M3W: Multistep Three-Way Clustering

A Robust and High-Dimensional Clustering Algorithm Based on Feature Weight and Entropy

Since the Fuzzy C-Means algorithm is incapable of considering the influence of different features and exponential constraints on high-dimensional and complex data, a fuzzy clustering algorithm based on non-Euclidean distance combining feature weights and entropy weights is proposed. The proposed algorithm is based on the Fuzzy C-Means soft clustering algorithm to deal with high-dimensional and complex data. The objective function of the new algorithm is modified with the help of two different entropy terms and a non-Euclidean way of computing the distance. The distance calculation formula enhances the efficiency of extracting the contribution of different features. The first entropy term helps to minimize the clusters' dispersion and maximize the negative entropy to control the clustering process, which also promotes the association between the samples. The second entropy term helps to control the weights of features since different features have different weights in the clustering process. Experiments on real-world datasets indicate that the proposed algorithm gives better clustering results than other algorithms. The experiments demonstrate the proposed algorithm's robustness by analyzing the parameters' sensitivity and comparing the computational distance formulas. In summary, the improved algorithm improves classification performance under noisy interference and high-dimensional datasets, increases computational efficiency, performs well in real-world high-dimensional datasets, and encourages the development of robust noise-resistant high-dimensional fuzzy clustering algorithms.

Grid-Based Clustering Using Boundary Detection

Clustering can be divided into five categories: partitioning, hierarchical, model-based, density-based, and grid-based algorithms. Among them, grid-based clustering is highly efficient in handling spatial data. However, the traditional grid-based clustering algorithms still face many problems: (1) Parameter tuning: density thresholds are difficult to adjust; (2) Data challenge: clusters with overlapping regions and varying densities are not well handled. We propose a new grid-based clustering algorithm named GCBD that can solve the above problems. Firstly, the density estimation of nodes is defined using the standard grid structure. Secondly, GCBD uses an iterative boundary detection strategy to distinguish core nodes from boundary nodes. Finally, two clustering strategies are combined to group core nodes and assign boundary nodes. Experiments on 18 datasets demonstrate that the proposed algorithm outperforms 6 grid-based competitors.