Distinct Modes of Pulsar Glitch Activity Revealed by the Waiting-Time--Amplitude Morphology
Pulsar glitches display diverse behaviors. They are commonly labeled as "Vela-like" or "Crab-like," yet these qualitative categories do not provide reproducible quantitative boundaries. We constructed an objective classification scheme based on the joint distribution of backward waiting time $\Delta t_{-}$ and fractional glitch amplitude $\Delta\nu/\nu$. A sample of 349 glitches from 22 pulsars was compiled by cross-matching the Jodrell Bank and ATNF glitch databases. For each source, we used two-dimensional kernel density estimation (KDE) together with highest-density regions (HDRs) to derive geometric descriptors, including the HDR area, anisotropy ratio, and out-of-HDR fraction. Hierarchical clustering of the KDE--HDR descriptors revealed two morphology classes independent of visual inspection. In this convention, the Compact class is associated with small HDR areas, elevated anisotropy, and limited peripheral occupancy. The Extended class is associated with broader HDR occupancy and stronger low-density extensions. We found that bootstrap resampling and hyperparameter sensitivity tests confirmed this partition for most sources. Nevertheless, two prolific pulsars (PSR J0537-6910 and PSR J1341-6220) were found to occupy intermediate positions. Logistic regression identified the mean backward waiting time $\langle\Delta t_{-}\rangle$ as the strongest class predictor (in-sample $\mathrm{AUC}=0.88$; leave-one-out $\mathrm{AUC}_{\mathrm{CV}}=0.59$, reflecting the limited sample size). Additionally, a parallel analysis using $\Delta t_{+}$ recovered the same two-class structure but with reduced stability. The data suggest that the Compact class is consistent with near-complete reservoir depletion, whereas the Extended class reflects partial, avalanche-like releases. As a result, short-term measurements of $G$ in Extended-class pulsars may underestimate the true crustal superfluid fraction.