SIMBAD references

We present a comprehensive analysis of the early spectra of type II and type IIb supernovae (SNe) to explore their diversity and distinguishable characteristics. Using 866 publicly available spectra from 393 SNe, including 407 from type IIb SNe (SNe IIb) and 459 from type II SNe (SNe II), we analysed Hα and He I 5876 Å at early phases (< 40 days from the explosion) to identify possible differences between these two SN types. By comparing the pseudo-equivalent width (pEW) and full width at half maximum (FWHM), we found that the strength of the absorption component of Hα and He I lines serves as a quantitative discriminator, with SNe IIb exhibiting stronger lines at all times. The most significant differences emerge within the first 10-20 days. To assess the statistical significance of these differences, we applied statistical methods and machine-learning techniques. Population density evolution reveals a clear distinction in both pEW and FWHM. A quadratic discriminant analysis (QDA) confirmed distinct evolutionary patterns, particularly in pEW, while FWHM variations were less pronounced. Effectively, a combination of t-distributed stochastic neighbour embedding (t-SNE) and linear discriminant analysis (LDA) distinguishes the two SN types. In addition, we used a a random forest classifier (RFC) to demonstrate the robustness of pEW and FWHM as classification criteria, allowing for accurate classifications of newly observed SNe II and IIb based on computed classification probabilities. Applying our method to low-resolution spectra obtained from the magnitude-limited survey carried out by the Zwicky Transient Facility (ZTF BTS), we identified 34 mis-classified SNe. This revision increases the estimated fraction of SNe IIb from 4.0% to 7.26%. This finding suggests that mis-classification significantly impacts the estimated core-collapse SN rate. Our approach enhances the classification accuracy and provides a valuable tool for future SN studies.