-scale datasets have demonstrated the scalability and robustness of our algorithms. The MATLAB code and experimental data are available at https://www.researchgate.net/publication/330760669.

• The paper introduces U-SPEC and U-SENC, which significantly reduce computational complexity while maintaining high clustering accuracy on large-scale datasets.
• It employs a hybrid representative selection and a coarse-to-fine K-nearest representative strategy to enhance the efficiency of spectral clustering.
• The ensemble approach in U-SENC integrates multiple clusterers to bolster robustness and scalability, demonstrating success on datasets with millions of data points.

Overview of "Ultra-Scalable Spectral Clustering and Ensemble Clustering"

This paper presents two innovative clustering algorithms, Ultra-Scalable Spectral Clustering (U-SPEC) and Ultra-Scalable Ensemble Clustering (U-SENC), designed to improve the scalability and robustness of clustering methodologies for extremely large-scale datasets. Traditional spectral clustering is known for its effectiveness in dealing with nonlinearly separable data but suffers from high computational demands, prohibiting its application to very large datasets. This paper addresses these challenges by proposing novel approaches that maintain high clustering accuracy while significantly reducing computational complexity.

Key Contributions and Methodologies

1. Hybrid Representative Selection: U-SPEC utilizes a hybrid representative selection strategy combining the efficiency of random sampling and the effectiveness of $k$-means clustering. This strategy reduces the computational demands of representative selection without sacrificing the quality of clustering results. Specifically, $p'$ candidates are randomly sampled from the dataset, and $k$-means is executed only on these candidates to select the final representatives. This reduces the representative selection complexity to $O(p^2dt)$, compared to $O(Npdt)$ if $k$-means were applied directly to the full dataset.
2. Efficient Approximation of K-Nearest Representatives: The paper introduces a coarse-to-fine approach to efficiently approximate $K$-nearest representatives. By partitioning the representative set into rep-clusters and restricting computations to candidate regions and local neighborhoods, the paper achieves a time complexity reduction from $O(Npd)$ to $O(Np^{1/2}d)$.
3. Bipartite Graph Partitioning: The constructed sparse affinity matrix forms the basis for a bipartite graph framework where transfer cut methods are applied for efficient eigen-decomposition. This results in time complexity for eigen-decomposition proportional to $O(NK(K+k)+p^3)$, highlighting a significant computational saving, facilitated by focusing on $p$ representatives instead of the original dataset size $N$.
4. Ultra-Scalable Ensemble Clustering: Building on U-SPEC, U-SENC integrates multiple base U-SPEC clusterers to enhance clustering robustness through ensemble methods. This strategy preserves the near-linear scalability in both time and space, suitable for extremely large datasets. By using diverse sets of representatives and varying cluster counts, U-SENC constructs a robust, consensus clustering outcome.

Experimental Evaluation and Results

The experimental evaluation conducted spans ten datasets with sizes ranging up to twenty million data points, showcasing the efficacy of U-SPEC and U-SENC. Key results demonstrate that both methods can achieve robust clustering performances with near-linear time complexity and efficiently utilize constrained computational resources, handling up to ten-million-level data on a regular PC configuration. The paper provides openly accessible MATLAB code, emphasizing reproducibility and practical applicability.

Implications and Future Directions

This research contributes significantly to the field of data mining and clustering, primarily granting spectral clustering techniques scalability to unprecedented dataset sizes without compromising accuracy. This evolution in scalability is crucial in contemporary applications that involve large-scale, complex data, such as IoT data streams, genomics, and large social networks. Looking forward, further refinement in approximation techniques, possibly integrating machine learning-based augmentation, can enhance both efficiency and effectiveness. Additionally, exploring the interoperability of these clustering frameworks with other machine learning paradigms might offer synergistic benefits, expanding the application spectrum even further.

In conclusion, this paper offers substantial advancements in spectral and ensemble clustering methodologies, providing a firm basis for future research while responding to the increasing data demands across various computational domains.