Feature　selection　aims　at　searching　the　most　discriminative　and　relevant　features　from　high-dimensional　data　to　improve　the　performance　of　certain　learning　tasks.　Whereas,　irrelevant　or　redundant　features　may　increase　the　over-fitting　risk　of　consequent　learning　algorithms.　Structured　learning　of　feature　selection　is　to　embed　intrinsic　structures　of　data,　such　as　geometric　structures　and　manifold　structures,　resulting　in　the　improvement　of　learning　performance.　In　this　paper,　three　types　of　structured　regularizers　are　embedded　into　the　feature　selection　framework　and　an　iterative　algorithm　with　proved　convergence　for　feature　selection　problem　is　proposed.　First,　serving　as　crucial　representation　pipelines　of　local　structures,　three　types　of　local　learning　regularizers,　including　graph　Laplacian,　neighborhood　preservation　and　sparsity　regularizer,　are　defined.　Second,　the　local　and　global　structures　are　integrated　into　one　joint　framework　for　the　feature　selection　problem.　Third,　the　framework　is　formulated　as　the　canonical　form　of　high-order　matrix　factorizations　and　then　an　efficient　convergent　iterative　algorithm　is　proposed　for　the　problem.　Besides,　the　proposed　framework　is　further　extended　to　multi-view　feature　selection　and　fusion　problems　from　an　algorithmic　view.　Finally,　the　proposed　algorithm　is　tested　on　eight　publicly　available　datasets　and　compared　to　several　state-of-the-art　feature　selection　methods.　Experimental　results　demonstrate　the　superiority　of　the　proposed　method　against　the　compared　algorithms　in　terms　of　clustering　performance.　©　2019　Elsevier　Ltd