In area like pattern recognition,data mining, machine learning and so on, clustering plays a significant role. However, intuitionistic fuzzy sets (IFSs) and interval-valued intuitionistic fuzzy sets (IVIFSs) cannot describe and process indeterminate and inconsistent information, while single valued neutrosophic sets (SVNSs) and interval neutrosophic sets (INSs) can describe and handle it. So far, the existing clustering techniques scarcely involve SVNSs, and do not involve INSs. Motivated by IFCA and single valued neutrosophic clustering algorithms(SVNCA), the paper firstly proposes another SVNCA using the cosine similarity measure based on a dimension root distance of SVNSs. In the clustering algorithm, we define a dimension root distance measure between SVNSs and its cosine similarity measure between SVNSs, and then present a clustering algorithm based on the cosine similarity measure of SVNSs for clustering single valued neutrosophic data. Then, we extend the clustering algorithm for SVNSs to cluster INSs and propose an interval neutrosophic clustering algorithm (INCA). Then we obtain an illustrative example to show the effectiveness and application of the proposed clustering algorithm under single valued neutrosophic and interval neutrosophic environments.