Related papers: The Unified Segment Tree and its Application to th…
This work addresses the intrinsic relationship between trees and networks (i.e. graphs). A complete (invertible) mapping is presented which allows trees to be mapped into weighted graphs and then backmapped into the original tree without…
In this paper we propose an approach for computing multiple high-quality near-isometric dense correspondences between a pair of 3D shapes. Our method is fully automatic and does not rely on user-provided landmarks or descriptors. This…
We introduce a new spatial data structure for high dimensional data called the \emph{approximate principal direction tree} (APD tree) that adapts to the intrinsic dimension of the data. Our algorithm ensures vector-quantization accuracy…
Tangles were originally introduced as a concept to formalize regions of high connectivity in graphs. In recent years, they have also been discovered as a link between structural graph theory and data science: when interpreting similarity in…
Decision trees and systems of decision rules are widely used as classifiers, as a means for knowledge representation, and as algorithms. They are among the most interpretable models for data analysis. The study of the relationships between…
Deep learning models have become popular in the analysis of tabular data, as they address the limitations of decision trees and enable valuable applications like semi-supervised learning, online learning, and transfer learning. However,…
One of the important features of an interconnection network is its ability to efficiently simulate programs or parallel algorithms written for other architectures. Such a simulation problem can be mathematically formulated as a graph…
Graph learning from data represents a canonical problem that has received substantial attention in the literature. However, insufficient work has been done in incorporating prior structural knowledge onto the learning of underlying…
Tree-structured multi-task architectures have been employed to jointly tackle multiple vision tasks in the context of multi-task learning (MTL). The major challenge is to determine where to branch out for each task given a backbone model to…
We present a method for reducing the treewidth of a graph while preserving all the minimal $s-t$ separators. This technique turns out to be very useful for establishing the fixed-parameter tractability of constrained separation and…
A graph is said to be a segment graph if its vertices can be mapped to line segments in the plane such that two vertices have an edge between them if and only if their corresponding line segments intersect. Kratochv\'{i}l and Kub\v{e}na…
This paper presents a new probabilistic generative model for image segmentation, i.e. the task of partitioning an image into homogeneous regions. Our model is grounded on a mid-level image representation, called a region tree, in which…
Nowadays, hyperspectral image classification widely copes with spatial information to improve accuracy. One of the most popular way to integrate such information is to extract hierarchical features from a multiscale segmentation. In the…
Many data management applications must deal with data which is uncertain, incomplete, or noisy. However, on existing uncertain data representations, we cannot tractably perform the important query evaluation tasks of determining query…
Artificial Neural Networks form the basis of very powerful learning methods. It has been observed that a naive application of fully connected neural networks to data with many irrelevant variables often leads to overfitting. In an attempt…
We review old and new uses of exchangeability, emphasizing the general theme of exchangeable representations of complex random structures. Illustrations of this theme include processes of stochastic coalescence and fragmentation; continuum…
The use of machine learning algorithms in finance, medicine, and criminal justice can deeply impact human lives. As a consequence, research into interpretable machine learning has rapidly grown in an attempt to better control and fix…
Knots are commonly represented and manipulated via diagrams, which are decorated planar graphs. When such a knot diagram has low treewidth, parameterized graph algorithms can be leveraged to ensure the fast computation of many invariants…
Key to structured prediction is exploiting the problem structure to simplify the learning process. A major challenge arises when data exhibit a local structure (e.g., are made by "parts") that can be leveraged to better approximate the…
Machine learning problems involving sparse datasets may benefit from the use of convolutional neural networks if the numbers of samples and features are very large. Such datasets are increasingly more frequently encountered in a variety of…