Spaces of Random trees: Testing, classification and clustering

FLESIA, ANA GEORGINA

Lima, Peru

Congreso; X CLAPEM congreso Latinoamericano de Probabilidad y estadística Matemática; 2007

Pontificia Universidad Católica del Peru

We consider a compact metric space of trees that have a root and evolve forward in time in discrete generations, having each parent node at most m offspring nodes. An example of such space is the set of all possible context trees of fixed depth M, constructed from an alphabet of m symbols.  In this space, it is possible to define random objects and its  expectations, and empiric mean trees that are consistent estimates of the expected mean tree. It may also be defined a Kolmogorov-type of goodness of fit test for the one sample and two sample problems, a K-means clustering procedure and k-nearest neighbor classification scheme, as well as  Ward type hierarchical clustering, all four being pattern recognition schemes based on distance. We will state some theoretical properties of each procedure, and we will show that they can be applied to different problems derived from genomics and linguistics.