Related papers: The Unified Segment Tree and its Application to th…

We propose a flexible and multi-scale method for organizing, visualizing, and understanding datasets sampled from or near stratified spaces. The first part of the algorithm produces a cover tree using adaptive thresholds based on a…

We demonstrate the versatility of the tangle-tree duality theorem for abstract separation systems by using it to prove tree-of-tangles theorems. This approach allows us to strengthen some of the existing tree-of-tangles theorems by bounding…

Machine learning systems regularly deal with structured data in real-world applications. Unfortunately, such data has been difficult to faithfully represent in a way that most machine learning techniques would expect, i.e. as a real-valued…

In several domains, data objects can be decomposed into sets of simpler objects. It is then natural to represent each object as the set of its components or parts. Many conventional machine learning algorithms are unable to process this…

Our goal is to visualize an additional data dimension of a tree with multifaceted data through superimposition on vertical strips, which we call columns. Specifically, we extend upward drawings of unordered rooted trees where vertices have…

Empirical data, on which deep learning relies, has substantial internal structure, yet prevailing theories often disregard this aspect. Recent research has led to the definition of structured data ensembles, aimed at equipping established…

Mechanistic interpretability aims to understand how models store representations by breaking down neural networks into interpretable units. However, the occurrence of polysemantic neurons, or neurons that respond to multiple unrelated…

Extracting structured representations from raw visual data is an important and long-standing challenge in machine learning. Recently, techniques for unsupervised learning of object-centric representations have raised growing interest. In…

Graph-structured data arise ubiquitously in many application domains. A fundamental problem is to quantify their similarities. Graph kernels are often used for this purpose, which decompose graphs into substructures and compare these…

Despite the promising results of disentangled representation learning in discovering latent patterns in graph-structured data, few studies have explored disentanglement for hypergraph-structured data. Integrating hyperedge disentanglement…

Starting from a variational formulation, we present a model for image segmentation that employs both region statistics and edge information. This combination allows for improved flexibility, making the proposed model suitable to process a…

Traversals are commonly seen in tree data structures, and performance-enhancing transformations between tree traversals are critical for many applications. Existing approaches to reasoning about tree traversals and their transformations are…

In this paper, we investigate adaptive nonlinear regression and introduce tree based piecewise linear regression algorithms that are highly efficient and provide significantly improved performance with guaranteed upper bounds in an…

Trees -- i.e., the type of data structure known under this name -- are central to many aspects of knowledge organization. We investigate some central design choices concerning the ontological modeling of such trees. In particular, we…

Multi-task learning improves generalization performance by sharing knowledge among related tasks. Existing models are for task combinations annotated on the same dataset, while there are cases where multiple datasets are available for each…

Automatic detection and segmentation of overlapping leaves in dense foliage can be a difficult task, particularly for leaves with strong textures and high occlusions. We present Dense-Leaves, an image dataset with ground truth segmentation…

The theory of complex trees is introduced as a new approach to study a broad class of self-similar sets. Systems of equations encoded by complex trees tip-to-tip equivalence relations are used to obtain one-parameter families of connected…

In data analysis, latent variables play a central role because they help provide powerful insights into a wide variety of phenomena, ranging from biological to human sciences. The latent tree model, a particular type of probabilistic…

A new concept called multilevel contours is introduced through this article by the author. Theorems on contours constructed on a bundle of complex planes are stated and proved. Multilevel contours can transport information from one complex…

We present a unified approach to the problems of reconstruction of large-scale structure distribution in the universe and determination of the underlying power spectrum. These have often been treated as two separate problems and different…