Radar high-resolution range profiles (HRRPs) are typical high-dimensional non-Gaussian and inter-dimensional dependently distributed data, the statistical modelling of which is a challenging task for HRRP based target recognition. Considering the inter-dimensional dependence, a recent work applied Factor Analysis (FA) to model radar HRRP data and showed promising recognition results, which however still restricts to Gaussian distribution. This paper aims to simultaneously consider the inter-dimensional dependence and the non-Gaussian distribution, by using Local Factor Analysis (LFA) model. For not only learning parameters but also appropriately selecting the component number and local hidden dimensionalities, we adopt the automatic Bayesian Ying-Yang (BYY) harmony learning, in order to relieve the extensive computation and inaccurate evaluation encountered in the conventional two-phase implementation. Moreover, a heuristic aspect-frame partition is implemented based on the BYY harmony criterion rather than AIC or BIC in the previous work, to tackle the radar HRRP's target-aspect sensitivity. Experiments show improved recognition performances over on the same measured HRRP dataset, i.e., for both equal interval and heuristic aspect-frame partitions, LFA automatically learned by BYY always outperforms FA selected by a two-phase procedure with either AIC or BIC.