Related papers: MANTRA: The Manifold Triangulations Assemblage

Interacting, self-propelled particles such as epithelial cells can dynamically self-organize into complex multicellular patterns, which are challenging to classify without a priori information. Classically, different phases and phase…

Deep learning methods have demonstrated outstanding performances on classification and regression tasks on homogeneous data types (e.g., image, audio, and text data). However, tabular data still pose a challenge, with classic machine…

A core challenge in the interpretation of deep neural networks is identifying commonalities between the underlying algorithms implemented by distinct networks trained for the same task. Motivated by this problem, we introduce DYNAMO, an…

The analysis of tabular data has traditionally been dominated by gradient-boosted decision trees (GBDTs), known for their proficiency with mixed categorical and numerical features. However, recent deep learning innovations are challenging…

Manifold learning builds on the "manifold hypothesis," which posits that data in high-dimensional datasets are drawn from lower-dimensional manifolds. Current tools generate global embeddings of data, rather than the local maps used to…

This survey provides a comprehensive exploration of applications of Topological Data Analysis (TDA) within neural network analysis. Using TDA tools such as persistent homology and Mapper, we delve into the intricate structures and behaviors…

We develop a framework for comparing data manifolds, aimed, in particular, towards the evaluation of deep generative models. We describe a novel tool, Cross-Barcode(P,Q), that, given a pair of distributions in a high-dimensional space,…

In recent years, Transformers have become the de-facto architecture for sequence modeling on text and a variety of multi-dimensional data, such as images and video. However, the use of self-attention layers in a Transformer incurs…

Tabular data represent one of the most prevalent data formats in applied machine learning, largely because they accommodate a broad spectrum of real-world problems. Existing literature has studied many of the shortcomings of neural…

Higher-order networks are widely used to describe complex systems in which interactions can involve more than two entities at once. In this paper, we focus on inclusion within higher-order networks, referring to situations where specific…

Topological Data Analysis (TDA) has been praised by researchers for its ability to capture intricate shapes and structures within data. TDA is considered robust in handling noisy and high-dimensional datasets, and its interpretability is…

Topological data analysis (TDA) is a rapidly evolving field in applied mathematics and data science that leverages tools from topology to uncover robust, shape-driven insights in complex datasets. The main workhorse is persistent homology,…

Classification and identification of the materials lying over or beneath the Earth's surface have long been a fundamental but challenging research topic in geoscience and remote sensing (RS) and have garnered a growing concern owing to the…

Deep Neural Networks (DNNs) have already become a crucial computational approach to revealing the spatial patterns in the human brain; however, there are three major shortcomings in utilizing DNNs to detect the spatial patterns in…

The manifold hypothesis, which assumes that data lies on or close to an unknown manifold of low intrinsic dimension, is a staple of modern machine learning research. However, recent work has shown that real-world data exhibits distinct…

We present a new manifold learning algorithm that takes a set of data points lying on or near a lower dimensional manifold as input, possibly with noise, and outputs a simplicial complex that fits the data and the manifold. We have…

All industries are trying to leverage Artificial Intelligence (AI) based on their existing big data which is available in so called tabular form, where each record is composed of a number of heterogeneous continuous and categorical columns…

We present a new nonlinear dimensionality reduction method, MAPLE, that enhances UMAP by improving manifold modeling. MAPLE employs a self-supervised learning approach to more efficiently encode low-dimensional manifold geometry. Central to…

Learning meaningful representations using deep neural networks involves designing efficient training schemes and well-structured networks. Currently, the method of stochastic gradient descent that has a momentum with dropout is one of the…

The emergence of low-cost sensor architectures for diverse modalities has made it possible to deploy sensor arrays that capture a single event from a large number of vantage points and using multiple modalities. In many scenarios, these…