Related papers: Topological Deep Learning for Speech Data

Despite the remarkable accuracies attained by machine learning classifiers to separate complex datasets in a supervised fashion, most of their operation falls short to provide an informed intuition about the structure of data, and, what is…

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…

Topological Data Analysis (TDA) combines computational topology and data science to extract and analyze intrinsic topological and geometric structures in data set in a metric space. While the persistent homology (PH), a widely used tool in…

Accurate bone strength prediction is essential for assessing fracture risk, particularly in aging populations and individuals with osteoporosis. Bone imaging has evolved from X-rays and DXA to clinical computed tomography (CT), and now to…

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,…

Deep convolutional neural networks are hindered by training instability and feature redundancy towards further performance improvement. A promising solution is to impose orthogonality on convolutional filters. We develop an efficient…

A fundamental challenge in neuroscience is to understand what structure in the world is represented in spatially distributed patterns of neural activity from multiple single-trial measurements. This is often accomplished by learning a…

Understanding how the spatial structure of blood vessel networks relates to their function in healthy and abnormal biological tissues could improve diagnosis and treatment for diseases such as cancer. New imaging techniques can generate…

Timbre allows us to distinguish between sounds even when they share the same pitch and loudness, playing an important role in music, instrument recognition, and speech. Traditional approaches, such as frequency analysis or machine learning,…

Topology applied to real world data using persistent homology has started to find applications within machine learning, including deep learning. We present a differentiable topology layer that computes persistent homology based on level set…

Despite significant advances in the field of deep learning in applications to various fields, explaining the inner processes of deep learning models remains an important and open question. The purpose of this article is to describe and…

We introduce a novel, data-driven topological data analysis (TDA) approach for embedding brain networks into a lower-dimensional space in quantifying the dynamics of temporal lobe epilepsy (TLE) obtained from resting-state functional…

Topological Data Analysis (TDA) is a rising field of computational topology in which the topological structure of a data set can be observed by persistent homology. By considering a sequence of sublevel sets, one obtains a filtration that…

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…

While the strength of Topological Data Analysis has been explored in many studies on high dimensional numeric data, it is still a challenging task to apply it to text. As the primary goal in topological data analysis is to define and…

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…

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) is a recent approach to analyze data sets from the perspective of their topological structure. Its use for time series data has been limited to the field of financial time series primarily and as a method for…

In recent years, graph neural networks (GNNs) have emerged as a potent tool for learning on graph-structured data and won fruitful successes in varied fields. The majority of GNNs follow the message-passing paradigm, where representations…

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…