Related papers: A Topological "Reading" Lesson: Classification of …

This study investigates whether Topological Data Analysis (TDA) can provide additional insights beyond traditional statistical methods in clustering currency behaviours. We focus on the foreign exchange (FX) market, which is a complex…

Inspired by the generation power of generative adversarial networks (GANs) in image domains, we introduce a novel hierarchical architecture for learning characteristic topological features from a single arbitrary input graph via GANs. The…

When training transformers on graph-structured data, incorporating information about the underlying topology is crucial for good performance. Topological masking, a type of relative position encoding, achieves this by upweighting or…

Exploring the shape of point configurations has been a key driver in the evolution of TDA (short for topological data analysis) since its infancy. This survey illustrates the recent efforts to broaden these ideas to model spatial…

Topological data analysis is a recent and fast growing field that approaches the analysis of datasets using techniques from (algebraic) topology. Its main tool, persistent homology (PH), has seen a notable increase in applications in the…

Neural networks are frequently used for image classification, but can be vulnerable to misclassification caused by adversarial images. Attempts to make neural network image classification more robust have included variations on…

Point cloud-based object/place recognition remains a problem of interest in applications such as autonomous driving, scene reconstruction, and localization. Extracting a meaningful global descriptor from a query point cloud that can be…

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…

Inspired by coarse-graining approaches used in physics, we show how similar algorithms can be adapted for data. The resulting algorithms are based on layered tree tensor networks and scale linearly with both the dimension of the input and…

Deep neural networks for 3D point cloud understanding have achieved remarkable success in object classification and recognition, yet recent work shows that these models remain highly vulnerable to adversarial perturbations. Existing 3D…

Topology and machine learning are two actively researched topics not only in condensed matter physics, but also in data science. Here, we propose the use of topological data analysis in unsupervised learning of the topological phase…

The impressive capabilities of recent generative models to create texts that are challenging to distinguish from the human-written ones can be misused for generating fake news, product reviews, and even abusive content. Despite the…

Data augmentation is widely used to train deep learning models to address data scarcity. However, traditional data augmentation (TDA) typically relies on simple geometric transformation, such as random rotation and rescaling, resulting in…

Recognizing handwritten digits is a challenging task primarily due to the diversity of writing styles and the presence of noisy images. The widely used MNIST dataset, which is commonly employed as a benchmark for this task, includes…

Topological clustering, and its main algorithm ToMATo, is a clustering method from Topological Data Analysis (TDA) which has been applied successfully in several applications during the last few years. This is due to its high versatility,…

A conceptually simple way to classify images is to directly compare test-set data and training-set data. The accuracy of this approach is limited by the method of comparison used, and by the extent to which the training-set data cover…

Persistent homology analysis provides means to capture the connectivity structure of data sets in various dimensions. On the mathematical level, by defining a metric between the objects that persistence attaches to data sets, we can…

We propose a deep network that can be trained to tackle image reconstruction and classification problems that involve detection of multiple object instances, without any supervision regarding their whereabouts. The network learns to extract…

This paper describes the systematic application of local topological methods for detecting interfaces and related anomalies in complicated high-dimensional data. By examining the topology of small regions around each point, one can…

Recognition of occluded objects in unseen indoor environments is a challenging problem for mobile robots. This work proposes a new slicing-based topological descriptor that captures the 3D shape of object point clouds to address this…