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Previous studies presented the phase diagram induced by the disorder existing separately either in the higher-order topological states or in the topological trivial states, respectively. However, the influence of disorder on the system with the coexistence of the higher-order topological states and other traditional topological states has not been investigated. In this paper, we investigate the disorder induced phase transition in the magnetic higher-order topological insulator. By using the convolutional neural network and non-commutative geometry methods, two independent phase diagrams are calculated. With the comparison between these two diagrams, a topological transition from the normal insulator to the Chern insulator is confirmed. Furthermore, the network based on eigenstate wavefunction studies also presents a transition between the higher-order topological insulator and the Chern insulator. [ABSTRACT FROM AUTHOR]