论文标题
alpha幅度
Alpha magnitude
论文作者
论文摘要
幅度是伦斯特（Leinster）在2010年左右引入的度量空间的等距不变性，目前是激烈研究的对象，因为已显示它编码许多已知的公制空间不变性。在最近的工作中，GoVC和Hepworth引入了持久幅度，这是与公制空间相关的过滤的简单复合物的数值。受政府和赫普沃思的定义的启发，我们引入了alpha幅度并研究了其一些关键特性。启发式观察结果使我们猜想与欧几里得空间紧凑子空间的Minkowski维度有关系。最后，alpha幅度在幅度和撕裂幅度上都呈现了计算优势，因此我们将其作为估算现实世界数据集的分形维度的新量度，易于计算。
Magnitude is an isometric invariant for metric spaces that was introduced by Leinster around 2010, and is currently the object of intense research, since it has been shown to encode many known invariants of metric spaces. In recent work, Govc and Hepworth introduced persistent magnitude, a numerical invariant of a filtered simplicial complex associated to a metric space. Inspired by Govc and Hepworth's definition, we introduce alpha magnitude and investigate some of its key properties. Heuristic observations lead us to conjecture a relationship with the Minkowski dimension of compact subspaces of Euclidean space. Finally, alpha magnitude presents computational advantages over both magnitude as well as Rips magnitude, and we thus propose it as a new measure for the estimation of fractal dimensions of real-world data sets that is easily computable.
