  In present work, the unfavored $\mathcal{\alpha}$ decay half-lives and
$\mathcal{\alpha}$ preformation probabilities of closed shell nuclei related to
ground and isomeric states around $Z=82$, $N=82$ and 126 shell closures are
investigated by adopting two-potential approach from the perspective of valence
nucleon (hole) and isospin asymmetry of the parent nucleus. The results
indicate that $\mathcal{\alpha}$ preformation probability is linear dependence
on $N_p N_n$ or $N_p N_n I$, the same as the case of favored $\mathcal{\alpha}$
decay in our previous work [X.-D. Sun \textit{et al.}, Phys. Rev. C 94, 024338
(2016)]. $N_p$, $N_n$, and $I$ represent the number of valence protons (holes),
the number of valence neutrons (holes), and the isospin of the parent nucleus,
respectively. Fitting the $\mathrm{\alpha}$ preformation probabilities data
extracted from the differences between experimental data and calculated
half-lives without a shell correction, we give two linear formulas of the
$\mathcal{\alpha}$ preformation probabilities and the values of corresponding
parameters. Based on the formulas and corresponding parameters, we calculate
the $\mathrm{\alpha}$ decay half-lives for those nuclei. The calculated results
can well reproduce the experimental data.
