摘要: The sample mean is one of the most fundamental concepts in statistics. Properties that are well-defined Euclidean spaces become unclear graph spaces. This paper proposes conditions under which following properties valid: existence, uniqueness, and consistency means, midpoint property, necessary optimality, convergence results algorithms. theoretical address common misconceptions about edit distance spaces, serve as a first step towards statistical analysis result theoretically well-founded algorithm outperformed six other algorithms with respect to solution quality on different datasets representing images molecules. HighlightsA theory space proposed.MMM-algorithm proposed algorithms.Necessary optimality proved.Convergence MMM-algorithm shown.Basic geometrical shown.