Clustering algorithms are a key element in the field of machine learning. They help identify patterns and structures in data and group similar items together. K-means and spectral clustering are two popular algorithms used for high-dimensional data clustering. The aim of this post is to provide an objective comparison of these two techniques in terms of strengths and weaknesses.
K-Means Clustering
K-means clustering is a method of partitioning a set of n observations into k clusters. Each observation belongs to the cluster whose mean is closest, with the objective of minimizing the sum of squared distances between each observation and the mean of its assigned cluster.
K-means works well when:
- Cluster shapes are circular
- Clusters have similar sizes
- The data has low dimensionality compared to the number of samples
However, K-means has some weaknesses. It may not be effective on non-globular clusters, which are irregular shapes. Moreover, K-means is sensitive to initial conditions, and the results of the clustering can vary based on the initial centroids' placement.
Spectral Clustering
Spectral clustering is a method of clustering data-points based on the characteristics of the eigenvectors. It works by transforming the data into a new space that is not defined by the original data's coordinates but rather by the relationship between each of them. This method can easily capture non-circular clusters and works effectively when the data is high-dimensional.
However, spectral clustering comes with a few weaknesses. It can be computationally expensive when working with large datasets, and it requires the selection of hyperparameters such as the number of eigenvectors and the weights for graph construction.
How do K-Means and Spectral Clustering Compare?
In terms of accuracy:
- Spectral clustering has been proven to be more accurate than K-means in some cases. A study by Ng et al. showed that spectral clustering outperformed K-means in datasets with non-circular clusters.
- K-means tends to perform better on smaller and circular datasets.
In terms of computational efficiency:
- K-means is usually faster than spectral clustering, especially for smaller datasets.
- Spectral clustering is more computationally expensive due to the eigenvalue decomposition required in graph construction.
In terms of parameters:
- K-means requires only the number of clusters k as a parameter
- Spectral clustering requires the selection of the number of eigenvectors and the weights for graph construction as hyperparameters.
Conclusion
Both clustering techniques have their own set of strengths and weaknesses. K-means is simple, fast, and reliable on circular geometries, while spectral clustering is effective on high-dimensional datasets, handling non-spherical geometry while allowing flexible construction of the similarity matrix. Ultimately, the choice of the clustering algorithm depends on the data and the specific requirements of the problem.
References
- Ng, A., Jordan, M., & Weiss, Y. (2002). On spectral clustering: Analysis and an algorithm. Advances in neural information processing systems, 2, 849-856.
- Luxburg, U. (2007). A tutorial on spectral clustering. Statistics and computing, 17(4), 395-416.