Hyper-sphere　support　vector　machine　is　an　important　method　for　unbalanced　classification　which　is　an　important　issue　in　biomedical　engineering　such　as　tongue　image　classification　in　traditional　chinese　medicine.　By　introducing　the　other　kind　of　samples,　one　class　support　vector　domain　description　classifier　is　modified　to　the　binary　hyper-sphere　classifier　to　improve　its　generalization　performance.　However,　among　the　methods　in　the　present　references,　it　is　proved　that　the　solution　of　margin　between　two　classes　of　samples　is　uncertain　when　there　is　no　support　vector　in　one　class　samples　from　the　point　of　the　optimal　solution　in　this　paper.　Meantime,　the　margin　between　two　classes　is　proved　to　be　zero　when　there　is　at　least　one　normal　support　vector　in　each　kind　of　samples.　The　generalization　performance　is　poor　if　the　margin　is　an　uncertain　value　or　it　equals　to　zero　to　some　extent.　To　improve　the　right　classification　rate　of　the　samples,　a　generalized　hyper-sphere　SVM　is　proposed　by　introducing　the　parameter　n　and　b　(n＞b)　and　the　margin　which　is　greater　than　zero　may　be　acquired,　which　balances　the　volume　of　the　hyper-sphere,　margin　and　the　experimental　error.　Theory　analysis　and　experimental　results　show　that　the　proposed　algorithm　has　better　generalization　performance　and　less　experimental　risk.