Related papers: A heuristic extending the Squarified treemapping a…
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…
Treemaps have been widely applied to the visualization of hierarchical data. A treemap takes a weighted tree and visualizes its leaves in a nested planar geometric shape, with sub-regions partitioned such that each sub-region has an area…
Rectangular layouts, subdivisions of an outer rectangle into smaller rectangles, have many applications in visualizing spatial information, for instance in rectangular cartograms in which the rectangles represent geographic or political…
Treemaps are a popular technique to visualize hierarchical data. The input is a weighted tree $\tree$ where the weight of each node is the sum of the weights of its children. A treemap for $\tree$ is a hierarchical partition of a rectangle…
We consider the problem of constructing an an optimal-weight tree from the 3*(n choose 4) weighted quartet topologies on n objects, where optimality means that the summed weight of the embedded quartet topologiesis optimal (so it can be the…
Merge trees are fundamental structures in topological data analysis. Interleaving distance is a widely accepted metric for comparing merge trees, with applications in visualization and scientific computing. While a greedy algorithm exists…
Fixed parameter tractable algorithms for bounded treewidth are known to exist for a wide class of graph optimization problems. While most research in this area has been focused on exact algorithms, it is hard to find decompositions of…
When solving ill-posed inverse problems, one often desires to explore the space of potential solutions rather than be presented with a single plausible reconstruction. Valuable insights into these feasible solutions and their associated…
Generalized Pythagoras trees were developed for visualizing hierarchical data, producing organic, fractal-like representations. However, the drawback of the original layout algorithm is visual overlap of tree branches. To avoid such…
Contour trees describe the topology of level sets in scalar fields and are widely used in topological data analysis and visualization. A main challenge of utilizing contour trees for large-scale scientific data is their computation at scale…
Large tree structures are ubiquitous and real-world relational datasets often have information associated with nodes (e.g., labels or other attributes) and edges (e.g., weights or distances) that need to be communicated to the viewers. Yet,…
Decision trees are well-known due to their ease of interpretability. To improve accuracy, we need to grow deep trees or ensembles of trees. These are hard to interpret, offsetting their original benefits. Shapley values have recently become…
We propose a new methodology to develop heuristic algorithms using tree decompositions. Traditionally, such algorithms construct an optimal solution of the given problem instance through a dynamic programming approach. We modify this…
Decision tree learning is a widely used approach in machine learning, favoured in applications that require concise and interpretable models. Heuristic methods are traditionally used to quickly produce models with reasonably high accuracy.…
A treap is a classic randomized binary search tree data structure that is easy to implement and supports O(\log n) expected time access. However, classic treaps do not take advantage of the input distribution or patterns in the input. Given…
A scalable graphical method is presented for selecting, and partitioning datasets for the training phase of a classification task. For the heuristic, a clustering algorithm is required to get its computation cost in a reasonable proportion…
In this paper we offer a new perspective on the well established agglomerative clustering algorithm, focusing on recovery of hierarchical structure. We recommend a simple variant of the standard algorithm, in which clusters are merged by…
A very simple heuristic approach to the unfolding problem will be described. An iterative algorithm starts with an empty histogram and every iteration aims to add one entry to this histogram. The entry to be added is selected according to a…
Tree search is a fundamental tool for planning, as many sequential decision-making problems can be framed as searching over tree-structured spaces. We propose an uncertainty-guided tree search algorithm for settings where the reward…
We propose a tree regularization framework, which enables many tree models to perform feature selection efficiently. The key idea of the regularization framework is to penalize selecting a new feature for splitting when its gain (e.g.…