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Radar high-resolution range profiles (HRRPs) are typical high-dimensional, non-Gaussian and interdimension dependently distributed data, the statistical modelling of which is a challenging task for HRRP based target recognition. Assuming the HRRP data follow interdimension dependent Gaussian distribution, factor analysis (FA) was recently applied to describe radar HRRPs and a two-phase procedure was used for model selection, showing promising recognition results. Besides the interdimensional dependence, this paper further models the non-Gaussianity of the radar HRRP data by local factor analysis (LFA). Moreover, since the two-phase procedure suffers from extensive computation and inaccurate evaluation on high-dimensional finite HRRPs, we adopt an automatic Bayesian Ying-Yang (BYY) harmony learning, which determines the component number and the hidden dimensionalities of LFA automatically during parameter learning. Experimental results show incremental improvements on recognition accuracy by three implementations, progressively from a two-phase FA, to a two-phase LFA, and then to an automatically learned LFA by BYY harmony learning.