# Vector Encoding of Phylogenetic Trees by Ordered Leaf Attachment

## TL;DR

This paper introduces a new method to convert phylogenetic trees into integer vectors, enabling efficient tree comparison and analysis using machine learning.

## Contribution

The novel OLA method uniquely encodes tree topologies as integer vectors with linear-time encoding/decoding and a simple structure.

## Key findings

- OLA encoding and decoding run in linear time relative to the number of leaf nodes.
- The OLA encoding defines a tree distance that is compared to NNI and SPR distances.
- The set of OLA vectors is a simply-described subset of integer sequences.

## Abstract

As part of work to connect phylogenetics with machine learning, there has been considerable recent interest in vector encodings of phylogenetic trees. We present a simple new “ordered leaf attachment” (OLA) method for uniquely encoding a binary, rooted phylogenetic tree topology as an integer vector. OLA encoding and decoding take linear time in the number of leaf nodes, and the set of vectors corresponding to trees is a simply-described subset of integer sequences. The OLA encoding is unique compared to other existing encodings in having these properties. The integer vector encoding induces a distance on the set of trees, and we investigate this distance in relation to the NNI and SPR distances.