Granular-ball computing: an efficient, robust, and interpretable adaptive multi-granularity representation and computation method

TL;DR

Granular-ball computing presents an adaptive multi-granularity framework that mimics the human global-first perception to improve AI efficiency, robustness, and interpretability. By replacing point inputs with coarse-to-fine granular-balls, the approach formalizes generation and learning through a balance of coverage, granularity, and quality, yielding specialized methods such as GBSVM, GBkNN, granular-ball rough sets, granular-ball clustering, granular-ball neural networks, evolutionary computing, and fuzzy-granular sets. These contributions collectively enable efficient, robust, and interpretable learning across classification, clustering, knowledge representation, and neural architectures, especially for large or complex data distributions. The framework holds practical impact for scalable AI systems, offering natural noise robustness and topologically meaningful representations that align with human cognition and real-world data structures.

Abstract

Human cognition operates on a "Global-first" cognitive mechanism, prioritizing information processing based on coarse-grained details. This mechanism inherently possesses an adaptive multi-granularity description capacity, resulting in computational traits such as efficiency, robustness, and interpretability. The analysis pattern reliance on the finest granularity and single-granularity makes most existing computational methods less efficient, robust, and interpretable, which is an important reason for the current lack of interpretability in neural networks. Multi-granularity granular-ball computing employs granular-balls of varying sizes to daptively represent and envelop the sample space, facilitating learning based on these granular-balls. Given that the number of coarse-grained "granular-balls" is fewer than sample points, granular-ball computing proves more efficient. Moreover, the inherent coarse-grained nature of granular-balls reduces susceptibility to fine-grained sample disturbances, enhancing robustness. The multi-granularity construct of granular-balls generates topological structures and coarse-grained descriptions, naturally augmenting interpretability. Granular-ball computing has successfully ventured into diverse AI domains, fostering the development of innovative theoretical methods, including granular-ball classifiers, clustering techniques, neural networks, rough sets, and evolutionary computing. This has notably ameliorated the efficiency, noise robustness, and interpretability of traditional methods. Overall, granular-ball computing is a rare and innovative theoretical approach in AI that can adaptively and simultaneously enhance efficiency, robustness, and interpretability. This article delves into the main application landscapes for granular-ball computing, aiming to equip future researchers with references and insights to refine and expand this promising theory.

Figures (19)

• Figure 1: The human brain's "Global-first" cognitive mechanism is highly efficient and important features such as robustness and multi-granularity description. (a) Efficiency and robustness; (b) Multi-granularity description capability.
• Figure 2: "Global-first" multi-granularity cognitive computing has important characteristics such as high efficiency, robustness and multi-granularity description. (a) The efficiency and robustness of multi-granularity cognition; (b) Multi-granularity description ability of multi-granularity cognition.
• Figure 3: The cognitive mechanism of "holistic perception" in the human brain has important characteristics such as efficiency, robustness, and multi-granularity description. (a) Efficiency and robustness; (b) Ability to describe with multiple granularities.
• Figure 4: Taking classification as an example, the basic idea of granular-ball computing. (a) The granular-ball covers the sample set; (b) The decision boundary of the ball is consistent with the original data.
• Figure 5: The process of granular-ball splitting generation on the UCI data set fourclass. The purity threshold is 1, and the colors of the three balls in the figure (corresponding to the colors of the three sample points) represent the three categories of labels. (a) The data label of the first iteration is 3 classes, so it is 3 granular-balls. (b) The structure after the second granular-ball splitting refinement; (c)-(d) Intermediate results; (e) The final stable results; (f) The extracted granular-balls.