Related papers: Binary Trees and Taxicab Correspondence Analysis o…

A cluster tree provides a highly-interpretable summary of a density function by representing the hierarchy of its high-density clusters. It is estimated using the empirical tree, which is the cluster tree constructed from a density…

In human microbiome studies, sequencing reads data are often summarized as counts of bacterial taxa at various taxonomic levels specified by a taxonomic tree. This paper considers the problem of analyzing two repeated measurements of…

Full binary trees naturally represent commutative non-associative products. There are many important examples of these products: finite-precision floating-point addition and NAND gates, among others. Balance in such a tree is highly…

We introduce a cluster evaluation technique called Tree Index. Our Tree Index algorithm aims at describing the structural information of the clustering rather than the quantitative format of cluster-quality indexes (where the representation…

Peca suggested in a recent paper on the arxiv to consider binary butterfly trees and their Horton-Strahler numbers. The trees are obtained by glueing two binary trees together in a special way; the results are again binary trees but with a…

Human language understanding operates at multiple levels of granularity (e.g., words, phrases, and sentences) with increasing levels of abstraction that can be hierarchically combined. However, existing deep models with stacked layers do…

The extraction of templates such as ``regard X as Y'' from a set of related phrases requires the identification of their internal structures. This paper presents an unsupervised approach for extracting templates on-the-fly from only tagged…

We introduce an automated method for structuring textual data into a model-agnostic schema, enabling alignment with any database model. It generates both a schema and its instance. Initially, textual data is represented as semantically…

There are several common ways to encode a tree as a matrix, such as the adjacency matrix, the Laplacian matrix (that is, the infinitesimal generator of the natural random walk), and the matrix of pairwise distances between leaves. Such…

Rare events have played an increasing role in molecular phylogenetics as potentially homoplasy-poor characters.In this contribution we analyze the phylogenetic information content from a combinatorial point of view by consid-ering the…

In order to develop reliable services using machine learning, it is important to understand the uncertainty of the model outputs. Often the probability distribution that the prediction target follows has a complex shape, and a mixture…

We train a bilingual Arabic-Hebrew language model using a transliterated version of Arabic texts in Hebrew, to ensure both languages are represented in the same script. Given the morphological, structural similarities, and the extensive…

This paper proposes a novel end-to-end architecture for task-oriented dialogue systems. It is based on a simple and practical yet very effective sequence-to-sequence approach, where language understanding and state tracking tasks are…

In this paper, we address an issue of finding explainable clusters of class-uniform data in labelled datasets. The issue falls into the domain of interpretable supervised clustering. Unlike traditional clustering, supervised clustering aims…

We introduce a new formal model -- based on the mathematical construct of sheaves -- for representing contradictory information in textual sources. This model has the advantage of letting us (a) identify the causes of the inconsistency; (b)…

This paper investigates the a-posteriori analysis of Branch-and-Bound~(BB) trees to extract structural information about the feasible region of mixed-binary linear programs. We introduce three novel outer approximations of the feasible…

Broadband infrastructure owners do not always know how their customers are connected in the local networks, which are structured as rooted trees. A recent study is able to infer the topology of a local network using discrete time series…

Sparse approximations using highly over-complete dictionaries is a state-of-the-art tool for many imaging applications including denoising, super-resolution, compressive sensing, light-field analysis, and object recognition. Unfortunately,…

When considering the number of subtrees of trees, the extremal structures which maximize this number among binary trees and trees with a given maximum degree lead to some interesting facts that correlate to other graphical indices in…

The $k^2$-tree is a successful compact representation of binary relations that exhibit sparseness and/or clustering properties. It can be extended to $d$ dimensions, where it is called a $k^d$-tree. The representation boils down to a long…