  Belief compression improves the tractability of large-scale partially
observable Markov decision processes (POMDPs) by finding projections from
high-dimensional belief space onto low-dimensional approximations, where
solving to obtain action selection policies requires fewer computations. This
paper develops a unified theoretical framework to analyse three existing linear
belief compression approaches, including value-directed compression and two
non-negative matrix factorisation (NMF) based algorithms. The results indicate
that all the three known belief compression methods have their own critical
deficiencies. Therefore, projective NMF belief compression is proposed (P-NMF),
aiming to overcome the drawbacks of the existing techniques. The performance of
the proposed algorithm is examined on four POMDP problems of reasonably large
scale, in comparison with existing techniques. Additionally, the
competitiveness of belief compression is compared empirically to a
state-of-the-art heuristic search based POMDP solver and their relative merits
in solving large-scale POMDPs are investigated.
