Related papers: Visualizing Topological Importance: A Class-Driven…
Many datasets can be viewed as a noisy sampling of an underlying space, and tools from topological data analysis can characterize this structure for the purpose of knowledge discovery. One such tool is persistent homology, which provides a…
Understanding the global organization of complicated and high dimensional data is of primary interest for many branches of applied sciences. It is typically achieved by applying dimensionality reduction techniques mapping the considered…
Networks are important representations in computer science to communicate structural aspects of a given system of interacting components. The evolution of a network has several topological properties that can provide us information on the…
Classification of large and dense networks based on topology is very difficult due to the computational challenges of extracting meaningful topological features from real-world networks. In this paper we present a computationally tractable…
Deep metric learning aims to learn a function mapping image pixels to embedding feature vectors that model the similarity between images. Two major applications of metric learning are content-based image retrieval and face verification. For…
Understanding the shape and structure of objects is undoubtedly extremely important for object recognition, but the most common pattern recognition method currently used is machine learning, which often requires a large number of training…
Point cloud stands as the most widely adopted format for representing 3D shapes and scenes due to its simplicity and geometric fidelity. However, its inherent unordered and irregular nature, exacerbated by sensor noise and occlusions,…
Visual attributes are great means of describing images or scenes, in a way both humans and computers understand. In order to establish a correspondence between images and to be able to compare the strength of each property between images,…
We present ShapeVis, a scalable visualization technique for point cloud data inspired from topological data analysis. Our method captures the underlying geometric and topological structure of the data in a compressed graphical…
As complex machine learning models continue to find applications in high-stakes decision-making scenarios, it is crucial that we can explain and understand their predictions. Post-hoc explanation methods provide useful insights by…
Figures visually represent an essential piece of information and provide an effective means to communicate scientific facts. Recently there have been many efforts toward extracting data directly from figures, specifically from tables,…
Topological data analysis uses tools from topology -- the mathematical area that studies shapes -- to create representations of data. In particular, in persistent homology, one studies one-parameter families of spaces associated with data,…
The context of this paper is the use of formal methods for topology-based geometric modelling. Topology-based geometric modelling deals with objects of various dimensions and shapes. Usually, objects are defined by a graph-based topological…
Topological methods are very rarely used in structural health monitoring (SHM), or indeed in structural dynamics generally, especially when considering the structure and topology of observed data. Topological methods can provide a way of…
The manifold hypothesis, which assumes that data lies on or close to an unknown manifold of low intrinsic dimension, is a staple of modern machine learning research. However, recent work has shown that real-world data exhibits distinct…
Most complex systems can be captured by graphs or networks. Networks connect nodes (e.g.\ neurons) through edges (synapses), thus summarizing the system's structure. A popular way of interrogating graphs is community detection, which…
Various kinds of data are routinely represented as discrete probability distributions. Examples include text documents summarized by histograms of word occurrences and images represented as histograms of oriented gradients. Viewing a…
This paper introduces progressive algorithms for the topological analysis of scalar data. Our approach is based on a hierarchical representation of the input data and the fast identification of topologically invariant vertices, which are…
Understanding and quantifying node importance is a fundamental problem in network science and engineering, underpinning a wide range of applications such as influence maximization, social recommendation, and network dismantling. Prior…
In an era where accumulating data is easy and storing it inexpensive, feature selection plays a central role in helping to reduce the high-dimensionality of huge amounts of otherwise meaningless data. In this paper, we propose a graph-based…