In two-dimensional topological insulators, a disorder induced topological phase transition is typically identified with an Anderson localization transition at the Fermi energy. However, in higher-order, spin-resolved topological insulators it is the spectral gap of the spin-spectrum, in addition to the bulk mobility gap, which protects the non-trivial topology of the ground state. I will study how these two gaps, the bulk electronic and spin gap, evolve distinctly upon introduction of disorder. Furthermore, in the clean limit the bulk-boundary correspondence of such higher-order insulators is dictated by crystalline protected topology, coexisting with the spin-resolved topology. By removing the crystalline symmetry, disorder allows for isolated study of the bulk-boundary correspondence of spin-resolved topology. The study of disordered systems is a computationally challenging task due to the prevalence of finite size effects and the necessity to average over many disorder configurations. We will attempt to overcome this challenge by first taking advantage of both traditional computational methods such as Kernel polynomial method which can be implemented in parallel on CPUs. We will further leverage recently developed software (arXiv:2312.13051) which is capable of utilizing GPUs to expedite computation of topological invariants, a critical step for the diagnosis of band topology. Finally, we will take a machine learning approach to the detection of corner states. Corner states can be notoriously difficult to identify in an automated fashion as they can mix with bulk states. As such we will utilize a machine learning network in which the wavefunction is the input vector, to determine whether the states are the corner localized states which are emblamatic of higher-order topology.