Given a sample of $n$ data points and an $n$ by $n$ dissimilarity matrix, data seriation methods produce a linear ordering of the objects, putting similar objects nearby in the ordering. One may visualize the reordered dissimilarity matrix with a heat map and thus understand the structure of the data, while still displaying the full matrix of dissimilarities. Good orderings produce heat maps that are easy to read and allow for clear interpretation.

We consider two popular seriation methods, minimizing path length by solving the Traveling Salesman Problem (TSP), and Optimal Leaf Ordering (OLO), which minimizes path length among all orderings consistent with a given tree structure. Learning from the strengths and weaknesses of the two methods, we introduce a new hybrid seriation method, tree-penalized Path Length (tpPL). The objective is a linear combination of path length and the extent of violations of the tree structure, with a parameter that transitions the optimal paths smoothly from TSP to OLO. We present a detailed study over 44 synthetic datasets which are designed to bring out the strengths and weaknesses of the three methods, finding that the hybrid nature of tpPL enables it to overcome the weaknesses of TSP and OLO.

给定一个样本$n$数据点和$n$经过$n$相异矩阵，数据序列化方法产生对象的线性排序，将相似的对象放在排序中的附近。人们可以使用热图可视化重新排序的差异矩阵，从而理解数据的结构，同时仍然显示完整的差异矩阵。良好的排序会产生易于阅读和清晰解释的热图。

我们考虑两种流行的序列化方法，通过解决旅行商问题 (TSP) 和最佳叶排序 (OLO) 来最小化路径长度，它最小化与给定树结构一致的所有排序之间的路径长度。通过学习这两种方法的优缺点，我们引入了一种新的混合序列化方法，树惩罚路径长度 (tpPL)。目标是路径长度和违反树结构的程度的线性组合，具有将最佳路径从 TSP 平滑过渡到 OLO 的参数。我们对 44 个合成数据集进行了详细研究，旨在揭示这三种方法的优缺点，发现 tpPL 的混合性质使其能够克服 TSP 和 OLO 的弱点。