A model-based clustering algorithm is proposed for a general class of functional data which the components could be curves or images. The random realizations measured with errors at discrete, and possibly random, points in definition domain. idea to build set binary trees by recursive splitting observations. number groups are determined data-driven way. new provides easily interpretable results...

A class of multiscale stochastic models based on scale-recursive dynamics on trees has recently been introduced. Theoretical and experimental results have shown that these models provide an extremely rich framework for representing both processes which are intrinsically multiscale, e.g., 1=f processes, as well as 1-D Markov processes and 2-D Markov random elds. Moreover, eecient optimal estimat...

A class of multiscale stochastic models based on scale-recursive dynamics on trees has previously been introduced. Theoretical and experimental results have shown that these models provide an extremely rich framework for representing both processes which are intrinsically multiscale, e.g., 1/f processes, as well as 1D Markov processes and 2D Markov random fields. Moreover, efficient optimal est...

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We are interested in the asymptotics of random trees built by linear preferential attachment, also known in the literature as Barabási–Albert trees or plane-oriented recursive trees. We first prove a conjecture of Bubeck, Mossel & Rácz [7] concerning the influence of the seed graph on the asymptotic behavior of such trees. Separately we study the geometric structure of nodes of large degrees in...

A random recursive tree on n vertices is either a single isolated vertex (for n = 1) or is a vertex vn connected to a vertex chosen uniformly at random from a random recursive tree on n− 1 vertices. Such trees have been studied before (see [11]) as models of boolean circuits. More recently, modifications of such models [2], have been used to model for the web and other “power-law” networks. A s...

In this work we provide a combinatorial analysis of bucket recursive trees, which have been introduced previously as a natural generalization of the growth model of recursive trees. Our analysis is based on the description of bucket recursive trees as a special instance of so called bucket increasing trees, which is a family of combinatorial objects introduced in this paper. Using this combinat...

ABSTRACT. In this work we provide a combinatorial analysis of bucket recursive trees, which have been introduced previously as a natural generalization of the growth model of recursive trees. Our analysis is based on the description of bucket recursive trees as a special instance of so called bucket increasing trees, which is a family of combinatorial objects introduced in this paper. Using thi...

This paper deals with the size of the spanning tree of p randomly chosen nodes in a binary search tree. It is shown via generating functions methods, that for fixed p, the (normalized) spanning tree size converges in law to the Normal distribution. The special case p = 2 reproves the recent result (obtained by the contraction method by Mahmoud and Neininger [Ann. Appl. Probab. 13 (2003) 253–276...