<p>In the era of ambiguity and vagueness, single-valued neutrosophic sets (SVNSs) are an eminent tool for handling indeterminate and uncertain information. SVNSs reduce information loss by considering three different aspects of an object. A similarity measure is an efficient tool used in various applications, including medical diagnosis, decision-making, and pattern recognition. Although many similarity measures have been established for SVNSs in the past, some do not fit the axiomatic definition of a similarity measure or exhibit issues that lead to inconsistent results. To overcome the shortcomings of the existing similarity measures, a new measure has been developed based on a novel definition of the inner product. The applicability and effectiveness of the proposed similarity measure are demonstrated through its application to medical diagnosis and pattern recognition problems. An algorithm for the face recognition problem is proposed using the proposed measure, and the maximum spanning tree (MST) technique is extended to the single-valued neutrosophic environment to offer a clustering analysis approach based on the proposed measure. Examples are provided to illustrate the algorithms, and their performances are compared with existing methods for addressing face recognition and clustering analysis problems. Experimental results verify that the proposed similarity measure produces reliable outcomes, addresses the problems found in existing similarity measures, and outperforms them in pattern recognition and medical diagnosis.</p>