Restricted　Boltzmann　machines　(RBMs)　are　often　used　as　building　blocks　to　construct　a　deep　belief　network.　By　optimizing　several　RBMs,　the　deep　networks　can　be　trained　quickly　to　achieve　good　performance　on　the　tasks　of　interest.　To　further　improve　the　performance　of　data　representation,　many　researches　focus　on　incorporating　sparsity　into　RBMs.　In　this　paper,　we　propose　a　novel　sparse　RBM　model,　referred　to　as　LogSumRBM.　Instead　of　constraining　the　expected　activation　of　every　hidden　unit　to　the　same　low　level　of　sparsity　as　done　in　[27],　we　explicitly　encourage　the　hidden　units　to　be　sparse　through　adding　a　log-sum　norm　constraint　on　the　totality　of　the　hidden　units＇　activation　probabilities.　In　this　approach,　we　do　not　need　to　keep　the　＂firing　rate＂　of　each　hidden　unit　at　a　certain　level　that　is　set　beforehand,　and　therefore　the　level　of　sparsity　corresponding　to　each　hidden　unit　can　be　automatically　learnt　based　on　the　task　at　hand.　Some　experiments　conducted　on　several　image　data　sets　of　different　scales　show　that　LogSumRBM　learns　sparser　and　more　discriminative　representations　compared　with　the　related　state-of-the-art　models,　and　stacking　two　LogSumRBMs　learns　more　significant　features　which　mimic　computations　in　the　cortical　hierarchy.　Meanwhile,　LogSumRBM　can　also　be　used　to　pre-train　deep　networks,　and　achieve　better　classification　performance.　(C)　2014　Elsevier　B.V.　All　rights　reserved.