Related papers: Visualizing Topological Importance: A Class-Driven…
Accurate delineation of fine-scale structures is a very important yet challenging problem. Existing methods use topological information as an additional training loss, but are ultimately making pixel-wise predictions. In this paper, we…
Real data is often given as a point cloud, i.e. a finite set of points with pairwise distances between them. An important problem is to detect the topological shape of data --- for example, to approximate a point cloud by a low-dimensional…
We present a novel method to explicitly incorporate topological prior knowledge into deep learning based segmentation, which is, to our knowledge, the first work to do so. Our method uses the concept of persistent homology, a tool from…
How to extract useful insights from data is always a challenge, especially if the data is multidimensional. Often, the data can be organized according to certain hierarchical structure that are stemmed either from data collection process or…
Topological data analysis is a relatively new branch of machine learning that excels in studying high dimensional data, and is theoretically known to be robust against noise. Meanwhile, data objects with mixed numeric and categorical…
A visualized graph is a powerful tool for data analysis and synthesis tasks. In this case, the task of visualization constitutes not only in displaying vertices and edges according to the graph representation, but also in ensuring that the…
Graph embeddings have become a key and widely used technique within the field of graph mining, proving to be successful across a broad range of domains including social, citation, transportation and biological. Graph embedding techniques…
Topological Data Analysis (TDA) has been praised by researchers for its ability to capture intricate shapes and structures within data. TDA is considered robust in handling noisy and high-dimensional datasets, and its interpretability is…
The topology of any complex system is key to understanding its structure and function. Fundamentally, algebraic topology guarantees that any system represented by a network can be understood through its closed paths. The length of each path…
Topological Data Analysis has grown in popularity in recent years as a way to apply tools from algebraic topology to large data sets. One of the main tools in topological data analysis is persistent homology. This paper uses undergraduate…
Methods from computational topology are becoming more and more popular in computer vision and have shown to improve the state-of-the-art in several tasks. In this paper, we investigate the applicability of topological descriptors in the…
The increasing ubiquity of smartphones and resurgence of VR/AR techniques, it is expected that our everyday environment may soon be decorating with objects connecting with virtual elements. Alerting to the presence of these objects is…
Due to the advent of the expressions of data other than tabular formats, the topological compositions which make samples interrelated came into prominence. Analogically, those networks can be interpreted as social connections, dataflow…
A graph with semantically attributed nodes are a common data structure in a wide range of domains. It could be interlinked web data or citation networks of scientific publications. The essential problem for such a data type is to determine…
Determining whether two graphs are isomorphic is a fundamental problem with practical applications in areas such as molecular chemistry or social network analysis, yet it remains a challenging task, with exact solutions often being…
In recent years, topological data analysis has been utilized for a wide range of problems to deal with high dimensional noisy data. While text representations are often high dimensional and noisy, there are only a few work on the…
Understanding how Large Language Models (LLMs) process information from prompts remains a significant challenge. To shed light on this "black box," attention visualization techniques have been developed to capture neuron-level perceptions…
Data generated in the fields of science, technology, business and in many other fields of research are increasing in an exponential rate. The way to extract knowledge from a huge set of data is a challenging task. This paper aims to propose…
Many state-of-the art visualization techniques must be tailored to the specific type of dataset, its modality (CT, MRI, etc.), the recorded object or anatomical region (head, spine, abdomen, etc.) and other parameters related to the data…
Supervised machine learning pipelines trained on features derived from persistent homology have been experimentally observed to ignore much of the information contained in a persistence diagram. Computing persistence diagrams is often the…