Aiming at the problems of the slow convergence speed of general partial binary tree support vector machine (SVM) classifier and the fault samples easy to accumulate caused by complete binary tree and partial binary tree SVM classifier. The thesis proposes a multi-category classification method based on the unbalanced binary tree support vector machine (SVM),which construct a unbalanced binary t...

Motivated by the concerns of theorem-proving, we generalise the notion of proof tree to that of hierarchical proof tree. Hierarchical trees extend ordinary trees by adding partial order structure to the set of nodes: that allows us to visualise a node as a rectangle in the plane rather than as a point, letting us use the containment relation to express structure additional to that given by a tr...

Support vector machine (SVM) with a binary tree architecture is popular since it requires the minimum number of binary SVM to be trained and tested. Many efforts have been made to design the optimal binary tree architecture. However, these methods usually construct a binary tree by a greedy search. They sequentially decompose classes into two groups so that they consider only local optimum at e...

An optimal binary search tree is a binary search tree for which the nodes are arranged on levels such that the tree cost is minimum. For the purpose of a better presentation of optimal binary search trees, we will consider “extended binary search trees”, which have the keys stored at their internal nodes. Suppose “n” keys k1, k2, ... , k n are stored at the internal nodes of a binary search tre...

The paper introduces an operation on a binary tree, called binary tree roll, or roll of a binary tree. Two versions of the binary tree roll, counterclockwise and clockwise, are presented. The operations are mathematically defined and graphically presented. It is explained how the binary tree roll actually coincides with the process of turning the entire tree 90 degrees counterclockwise or clock...

Considering a random binary tree with n labelled leaves, we use a pruning procedure on this tree in order to construct a β( 3 2 , 1 2 )-coalescent process. We also use the continuous analogue of this construction, i.e. a pruning procedure on Aldous’s continuum random tree, to construct a continuous state space process that has the same structure as the β-coalescent process up to some time chang...

We prove that any logarithmic binary tree admits a linear-area straight-line strictly-upward planar grid drawing (in short, strictly-upward drawing), that is, a drawing in which (a) each edge is mapped into a single straight-line segment, (b) each node is placed below its parent, (c) no two edges intersect, and (d) each node is mapped into a point with integer coordinates. Informally, a logarit...

The weighted path length of optimum binary search trees is bounded above by Y'./3i + 2 a. + H where H is the entropy of the frequency distribution, /3i is the total weight of the internal nodes, and aj is the total weight of the leaves. This bound is best possible. A linear time algorithm for constructing nearly optimal trees is described. One of the popular methods for retrieving information b...

Hierarchical text classification or simply hierarchical classification refers to assigning a document to one or more suitable categories from a hierarchical category space. In our literature survey, we have found that the existing hierarchical classification experiments used a variety of measures to evaluate performance. These performance measures often assume independence between categories an...