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Despite significant advances in the field of deep learning in ap-plications to various areas, an explanation of the learning pro-cess of neural network models remains an important open ques-tion. The purpose of this paper is a comprehensive…

Over the last two decades, topological data analysis (TDA) has emerged as a very powerful data analytic approach which can deal with various data modalities of varying complexities. One of the most commonly used tools in TDA is persistent…

The acquisition of large-scale, high-quality data is a resource-intensive and time-consuming endeavor. Compared to conventional Data Augmentation (DA) techniques (e.g. cropping and rotation), exploiting prevailing diffusion models for data…

Unsupervised Domain Adaptation (UDA) addresses the problem of performance degradation due to domain shift between training and testing sets, which is common in computer vision applications. Most existing UDA approaches are based on…

Convolutional Neural Network (CNN) struggle to capture the multi-dimensional structural information of complex high-dimensional data, which limits their feature learning capability. This paper proposes a feature fusion method based on…

One of the most interesting tools that have recently entered the data science toolbox is topological data analysis (TDA). With the explosion of available data sizes and dimensions, identifying and extracting the underlying structure of a…

We present a way to use Topological Data Analysis (TDA) for machine learning tasks on grayscale images. We apply persistent homology to generate a wide range of topological features using a point cloud obtained from an image, its natural…

We explore the role of torsion in hybrid deep learning models that incorporate topological data analysis, focusing on autoencoders. While most TDA tools use field coefficients, this conceals torsional features present in integer homology.…

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…

This paper introduces a 3D shape generative model based on deep neural networks. A new image-like (i.e., tensor) data representation for genus-zero 3D shapes is devised. It is based on the observation that complicated shapes can be well…

Topological data analysis (TDA) approaches are becoming increasingly popular for studying the dependence patterns in multivariate time series data. In particular, various dependence patterns in brain networks may be linked to specific tasks…

Under the banner of `Big Data', the detection and classification of structure in extremely large, high dimensional, data sets, is, one of the central statistical challenges of our times. Among the most intriguing approaches to this…

Semiconductor manufacturing generates vast amounts of image data, crucial for defect identification and yield optimization, yet often exceeds manual inspection capabilities. Traditional clustering techniques struggle with high-dimensional,…

The topological analysis of four-dimensional (4D) image-type data is challenged by the immense size that these datasets can reach. This can render the direct application of methods, like persistent homology and convolutional neural networks…

Modern business and economic datasets often exhibit nonlinear, multi-scale structures that traditional linear tools under-represent. Topological Data Analysis (TDA) offers a geometric lens for uncovering robust patterns, such as connected…

Deep learning has revolutionized the performance of classification, but meanwhile demands sufficient labeled data for training. Given insufficient data, while many techniques have been developed to help combat overfitting, the challenge…

Assessing the quality of 3D printed models before they are printed remains a challeng- ing problem, particularly when considering point cloud-based models. This paper introduces an approach to quality assessment, which uses techniques from…

In this article, we introduce a Topological Data Analysis (TDA) pipeline for neural spike train data. Understanding how the brain transforms sensory information into perception and behavior requires analyzing coordinated neural population…

Topological Data Analysis (TDA) offers a suite of computational tools that provide quantified shape features in high dimensional data that can be used by modern statistical and predictive machine learning (ML) models. In particular,…

The development of machine learning models based on computed tomography (CT) imaging has been a major focus due to the promise that imaging holds for diagnosis, staging, and prognostication. These models often rely on the extraction of…