In　extreme　learning　machines　(ELM),　the　hidden　node　parameters　are　randomly　generated　and　the　output　weights　can　be　analytically　computed.　To　overcome　the　bad　feature　extraction　ability　of　the　shallow　architecture　of　ELM,　the　hierarchical　ELM　has　been　extensively　studied　as　a　deep　architecture　with　multilayer　neural　network.　However,　the　commonly　used　mean　square　error　(MSE)　criterion　is　very　sensitive　to　outliers　and　impulsive　noises,　generally　existing　in　real　world　data.　In　this　paper,　we　investigate　the　correntropy　to　improve　the　robustness　of　the　multilayer　ELM　and　provide　sparser　representation.　The　correntropy,　as　a　nonlinear　measure　of　similarity,　is　robust　to　outliers　and　can　approximate　different　norms　(from　l(0)　to　l(2)).　A　new　full　correntropy　based　multilayer　extreme　learning　machine　(FC-MELM)　algorithm　is　proposed　to　handle　the　classification　of　datasets　which　are　corrupted　by　impulsive　noises　or　outliers.　The　contributions　of　this　paper　are　three-folds:　(1)　The　MSE　based　reconstruction　loss　is　replaced　by　the　correntropy　based　loss　function;　In　this　way,　the　robustness　of　the　ELM　based　multilayer　algorithms　is　enhanced.　(2)　The　traditional　l(1)-based　sparsity　penalty　term　is　also　replaced　by　a　correntropy-based　sparsity　penalty　term,　which　can　further　improve　the　performance　of　the　proposed　algorithm　with　a　sparser　representation　of　the　data.　The　combination　of　(1)　and　(2)　provides　the　correntropy-based　ELM　autoencoder.　(3)　The　FC-MELM　is　proposed　by　using　the　correntropy-based　ELM　autoencoder　as　a　building　block.　It　is　notable　that　the　FC-MELM　is　trained　in　a　forward　manner,　which　means　fine-tuning　procedure　is　not　required.　Thus,　the　FC-MELM　has　great　advantage　in　learning　efficiently　when　compared　with　traditional　deep　learning　algorithms.　The　good　property　of　the　proposed　algorithm　is　confirmed　by　the　experiments　on　well-known　benchmark　datasets,　including　the　MNIST　datasets,　the　NYU　Object　Recognition　Benchmark　dataset,　and　the　Moore　network　traffic　dataset.　Finally,　the　proposed　FC-MELM　algorithm　is　applied　to　address　Computer　Aided　Cancer　Diagnosis.　Experiments　conducted　on　the　well-known　Wisconsin　Breast　Cancer　Data　(Diagnostic)　dataset　are　presented　and　show　that　the　proposed　FC-MELM　outperforms　state-of-the-art　methods　in　solving　computer　aided　cancer　diagnosis　problems.　(C)　2018　Elsevier　Ltd.　All　rights　reserved.