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Among many unsolved puzzles in theories of Deep Neural Networks (DNNs), there are three most fundamental challenges that highly demand solutions, namely, expressibility, optimisability, and generalisability. Although there have been…

Topological Data Analysis (TDA) is a recent approach to analyze data sets from the perspective of their topological structure. Its use for time series data has been limited. In this work, a system developed for a leading provider of cloud…

Machine learning models often struggle to generalize across domains with varying data distributions, such as differing noise levels, leading to degraded performance. Traditional strategies like personalized training, which trains separate…

Unsupervised learning aims at the discovery of hidden structure that drives the observations in the real world. It is essential for success in modern machine learning. Latent variable models are versatile in unsupervised learning and have…

Persistent homology is a widely-used tool in topological data analysis (TDA) for understanding the underlying shape of complex data. By constructing a filtration of simplicial complexes from data points, it captures topological features…

Topological Data Analysis (TDA) is a discipline that applies algebraic topology techniques to analyze complex, multi-dimensional data. Although it is a relatively new field, TDA has been widely and successfully applied across various…

Annotating large scale datasets to train modern convolutional neural networks is prohibitively expensive and time-consuming for many real tasks. One alternative is to train the model on labeled synthetic datasets and apply it in the real…

The published literature on topology optimization has exploded over the last two decades to include methods that use shape and topological derivatives or evolutionary algorithms formulated on various geometric representations and…

This paper deals with computing topological invariants such as connected components, boundary surface genus, and homology groups. For each input data set, we have designed or implemented algorithms to calculate connected components,…

Semantic scene understanding is crucial for robotics and computer vision applications. In autonomous driving, 3D semantic segmentation plays an important role for enabling safe navigation. Despite significant advances in the field, the…

This paper introduces advanced techniques of Topological Data Analysis (TDA) for unsupervised anomaly detection and customer segmentation in banking data. Using the Mapper algorithm and persistent homology, we develop unsupervised…

Geometric 3D scene classification is a very challenging task. Current methodologies extract the geometric information using only a depth channel provided by an RGB-D sensor. These kinds of methodologies introduce possible errors due to…

Topological Data Analysis (TDA) has been successfully used for various tasks in signal/image processing, from visualization to supervised/unsupervised classification. Often, topological characteristics are obtained from persistent homology…

The study of topology is strictly speaking, a topic in pure mathematics. However in only a few years, Topological Data Analysis (TDA), which refers to methods of utilizing topological features in data (such as connected components, tunnels,…

Neural implicit representations have become a popular choice for modeling surfaces due to their adaptability in resolution and support for complex topology. While previous works have achieved impressive reconstruction quality by training on…

Given large amount of real photos for training, Convolutional neural network shows excellent performance on object recognition tasks. However, the process of collecting data is so tedious and the background are also limited which makes it…

In this paper, a novel 3D deep learning network is proposed for brain MR image segmentation with randomized connection, which can decrease the dependency between layers and increase the network capacity. The convolutional LSTM and 3D…

Training Data Attribution (TDA) seeks to trace model predictions back to influential training examples, enhancing interpretability and safety. We formulate TDA as a Bayesian information-theoretic problem: subsets are scored by the…

Despite the success of the carefully-annotated benchmarks, the effectiveness of existing graph neural networks (GNNs) can be considerably impaired in practice when the real-world graph data is noisily labeled. Previous explorations in…

Flow in porous media is difficult to address using standard analytical or numerical methods due to its complexity. However, since synthetic representations of porous media are easy to produce and data from physical experiments are becoming…