naspaclust: A hybridisation of spatial fuzzy clustering with nature-inspired optimisation

This work presents a novel variant of the Firefly Algorithm (FA) for data clustering, addressing limitations of traditional methods like K-Means that struggle with non-uniform cluster shapes, densities, and the need for pre-defining the number of clusters. The proposed algorithm introduces a centroid movement strategy and a multi-objective fitness function that balances compactness, separation, and a novel TSP-based navigation penalty. It automatically estimates the optimal number of clusters and dynamically adjusts cluster boundaries. Application to robotic sensor networks highlights its practical value, with experiments showing improved clustering quality and reduced intra-cluster path distances compared to K-Means. These results confirm the algorithm's robustness in complex spatial clustering tasks, with potential for future extensions to higher-dimensional and adaptive scenarios.

Streaming clustering is a domain that has become extremely relevant in the age of big data, such as in network traffic analysis or in processing continuously-running sensor data. Furthermore, possibilistic models offer unique benefits over approaches from the literature, especially with the introduction of a "fuzzifier" parameter that controls how quickly typicality degrades as one gets further from cluster centers. We propose a single-pass possibilistic clustering (SPC) algorithm that is effective and easy to apply to new datasets. Key contributions of SPC include the ability to model non-spherical clusters, closed-form footprint updates over arbitrarily sized damped windows, and the employment of covariance union from the multiple hypothesis tracking literature to merge two cluster mean and covariance estimates. SPC is validated against five other streaming clustering algorithm on the basis of cluster purity and normalized mutual information.

K-plane clustering (KPC), hyperplane clustering, and mixture regression all essentially fall within the same class of problems. This problem can be conceptualized as clustering in relatively high-dimensional K subspaces or K linear manifolds. Traditional KPC or fuzzy KPC models demonstrate a pronounced susceptibility to outliers, as they presuppose that the projection distance between data points and the plane normal vector adheres to the L2 distance. Meanwhile, the assumption of infinitely extending clusters adversely affects clustering performance. To solve these problems, this paper proposed a new robust fuzzy local k-plane clustering (RFLkPC) method that combines the mixture distance of hinge loss and L1 norm. The RFLkPC model assumes that each plane cluster is bounded to a finite area, which can flexibly and robustly handle plane clustering tasks with outliers or not. The corresponding model and optimization algorithms of RFLkPC were provided. Compared to other related models on this topic, a large number of experiments verify the efficiency of RFLkPC on simulated data and real data. The source code for the proposed RFLkPC method is publicly available at https://github.com/xuelin-xie/RFLkPC.