Graph-based　approaches　have　been　successfully　used　in　semi-supervised　learning　(SSL)　by　weighting　the　affinity　between　the　corresponding　pairs　of　samples.　Low-rank　representation　(LRR)　is　one　of　the　state-of-the-art　methods,　has　been　extensively　employed　in　the　existing　graph-based　learning　models.　In　graph-based　SSL,　a　weighted　affinity　graph　induced　by　LRR　coefficients　is　used　to　reflect　the　relationships　among　data　samples.　Constructing　a　robust　and　discriminative　graph　to　discover　the　intrinsic　structures　of　the　data　is　critical　for　SSL,　because　the　central　idea　behind　the　graph-based　SSL　approaches　is　to　explore　the　pairwise　affinity　between　data　samples　to　infer　those　unknown　labels.　However,　most　of　existing　LRR-based　approaches　fail　to　guarantee　weight　consistency　for　each　pair　of　data　samples,　which　is　beneficial　to　preserve　the　subspace　structures　of　high　dimensional　data.　In　this　paper,　we　propose　a　symmetric　LRR　with　adaptive　distance　penalty　(SLRRADP)　method　for　the　small　sample　size　(SSS)　recognition　problem.　The　graph　identified　by　SLRRADP　can　not　only　preserve　global　and　local　structures　of　data,　but　also　exploit　intrinsic　correlation　information　of　data　samples.　Extensive　experimental　results　on　semi-supervised　classification　tasks　demonstrate　the　effectiveness　of　the　proposed　method　and　its　superiority　in　performance　over　the　state-of-the-art　graph　construction　approaches.　(C)　2018　Elsevier　B.V.　All　rights　reserved.