Machine learning offers a promising approach to addressing the unique challenges of non-Hermitian systems, particularly in classifying topological phases and overcoming the limitations of traditional methods. However, research remains sparse for complex non-Hermitian systems involving higher-order hopping terms. In this work, we employ uniform manifold approximation and projection (UMAP), an unsupervised machine learning technique, to identify phase transition points in systems exhibiting the non-Hermitian skin effect (NHSE). Conventionally, NHSE is analyzed using non-Bloch theory, which requires redefining the Brillouin zone as the generalized Brillouin zone and solving for the complex eigenvalue contours. In contrast, our UMAP-based approach can successfully identify NHSE phase transitions in a system featuring higher-order hopping terms without relying on prior knowledge. Beyond classification, we introduce a unified framework that integrates information from three major theoretical perspectives: numerical solutions under different boundary conditions, non-Bloch theory, and Bloch theory. This framework quantitatively connects these traditionally separate and sometimes incompatible analyses. UMAP's distance metric captures the topological phase structure in a way that bypasses the need for selecting specific analytical methods or performing multiple complex computations. This approach not only circumvents the limitations of detailed analytical methods but also offers physical insights into complex topological phenomena, representing a fundamental theoretical advancement in non-Hermitian physics. We anticipate that our work will further stimulate interdisciplinary research at the intersection of physics, photonics, and artificial intelligence.

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• Skin effect
• Topological phase transition
• Non-Hermitian systems
• Machine learning