相关论文: Classification of Firn Data via Topological Featur…

Federated Learning is widely employed to tackle distributed sensitive data. Existing methods primarily focus on addressing in-federation data heterogeneity. However, we observed that they suffer from significant performance degradation when…

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…

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. In this work, a system developed for a leading provider of cloud…

We present a way to apply topological data analysis for classifying encrypted bits into distinct classes. Persistent homology is applied to generate topological features of a point cloud obtained from sets of encryptions. We see that this…

LiDAR point clouds contain measurements of complicated natural scenes and can be used to update digital elevation models, glacial monitoring, detecting faults and measuring uplift detecting, forest inventory, detect shoreline and beach…

Our goal is to provide a review of deep learning methods which provide insight into structured high-dimensional data. Rather than using shallow additive architectures common to most statistical models, deep learning uses layers of…

Topological data analysis (TDA) is an expanding field that leverages principles and tools from algebraic topology to quantify structural features of data sets or transform them into more manageable forms. As its theoretical foundations have…

Unsupervised representation learning methods are widely used for gaining insight into high-dimensional, unstructured, or structured data. In some cases, users may have prior topological knowledge about the data, such as a known cluster…

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…

In this paper, the training dynamics of PINNs with a feature mapping layer via the limiting Conjugate Kernel and Neural Tangent Kernel is investigated, shedding light on the convergence of PINNs; Although the commonly used Fourier-based…

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…

Lithology discrimination is a crucial activity in characterizing oil reservoirs, and processing lithology microscopic images is an essential technique for investigating fossils and minerals and geological assessment of shale oil…

Topological data analysis (TDA) is a rising branch in modern applied mathematics. It extracts topological structures as features of a given space and uses these features to analyze digital data. Persistent homology, one of the central tools…

The $DD\alpha$-classifier, a nonparametric fast and very robust procedure, is described and applied to fifty classification problems regarding a broad spectrum of real-world data. The procedure first transforms the data from their original…

Topological Data Analysis (TDA) provides a pipeline to extract quantitative topological descriptors from structured objects. This enables the definition of topological loss functions, which assert to what extent a given object exhibits some…

This research addresses a new tool for data analysis known as Topological Data Analysis TDA It underlies an area of Mathematics known as Combinatorial Algebra or more recently Algebraic Topology which through making strong use of…

The standard cosmological model with cold dark matter posits a hierarchical formation of structures. We introduce topological neural networks (TNNs), implemented as message-passing neural networks on higher-order structures, to effectively…

Weather regimes provide a useful framework for describing large-scale atmospheric variability and its impacts on regional weather. Despite extensive study, there is still no universally accepted definition or method for identifying weather…

Many computer vision and machine learning problems are modelled as learning tasks on graphs where graph neural networks GNNs have emerged as a dominant tool for learning representations of graph structured data A key feature of GNNs is…

Topological Data Analysis (TDA) is a recent and growing branch of statistics devoted to the study of the shape of the data. In this work we investigate the predictive power of TDA in the context of supervised learning. Since topological…