数据矩阵中系统发生树的信息量
Information Content of a Phylogenetic Tree in a Data Matrix
摘要：
遗传学和生物学中的系统发育树一般都是二元的。我们试图回答一个基本的问题：这种二进制分支从粗到细的尺度持续的数据？我们将这个问题转化为一个等价的问题：树的结构信息在数据矩阵中的位置？从这个概念以及计算问题的结果，我们得出一个否定的答案：每个分支分裂成两个在每个节点的树从顶部到底部的水平是一个人造的结构。数据驱动的计算范式数据力学在这里揭示了树的信息是由一组选定的温度（或尺度），其中每一个有一个集群组成严格规定的温度特定的集群共享概率矩阵。由此产生的数据云几何（DCG）树的空间上的物种被建议作为真实的结构中包含的数据。特别是DCG树最细规模（底层）上的每个核心集群由于均匀性而不应进一步划分。在最细尺度之外，DCG树的分支主要基于概率，这导致了满足超三角不等式的超度量性质。这种超度量属性将DCG树与基于层次聚类（HC）算法的所有流行树区分开来，该算法通常采用经验的，通常是临时的距离度量。由于这个测度受三角不等式的约束，它不能产生一个“平的”分支，在这个分支中，所有成员（两个以上）彼此之间的距离相等。我们展示了这样的信息内容的说明性动物园的数据，然后在两个基因组数据。
英文摘要：
Phylogenetic trees in genetics and biology in general are all binary. We make an attempt to answer one fundamental question: Is such binary branching from the coarsest to the finest scales sustained by data? We convert this question into an equivalent one: where is the structural information of tree in a data matrix? Results from this conceptual as well as computing issue afford us to conclude a negative answer: Each branch being split into two at each inter-node of tree from the top to bottom levels is a man-made structure. The data-driven computing paradigm Data Mechanics is employed here to reveal that information of tree is composed of a set of selected temperatures (or scales), each of which has a clustering composition strictly regulated by a temperature-specific cluster-sharing probability matrix. The resultant Data Cloud Geometry (DCG) tree on the space of species is proposed as the authentic structure contained in data. Particularly each core clusters on the finest scale, the bottom level, of DCG tree should not be further partitioned because of uniformity. Beyond the finest scale, the branching of DCG tree is primarily based on probability, which induces an Ultrametric satisfying super triangular inequality property. This Ultrametric property differentiates DCG tree from all popular trees based on Hierarchical clustering (HC) algorithm, which typically employs an empirical, often ad hoc distance measure. Since this measure is regulated by the triangular inequality, it is not capable of producing a "flat" branch, in which all its members (more than two) have equal distances to each others. We demonstrate such information content on an illustrative zoo data first, and then on two genomic data.
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