TREE ASYMMETRY - A SENSITIVE AND PRACTICAL MEASURE FOR BINARY TOPOLOGICAL TREES
TREE ASYMMETRY - A SENSITIVE AND PRACTICAL MEASURE FOR BINARY TOPOLOGICAL TREES
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DOI：
10.1016/s0092-8240(05)80142-9
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发表时间：
1992-09-01
影响因子：
3.5
通讯作者：
WOLDENBERG, MJ
中科院分区：
文献类型：
--
作者：
VANPELT, J;UYLINGS, HBM;WOLDENBERG, MJ
二叉树的拓扑结构由称为树不对称性的度量来表征，定义为其分区不对称性的平均值。已经使用二叉树的生长模型研究了这种树不对称度量的统计特性。树不对称度量似乎对拓扑差异敏感，并且我们使用的生长模型的树不对称期望似乎几乎独立于树的大小。这些属性和简单的定义使得该测量适合实际使用，例如用于表征、比较和解释分支模式集。给出了三组神经元分支模式的分析示例。结果表明，这些观察到的分支模式的树不对称值的方差与所使用的生长模型预测的方差完全一致。
The topological structure of a binary tree is characterized by a measure called tree asymmetry, defined as the mean value of the asymmetry of its partitions. The statistical properties of this tree-asymmetry measure have been studied using a growth model for binary trees. The tree-asymmetry measure appears to be sensitive for topological differences and the tree-asymmetry expectation for the growth model that we used appears to be almost independent of the size of the trees. These properties and the simple definition make the measure suitable for practical use, for instance for characterizing, comparing and interpreting sets of branching patterns. Examples are given of the analysis of three sets of neuronal branching patterns. It is shown that the variance in tree-asymmetry values for these observed branching patterns corresponds perfectly with the variance predicted by the used growth model.