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Information, stored or transmitted in digital form, is often structured. Individual data records are usually represented as hierarchies of their elements. Together, records form larger structures. Information processing applications have to…
Treemaps have been used in information visualisation for over two decades. They make use of nested filled areas to represent information hierarchies such as file systems, library catalogues, etc. Recent years have witnessed the emergence of…
Pretrained deep-learning models are the go-to solution for images or text. However, for tabular data the standard is still to train tree-based models. Indeed, transfer learning on tables hits the challenge of data integration: finding…
A wavelet forest for a text $T [1..n]$ over an alphabet $\sigma$ takes $n H_0 (T) + o (n \log \sigma)$ bits of space and supports access and rank on $T$ in $O (\log \sigma)$ time. K\"arkk\"ainen and Puglisi (2011) implicitly introduced…
Real world arrays often contain underlying structure, such as sparsity, runs of repeated values, or symmetry. Specializing for structure yields significant speedups. But automatically generating efficient code for structured data is…
In this paper, we provide new insights and analysis for the two elementary tree-based data structures - the AVL tree and binary heap. We presented two simple properties that gives a more direct way of relating the size of an AVL tree and…
Model trees provide an appealing way to perform interpretable machine learning for both classification and regression problems. In contrast to ``classic'' decision trees with constant values in their leaves, model trees can use linear…
We show how to use a balanced wavelet tree as a data structure that stores a list of numbers and supports efficient {\em range quantile queries}. A range quantile query takes a rank and the endpoints of a sublist and returns the number with…
When dealing with evolving or multi-dimensional complex systems, network theory provides with elegant ways of describing their constituting components, through respectively time-varying and multi-layer complex networks. Nevertheless, the…
The Simplex Tree (ST) is a recently introduced data structure that can represent abstract simplicial complexes of any dimension and allows efficient implementation of a large range of basic operations on simplicial complexes. In this paper,…
We consider an index data structure for similar strings. The generalized suffix tree can be a solution for this. The generalized suffix tree of two strings $A$ and $B$ is a compacted trie representing all suffixes in $A$ and $B$. It has…
Decision trees and their ensembles are very popular models of supervised machine learning. In this paper we merge the ideas underlying decision trees, their ensembles and FCA by proposing a new supervised machine learning model which can be…
Succinct data structures give space-efficient representations of large amounts of data without sacrificing performance. They rely one cleverly designed data representations and algorithms. We present here the formalization in Coq/SSReflect…
Comparative analysis of scalar fields is an important problem with various applications including feature-directed visualization and feature tracking in time-varying data. Comparing topological structures that are abstract and succinct…
Traditionally, most complex intelligence architectures are extremely non-convex, which could not be well performed by convex optimization. However, this paper decomposes complex structures into three types of nodes: operators, algorithms…
Graph searches and their respective search trees are widely used in algorithmic graph theory. The problem whether a given spanning tree can be a graph search tree has been considered for different searches, graph classes and search tree…
In Image Compression, the researchers' aim is to reduce the number of bits required to represent an image by removing the spatial and spectral redundancies. Recently discrete wavelet transform and wavelet packet has emerged as popular…
This paper presents an efficient method to perform Structured Matrix Approximation by Separation and Hierarchy (SMASH), when the original dense matrix is associated with a kernel function. Given points in a domain, a tree structure is first…
Phylogenetic mixtures model the inhomogeneous molecular evolution commonly observed in data. The performance of phylogenetic reconstruction methods where the underlying data is generated by a mixture model has stimulated considerable recent…
Matrices are two-dimensional data structures allowing one to conceptually organize information. For example, adjacency matrices are useful to store the links of a network; correlation matrices are simple ways to arrange gene co-expression…