Related papers: Binary Trees and Taxicab Correspondence Analysis o…
We present an overview of taxicab correspondence analysis, a robust variant of correspondence analysis, for visualization of extremely sparse ontingency tables. In particular we visualize an extremely sparse textual data set of size 590 by…
We present sparse tree-based and list-based density estimation methods for binary/categorical data. Our density estimation models are higher dimensional analogies to variable bin width histograms. In each leaf of the tree (or list), the…
The representation of binary relations has been intensively studied and many different theoretical and practical representations have been proposed to answer the usual queries in multiple domains. However, ternary relations have not…
Texts, whether literary or historical, exhibit structural and stylistic patterns shaped by their purpose, authorship, and cultural context. Formulaic texts, characterized by repetition and constrained expression, tend to have lower…
Large spatial datasets often represent a number of spatial point processes generated by distinct entities or classes of events. When crossed with covariates, such as discrete time buckets, this can quickly result in a data set with millions…
We propose a new outline for adaptive dictionary learning methods for sparse encoding based on a hierarchical clustering of the training data. Through recursive application of a clustering method, the data is organized into a binary…
We introduce a dynamic data structure for the compact representation of binary relations $\mathcal{R} \subseteq A \times B$. The data structure is a dynamic variant of the k$^2$-tree, a static compact representation that takes advantage of…
Knowledge representation and reasoning in law are essential to facilitate the automation of legal analysis and decision-making tasks. In this paper, we propose a new approach based on legal science, specifically legal taxonomy, for…
Tabular datasets are widely used in scientific disciplines such as biology. While these disciplines have already adopted AI methods to enhance their findings and analysis, they mainly use tree-based methods due to their interpretability. At…
This paper is devoted to a systematic study of a class of binary trees encoding the structure of rational numbers both from arithmetic and dynamical point of view. The paper is divided into two parts. The first one is a critical review of…
Long document classification presents challenges in capturing both local and global dependencies due to their extensive content and complex structure. Existing methods often struggle with token limits and fail to adequately model…
This is a largely expository paper in which we discuss various sets having a Catalan number of objects and some well-known bijections between these sets presented in a new and hopefully interesting way. We call these concepts "bookshelf"…
Integrated interpretability without sacrificing the prediction accuracy of decision making algorithms has the potential of greatly improving their value to the user. Instead of assigning a label to an image directly, we propose to learn…
Binary trait data record the presence or absence of distinguishing traits in individuals. We treat the problem of estimating ancestral trees with time depth from binary trait data. Simple analysis of such data is problematic. Each homology…
We congratulate Lee, Nadler and Wasserman (henceforth LNW) on a very interesting paper on new methodology and supporting theory [arXiv:0707.0481]. Treelets seem to tackle two important problems of modern data analysis at once. For datasets…
Chinese word segmentation is a fundamental task for Chinese language processing. The granularity mismatch problem is the main cause of the errors. This paper showed that the binary tree representation can store outputs with different…
Motivated by the continuing interest in the tree data model, we study the expressive power of downward navigational query languages on trees and chains. Basic navigational queries are built from the identity relation and edge relations…
Consider the problem of learning undirected graphical models on trees from corrupted data. Recently Katiyar et al. showed that it is possible to recover trees from noisy binary data up to a small equivalence class of possible trees. Their…
A central limit theorem for binary tree is numerically examined. Two types of central limit theorem for higher-order branches are formulated. A topological structure of a binary tree is expressed by a binary sequence, and the…
We describe a method for fast approximation of sparse coding. The input space is subdivided by a binary decision tree, and we simultaneously learn a dictionary and assignment of allowed dictionary elements for each leaf of the tree. We…