Related papers: Filtration learning in exact multi-parameter persi…

Persistent (co)homology is a central construction in topological data analysis, where it is used to quantify prominence of features in data to produce stable descriptors suitable for downstream analysis. Persistence is challenging to…

We show how event topology classification based on deep learning could be used to improve the purity of data samples selected in real time at at the Large Hadron Collider. We consider different data representations, on which different kinds…

Persistent homology has recently emerged as a powerful technique in topological data analysis for analyzing the emergence and disappearance of topological features throughout a filtered space, shown via persistence diagrams. Additionally,…

Topological descriptors have been increasingly utilized for capturing multiscale structural information in relational data. In this work, we consider various filtrations on the (box) product of graphs and the effect on their outputs on the…

Persistent homology, an algebraic method for discerning structure in abstract data, relies on the construction of a sequence of nested topological spaces known as a filtration. Two-parameter persistent homology allows the analysis of data…

Graph neural networks have become the default choice by practitioners for graph learning tasks such as graph classification and node classification. Nevertheless, popular graph neural network models still struggle to capture higher-order…

We propose PLLay, a novel topological layer for general deep learning models based on persistence landscapes, in which we can efficiently exploit the underlying topological features of the input data structure. In this work, we show…

As neural networks are increasingly being applied to real-world applications, mechanisms to address distributional shift and sequential task learning without forgetting are critical. Methods incorporating network expansion have shown…

Persistent homology is a central methodology in topological data analysis that has been successfully implemented in many fields and is becoming increasingly popular and relevant. The output of persistent homology is a persistence diagram --…

The goal of Feature Selection - comprising filter, wrapper, and embedded approaches - is to find the optimal feature subset for designated downstream tasks. Nevertheless, current feature selection methods are limited by: 1) the selection…

The fingerprint classification problem is to sort fingerprints into pre-determined groups, such as arch, loop, and whorl. It was asserted in the literature that minutiae points, which are commonly used for fingerprint matching, are not…

Mathematical morphology (MM) is a powerful and widely used framework in image processing. Through set-theoretic and discrete geometric principles, MM operations such as erosion, dilation, opening, and closing effectively manipulate digital…

In today's world of health care, brain tumor detection has become common. However, the manual brain tumor classification approach is time-consuming. So Deep Convolutional Neural Network (DCNN) is used by many researchers in the medical…

An Important tool in the field topological data analysis is known as persistent Homology (PH) which is used to encode abstract representation of the homology of data at different resolutions in the form of persistence diagram (PD). In this…

The problem of monotone missing data has been broadly studied during the last two decades and has many applications in different fields such as bioinformatics or statistics. Commonly used imputation techniques require multiple iterations…

Segmentation algorithms are prone to make topological errors on fine-scale structures, e.g., broken connections. We propose a novel method that learns to segment with correct topology. In particular, we design a continuous-valued loss…

We study the problem of learning similarity by using nonlinear embedding models (e.g., neural networks) from all possible pairs. This problem is well-known for its difficulty of training with the extreme number of pairs. For the special…

Tools of Topological Data Analysis provide stable summaries encapsulating the shape of the considered data. Persistent homology, the most standard and well studied data summary, suffers a number of limitations; its computations are hard to…

We consider the use of extreme learning machines (ELM) for computational partial differential equations (PDE). In ELM the hidden-layer coefficients in the neural network are assigned to random values generated on $[-R_m,R_m]$ and fixed,…

Hidden Markov Models (HMMs) are fundamental for modeling sequential data, yet learning their parameters from observations remains challenging. Classical methods like the Baum-Welch algorithm are computationally intensive and prone to local…