Fast Clustering using MapReduce (1109.1579v1)

Abstract: Clustering problems have numerous applications and are becoming more challenging as the size of the data increases. In this paper, we consider designing clustering algorithms that can be used in MapReduce, the most popular programming environment for processing large datasets. We focus on the practical and popular clustering problems, $k$-center and $k$-median. We develop fast clustering algorithms with constant factor approximation guarantees. From a theoretical perspective, we give the first analysis that shows several clustering algorithms are in $\mathcal{MRC}^0$, a theoretical MapReduce class introduced by Karloff et al. \cite{KarloffSV10}. Our algorithms use sampling to decrease the data size and they run a time consuming clustering algorithm such as local search or Lloyd's algorithm on the resulting data set. Our algorithms have sufficient flexibility to be used in practice since they run in a constant number of MapReduce rounds. We complement these results by performing experiments using our algorithms. We compare the empirical performance of our algorithms to several sequential and parallel algorithms for the $k$-median problem. The experiments show that our algorithms' solutions are similar to or better than the other algorithms' solutions. Furthermore, on data sets that are sufficiently large, our algorithms are faster than the other parallel algorithms that we tested.

• The paper introduces constant factor approximation guarantees for the k-center and k-median problems using a novel Iterative-Sample technique.
• It leverages a constant number of MapReduce rounds by applying sampling methods that reduce data size while preserving key clustering properties.
• Empirical results demonstrate that the proposed algorithms outperform other parallel approaches in speed and quality, particularly for the k-median problem.

Overview of Fast Clustering using MapReduce

This paper presents innovative approaches to addressing the computational challenges related to clustering large datasets on distributed platforms, specifically focusing on the MapReduce environment. The authors tackle the $k$-center and $k$-median problems, which are fundamental in various applications across machine learning, data mining, and networking. These problems become increasingly intricate as data volume escalates, necessitating efficient algorithms that leverage distributed computing frameworks.

Theoretical Contributions

The algorithms introduced offer constant factor approximation guarantees for both the $k$-center and $k$-median problems, presenting the first such analysis within the theoretical MapReduce class, $\mathcal{MRC}^0$. The paper demonstrates that these clustering tasks can be effectively executed using a constant number of MapReduce rounds, indicating substantial theoretical advancements in processing large-scale data using distributed systems.

The primary algorithmic strategy involves the use of sampling to reduce data size, thereby enabling the execution of computationally expensive clustering algorithms like local search on manageable subsets. Key innovations include the $Iterative-Sample$ technique, which iteratively reduces the dataset while preserving essential clustering properties, ensuring a representative sample is utilized in subsequent stages.

Empirical Validation

The practical applicability of these algorithms is validated through extensive experimentation. The results show that the solutions provided by these algorithms are comparable or superior to those generated by other sequential and parallel algorithms, particularly for the $k$-median problem. On expansive datasets, the proposed algorithms demonstrate significant speed advantages, being faster than other tested parallel algorithms.

Implications and Future Directions

The successful mapping of the $k$-center and $k$-median problems to the $\mathcal{MRC}^0$ class underlines their suitability for practical implementation in big data scenarios. This work opens avenues for further research in designing efficient clustering algorithms tailored for distributed platforms. The insight on clustering within the MapReduce framework can be extended to explore other complex data processing tasks, potentially transforming how large datasets are managed and analyzed in practice.

Furthermore, potential expansions of these methods to related clustering frameworks, such as $k$-means, suggest future research directions to broaden the applicability of MapReduce in data-intensive tasks beyond the current scope. Optimization of the sampling techniques and exploration of heuristics fine-tuned to specific data characteristics could further enhance the performance and applicability of these methods.

Conclusion

This paper makes a valuable contribution to the field of distributed computing by showcasing how complex clustering problems can be effectively addressed within the MapReduce paradigm. By providing robust theoretical foundations coupled with strong empirical evidence, the paper sets a benchmark for future work on scalable clustering solutions in distributed environments, ensuring both efficiency and practicality are achieved.