Pruned tree-structured scalar quantizers are a form of non-uniform scalar quantizer that are named due to being designed via pruning a tree-structured scalar quantizer [1]. If designed via pruning a uniform tree-structured scalar quantizer, such a quantizer may be mapped to a piecewise linear compandor. An algorithm has been developed for mapping a piecewise linear compandor onto a a tree-struc...

Tree structured data such as HTML/XML files are represented by rooted trees with ordered children and edge labels. As a representation of a tree structured pattern in such tree structured data, we propose an ordered tree pattern, called a term tree, which is a rooted tree pattern consisting of ordered children and internal structured variables. A term tree is a generalization of standard tree p...

Information Extraction from semistructured data becomes more and more important. In order to extract meaningful or interesting contents from semistructured data, we need to extract common structured patterns from semistructured data. Many semistructured data have irregularities such as missing or erroneous data. A tag tree pattern is an edge labeled tree with ordered children which has tree str...

Tree-structured models have been widely used for human pose estimation, in either 2D or 3D. While such models allow efficient learning and inference, they fail to capture additional dependencies between body parts, other than kinematic constraints between connected parts. In this paper, we consider the use of multiple tree models, rather than a single tree model for human pose estimation. Our m...

Nowadays, huge volumes of Web data are organized or exported in tree-structured form. Popular examples of such structures are product catalogs of e-market stores, taxonomies of thematic categories, XML data encodings, etc. Even for a single knowledge domain, name mismatches, structural differences and structural inconsistencies raise difficulties when many data sources need to be integrated and...

In this note, we present a self-contained proof of the following property in tree-structured graphs, including trees, junction trees, and hypertrees: The global joint distribution of any tree-structured graph factorizes in terms of the local marginal distributions. In tree-structured graphs, this property plays a central role in the proof of many properties, which are unique to trees amongst al...

An Ant Colony Optimization (ACO) algorithm is proposed for optimal tree-structured natural gas distribution network. Design of pipelines, facilities, and equipment systems are necessary tasks to configure an optimal natural gas network. A mixed integer programming model is formulated to minimize the total cost in the network. The aim is to optimize pipe diameter sizes so that the location-alloc...

Tree-structured models have been widely used for human pose estimation, in either 2D or 3D. While such models allow efficient learning and inference, they fail to capture additional dependencies between body parts, other than kinematic constraints. In this paper, we consider the use of multiple tree models, rather than a single tree model for human pose estimation. Our model can alleviate the l...

Designers of statistical machine translation (SMT) systems have begun to employ tree-structured translation models. Systems involving tree-structured translation models tend to be complex. This article aims to reduce the conceptual complexity of such systems, in order to make them easier to design, implement, debug, use, study, understand, explain, modify, and improve. In service of this goal, ...

We consider the tree structured group Lasso where the structure over the features can be represented as a tree with leaf nodes as features and internal nodes as clusters of the features. The structured regularization with a pre-defined tree structure is based on a group-Lasso penalty, where one group is defined for each node in the tree. Such a regularization can help uncover the structured spa...