  Granular ball computing (GBC), as an efficient, robust, and scalable learning
method, has become a popular research topic of granular computing. GBC includes
two stages: granular ball generation (GBG) and multi-granularity learning based
on the granular ball (GB). However, the stability and efficiency of existing
GBG methods need to be further improved due to their strong dependence on
$k$-means or $k$-division. In addition, GB-based classifiers only unilaterally
consider the GB's geometric characteristics to construct classification rules,
but the GB's quality is ignored. Therefore, in this paper, based on the
attention mechanism, a fast and stable GBG (GBG++) method is proposed first.
Specifically, the proposed GBG++ method only needs to calculate the distances
from the data-driven center to the undivided samples when splitting each GB
instead of randomly selecting the center and calculating the distances between
it and all samples. Moreover, an outlier detection method is introduced to
identify local outliers. Consequently, the GBG++ method can significantly
improve effectiveness, robustness, and efficiency while being absolutely
stable. Second, considering the influence of the sample size within the GB on
the GB's quality, based on the GBG++ method, an improved GB-based $k$-nearest
neighbors algorithm (GB$k$NN++) is presented, which can reduce
misclassification at the class boundary. Finally, the experimental results
indicate that the proposed method outperforms several existing GB-based
classifiers and classical machine learning classifiers on $24$ public benchmark
datasets.
