Related papers: The Stellar decomposition: A compact representatio…
Topological Signal Processing (TSP) over simplicial complexes is a framework that has been recently proposed, as a generalization of graph signal processing (GSP), to extend GSP to analyzing signals defined over sets of any order (i.e., not…
Data-aware methods for dimensionality reduction and matrix decomposition aim to find low-dimensional structure in a collection of data. Classical approaches discover such structure by learning a basis that can efficiently express the…
This paper investigates one of the most fundamental computer vision problems: image segmentation. We propose a supervised hierarchical approach to object-independent image segmentation. Starting with over-segmenting superpixels, we use a…
Analysis on fractals is a growing field, with hints of potential for widespread applicability across all of STEM. One of the most heavily researched type of fractals are the nested fractals, fractal shapes defined by virtue of being made of…
This is a sequel to [1106.3772], in which a systematic study of cellular stratified spaces and related concepts was initiated. In this paper, we study important operations on cellular and stellar stratified spaces, including taking…
Different cell types aggregate and sort into hierarchical architectures during the formation of animal tissues. The resulting spatial organization depends (in part) on the strength of adhesion of one cell type to itself relative to other…
Although Transformer has achieved great successes on many NLP tasks, its heavy structure with fully-connected attention connections leads to dependencies on large training data. In this paper, we present Star-Transformer, a lightweight…
The segment tree is an extremely versatile data structure. In this paper, a new heap based implementation of segment trees is proposed. In such an implementation of segment tree, the structural information associated with the tree nodes can…
This paper introduces a method to extract a hierarchical tree representation from 3D unorganized polygonal data. The proposed approach first extracts a graph representation of the surface, which serves as the foundation for structural…
This work seeks to tackle the inherent complexity of dataspaces by introducing a novel data structure that can represent datasets across multiple levels of abstraction, ranging from local to global. We propose the concept of a multilevel…
Modeling the distribution of high dimensional data by a latent tree graphical model is a prevalent approach in multiple scientific domains. A common task is to infer the underlying tree structure, given only observations of its terminal…
This paper explores the point set representation for tubular structure extraction tasks. Compared with the traditional mask representation, the point set representation enjoys its flexibility and representation ability, which would not be…
We used the dendrogram algorithm to decompose the surface density distributions of stars into hierarchical structures. These structures were tied to the multiscale structures of star clusters. A similar power-law for the mass-size relation…
Over the past decades, the increasing dimensionality of data has increased the need for effective data decomposition methods. Existing approaches, however, often rely on linear models or lack sufficient interpretability or flexibility. To…
In this paper we introduce a variation on the multidimensional segment tree, formed by unifying different interpretations of the dimensionalities of the data structure. We give some new definitions to previously well-defined concepts that…
Extracting geometric edges from unstructured point clouds remains a significant challenge, particularly in thin-walled structures that are commonly found in everyday objects. Traditional geometric methods and recent learning-based…
The structure of cloud complexes appears to be well described by a "tree structure" representation when the image is partitioned into "clouds". In this representation, the parent-child relationships are assigned according to containment.…
Model merging is an efficient way of obtaining a multi-task model from several pretrained models without further fine-tuning, and it has gained attention in various domains, including natural language processing (NLP). Despite the…
Much information about a graph can be obtained by studying its spanning trees. On the other hand, a graph can be regarded as a 1-dimensional cell complex, raising the question of developing a theory of trees in higher dimension. As observed…
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…