Ultraviolet communication (UVC) has been regarded as a promising supplement for overloaded conventional wireless communications. One challenge lies in the communication deterioration caused by the UV-photon scattering induced intersymbol-interference (ISI), which will be even worse when encountering multilevel pulse amplitude modulation (multi-PAM) symbols. To address this ISI, traditional coherent detection methods (e.g., maximum-likelihood sequence detection, MLSD) require high computational complexities for UV channel estimation and sequential detection space formation, thereby making them less attractive. Current non-coherent detection, which simply combines the ISI-insensitive UV signal features (e.g., the rising edge) into a one-dimensional (1D) metric, cannot guarantee reliable communication accuracy. In this work, a novel high-dimensional (HD) non-coherent detection scheme is proposed, leveraging a HD construction of the ISI-insensitive UV signal features. By doing so, we transform the ISI caused sequential detection into an ISI-released HD detection framework, which avoids complex channel estimation and sequential detection space computation. Then, to compute the detection surface, a UV feature based unsupervised learning approach is designed. We deduce the theoretical bit error rate (BER), and prove that the proposed HI) non-coherent detection method has a lower BER than that of the current 1D non-coherent scheme. Simulation results validate our results, and more importantly, demonstrate a BER that approaches that of the state-of-the-art coherent MLSD (<1 dB in SNR at BER = 4.5 x 10(-8), the 7% overhead forward-error-correction limit), and also a reduction of computational complexity by at least two orders of magnitude.