CLIQUE Clustering Algorithm: A Grid-Based and Density-Based Method for High-Dimensional Data Spaces

The CLIQUE algorithm is a clustering method specifically designed for high-dimensional data spaces, skillfully integrating the advantages of both grid-based and density-based clustering techniques. Originally proposed by Rakesh Agrawal's team at IBM Almaden Research Center in 1998, it specifically addresses the "curse of dimensionality" problems encountered by traditional clustering methods in high-dimensional datasets.

The core concept involves partitioning the data space into grid units and identifying dense units through density thresholds. In implementation, the algorithm first divides each dimension into equal-width intervals to form a grid structure. It then employs a bottom-up approach, starting from low-dimensional subspaces to search for dense units and progressively expanding to higher-dimensional subspaces. This strategy avoids the computational complexity of directly handling high-dimensional spaces. Code implementation typically involves creating multidimensional histograms and using depth-first search with pruning techniques to efficiently navigate subspace lattices.

CLIQUE exhibits three distinctive characteristics: automatic discovery of the highest-dimensional subspaces containing clusters, insensitivity to input data ordering, and linear time complexity with respect to data size. It is particularly suitable for processing large high-dimensional datasets such as customer behavior analysis and gene expression data. The algorithm output includes not only clustering results but also reveals association rules between different dimensions. Key algorithmic steps involve frequent itemset mining techniques similar to those used in Apriori algorithm for subspace cluster generation.

The main advantage lies in its effectiveness in handling high-dimensional sparse data while maintaining robustness to noise. However, being grid-based, the clustering results are sensitive to grid parameters and may miss cluster structures that cross grid boundaries. Subsequent improved algorithms like MAFIA have addressed some limitations through adaptive grid partitioning techniques that dynamically adjust cell sizes based on data distribution.