Functional Phylogenies

We now regularly use the genetic sequences of different creatures to make guesses about their common ancestors. A creature's genetic sequence is a long string of symbols. But how can we discuss common ancestors if, instead of knowing strings of symbols about each creature, we only have information about their shapes? Though this is a particularly difficult situation, it is very common. Many objects in the world around us evolve and change their shape but do not have a genetic sequence. For example, the shapes of consumer items, from toothbrushes to cars, are under continual shape evolution but no-one supposes they have genomes. The challenge of making inferences about the past evolution of shapes, and of making guesses about which shapes have recent ancestors in common, is well established. The standard approach to this challenge is to extract sets of numbers that describe the shapes of interest and to use these summary sets to make guesses about the past. This proposal takes a different approach. We aim to develop mathematical techniques that use the shapes themselves, rather than summaries of them, to make inferences about the past. This approach has some advantages: it uses more of the information that we have; it allows us to characterize the process that yields shape evolution; and it allows us to make guesses about the shapes of unseen ancestors (rather than guesses about a restricted set of their features).This proposal aims to advance the study of shape evolution by considering the evolution of mathematical functions. A functional phylogeny is akin to a genetic evolutionary tree where it is a mathematical function, rather than a genetic sequence, that changes through time. We will test our theory by: using computer generated data; performing `Spatial Chinese Whispers' experiments; and investigating how the pronunciation of words has evolved in Romance languages. Our `Spatial Chinese Whispers' experiments will involve the task of drawing curves, one after the other, so that small errors in copying yield a slow drift in curve shape. Our investigation of speech sound evolution first converts the sounds of modern speakers into shapes and then exploits the fact that we are confident about the evolutionary tree of Romance languages. Just as information about current genetic sequences allow us to make guesses about the sequences of past organisms, this approach might allow us to test hypotheses about the sounds of languages we can no longer hear.This work has relevance to those interested in designing shapes for the future, as well as those interested in past shapes. By understanding past shape evolution one can use this to generate reasonable shape transformations which might help in product design. This work aims to take sets of shapes and to make guesses about which is most related to which: this can be very useful in areas which have nothing to do with shape evolution. The ability to detect unusual or familiar shapes has relevance to numerous public and commercial challenges from spotting unusual vehicles to guessing the shapes of letters.

This project aims to reconstruct evolutionary history for general data that comprise smooth functions or shapes, going beyond the use of summary statistics: treating the evolution of shape as the evolution of mathematical functions. {Modern} phylogenetic inference allows us to take genetic sequences from creatures that we observe today and construct evolutionary histories that inform us about their ancestors. We propose to develop statistical methods that allow inference of the evolution of curves and shapes rather than the evolution of symbolic strings. By analogy, one application is to look at shapes that we observe today and make statistical statements about their common ancestors. Further, methods for identifying structure in data are extremely widely used across our scientific and industrial endeavours. A very useful class of tools are those of unsupervised learning, which work on unsorted and unlabelled data. The work proposed can be viewed as extending existing methods for unsupervised learning to data which are shapes or functions. The method discussed here thus has an alternative interpretation as a new approach to the hierarchical clustering of shapes: the shapes are imagined to have evolved from common ancestors and a corresponding dendrogram is inferred. This dendrogram could expose the structure of the set of shapes by invoking a purely notional evolutionary history. Who will benefit from this research and how? As noted above, the algorithm can either a) be viewed as a tool for informing about the evolution of shapes or b) as a means of finding natural clusters of shape data. The audiences for these two uses are slightly different. a) Product designers might like to use information about the process of shape evolution in Nature to find ways of generating new designs (effectively running the algorithms we describe forward in time) or for investigating the evolution of designs in the past. Similarly, those working in museums and galleries who are interested in the evolution of artistic styles and forms might profit from algorithms of this kind. Handwriting and picture authenticity checking could potentially be assisted by work related to ours. b) Data mining tools have found varied uses, for example within industry, government and intelligence. The ability to assess which groups of shapes cluster together---be they speech recordings, body outlines or trajectories---is very useful. It might allow improved surveillance tools (by identifying threatening shapes or motions), better product recommendations (by relating a selected product to other similarly shaped items for purchase), or automated advice on pronunciation (relating new speech signals to existing stored signals). What will be done to ensure that they have the opportunity to benefit from this research? The algorithms that are produced, and the associated data, will be freely available from our webpages. We will consult with the intellectual property and consulting parts of our respective universities to ensure that possible commercial exploitation is considered. For each of the papers that we publish we will make two short video presentations. One will be designed to be accessed by the general public and the other by a more technical scientific audience. The major paper which unites the full algorithm with synthetic, experimental and real data will be circulated to the publicity offices of the EPSRC and our respective institutions.