相关论文: Topological Data Analysis for Neural Network Analy…

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…

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.…

Topological data analysis (TDA) uses persistent homology to quantify loops and higher-dimensional holes in data, making it particularly relevant for examining the characteristics of images of cells in the field of cell biology. In the…

This work is devoted to a comprehensive analysis of topological data analysis fortime series classification. Previous works have significant shortcomings, such aslack of large-scale benchmarking or missing state-of-the-art methods. In this…

Recently, deep learning (DL) approaches to vulnerability detection have gained significant traction. These methods demonstrate promising results, often surpassing traditional static code analysis tools in effectiveness. In this study, we…

Algebraic topology has been widely applied to point cloud data to capture geometric shapes and topological structures. However, its application to genome sequence analysis remains rare. In this work, we propose topological sequence analysis…

Recent years have witnessed an increased interest in the application of persistent homology, a topological tool for data analysis, to machine learning problems. Persistent homology is known for its ability to numerically characterize the…

Scientific data has been growing in both size and complexity across the modern physical, engineering, life and social sciences. Spatial structure, for example, is a hallmark of many of the most important real-world complex systems, but its…

A community reveals the features and connections of its members that are different from those in other communities in a network. Detecting communities is of great significance in network analysis. Despite the classical spectral clustering…

Deep Neural Networks have shown tremendous success in the area of object recognition, image classification and natural language processing. However, designing optimal Neural Network architectures that can learn and output arbitrary graphs…

Representation learning on graphs is a fundamental problem that can be crucial in various tasks. Graph neural networks, the dominant approach for graph representation learning, are limited in their representation power. Therefore, it can be…

Deep neural networks are known to have security issues. One particular threat is the Trojan attack. It occurs when the attackers stealthily manipulate the model's behavior through Trojaned training samples, which can later be exploited.…

The design of periodic nanostructures allows to tailor the transport of photons, phonons, and matter waves for specific applications. Recent years have seen a further expansion of this field by engineering topological properties. However,…

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…

The natural world is full of complex systems characterized by intricate relations between their components: from social interactions between individuals in a social network to electrostatic interactions between atoms in a protein.…

This paper introduces new methodology based on the field of Topological Data Analysis for detecting anomalies in multivariate time series, that aims to detect global changes in the dependency structure between channels. The proposed…

With the widespread use of information technologies, information networks are becoming increasingly popular to capture complex relationships across various disciplines, such as social networks, citation networks, telecommunication networks,…

Deep learning has been shown to be successful in a number of domains, ranging from acoustics, images, to natural language processing. However, applying deep learning to the ubiquitous graph data is non-trivial because of the unique…

Topological Machine Learning (TML) is an emerging field that leverages techniques from algebraic topology to analyze complex data structures in ways that traditional machine learning methods may not capture. This tutorial provides a…

In this study, we present and analyze a framework for geometric and topological estimation for mapping of unknown environments. We consider agents mimicking motion behaviors of cyborg insects, known as biobots, and exploit coordinate-free…