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Belief compression improves the tractability of large-scale partiallyobservable Markov decision processes (POMDPs) by finding projections fromhigh-dimensional belief space onto low-dimensional approximations, wheresolving to obtain action selection policies requires fewer computations. Thispaper develops a unified theoretical framework to analyse three existing linearbelief compression approaches, including value-directed compression and twonon-negative matrix factorisation (NMF) based algorithms. The results indicatethat all the three known belief compression methods have their own criticaldeficiencies. Therefore, projective NMF belief compression is proposed (P-NMF),aiming to overcome the drawbacks of the existing techniques. The performance ofthe proposed algorithm is examined on four POMDP problems of reasonably largescale, in comparison with existing techniques. Additionally, thecompetitiveness of belief compression is compared empirically to astate-of-the-art heuristic search based POMDP solver and their relative meritsin solving large-scale POMDPs are investigated.

On the Linear Belief Compression of POMDPs: A re-examination of current methods