Related papers: A Comparative Study of the Perceptual Sensitivity …
Graphs are a basic tool for the representation of modern data. The richness of the topological information contained in a graph goes far beyond its mere interpretation as a one-dimensional simplicial complex. We show how topological…
We study the probabilistic convergence between the mapper graph and the Reeb graph of a topological space $\mathbb{X}$ equipped with a continuous function $f: \mathbb{X} \rightarrow \mathbb{R}$. We first give a categorification of the…
The Reeb graph is a construction that studies a topological space through the lens of a real valued function. It has widely been used in applications, however its use on real data means that it is desirable and increasingly necessary to…
Techniques from computational topology, in particular persistent homology, are becoming increasingly relevant for data analysis. Their stable metrics permit the use of many distance-based data analysis methods, such as multidimensional…
Graph classification has gained significant attention due to its applications in chemistry, social networks, and bioinformatics. While Graph Neural Networks (GNNs) effectively capture local structural patterns, they often overlook global…
Statistical analysis on object data presents many challenges. Basic summaries such as means and variances are difficult to compute. We apply ideas from topology to study object data. We present a framework for using persistence landscapes…
Topological data analysis is becoming increasingly relevant to support the analysis of unstructured data sets. A common assumption in data analysis is that the data set is a sample---not necessarily a uniform one---of some high-dimensional…
Many works in the recent literature introduce semantic mapping methods that use CNNs (Convolutional Neural Networks) to recognize semantic properties in images. The types of properties (eg.: room size, place category, and objects) and their…
Topological correctness is critical for segmentation of tubular structures, which pervade in biomedical images. Existing topological segmentation loss functions are primarily based on the persistent homology of the image. They match the…
This paper is a cursory study on how topological features are preserved within the internal representations of neural network layers. Using techniques from topological data analysis, namely persistent homology, the topological features of a…
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…
Graph convolution (GConv) is a widely used technique that has been demonstrated to be extremely effective for graph learning applications, most notably node categorization. On the other hand, many GConv-based models do not quantify the…
We combine standard persistent homology with image persistent homology to define a novel way of characterizing shapes and interactions between them. In particular, we introduce: (1) a mixup barcode, which captures geometric-topological…
Graph contrastive learning (GCL) aims to align the positive features while differentiating the negative features in the latent space by minimizing a pair-wise contrastive loss. As the embodiment of an outstanding discriminative unsupervised…
In this paper, we consider topological featurizations of data defined over simplicial complexes, like images and labeled graphs, obtained by convolving this data with various filters before computing persistence. Viewing a convolution…
Inferring topological and geometrical information from data can offer an alternative perspective on machine learning problems. Methods from topological data analysis, e.g., persistent homology, enable us to obtain such information,…
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…
Unsupervised feature learning often finds low-dimensional embeddings that capture the structure of complex data. For tasks for which prior expert topological knowledge is available, incorporating this into the learned representation may…
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…
Complex systems are difficult to study not only because they are nonlinear, multiscale, and often nonstationary, but because their scientifically relevant organization is often invisible at the level of individual components, pairwise…