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

The classification of weather data involves categorizing meteorological phenomena into classes, thereby facilitating nuanced analyses and precise predictions for various sectors such as agriculture, aviation, and disaster management. This…

Recently, convolution neural networks (CNNs) have attracted a great deal of attention due to their remarkable performance in various domains, particularly in image and text classification tasks. However, their application to tabular data…

Unsupervised data representation and visualization using tools from topology is an active and growing field of Topological Data Analysis (TDA) and data science. Its most prominent line of work is based on the so-called Mapper graph, which…

Geometric data pruning methods, while practical for leveraging pretrained models, are fundamentally unstable. Their reliance on extrinsic geometry renders them highly sensitive to latent space perturbations, causing performance to degrade…

One of the most important problems arising in time series analysis is that of bifurcation, or change point detection. That is, given a collection of time series over a varying parameter, when has the structure of the underlying dynamical…

Topological data analysis has emerged as a powerful tool for extracting the metric, geometric and topological features underlying the data as a multi-resolution summary statistic, and has found applications in several areas where data…

This paper proposes topology optimization for considering shielding and penetrating features. Based on the fictitious physical model, which is a useful approach to control geometric features, the proposed method analyzes fictitious…

Semiconductor manufacturing generates vast amounts of image data, crucial for defect identification and yield optimization, yet often exceeds manual inspection capabilities. Traditional clustering techniques struggle with high-dimensional,…

Topological data analysis (TDA) provides a growing body of tools for computing geometric and topological information about spaces from a finite sample of points. We present a new adaptive algorithm for finding provably dense samples of…

Topological data analysis (TDA) is an emerging mathematical concept for characterizing shapes in complex data. In TDA, persistence diagrams are widely recognized as a useful descriptor of data, and can distinguish robust and noisy…

We construct a pairing, which we call factorization homology, between framed manifolds and higher categories. The essential geometric notion is that of a vari-framing of a stratified manifold, which is a framing on each stratum together…

Deep learning is recognized to be capable of discovering deep features for representation learning and pattern recognition without requiring elegant feature engineering techniques by taking advantage of human ingenuity and prior knowledge.…

Deep learning is one of the new and important branches in machine learning. Deep learning refers to a set of algorithms that solve various problems such as images and texts by using various machine learning algorithms in multi-layer neural…

Deep learning applies multiple processing layers to learn representations of data with multiple levels of feature extraction. This emerging technique has reshaped the research landscape of face recognition (FR) since 2014, launched by the…

Recent advancements in deep learning for tabular data have shown promise, but challenges remain in achieving interpretable and lightweight models. This paper introduces Table2Image, a novel framework that transforms tabular data into…

Fine-grained image classification (FGIC) is a challenging task in computer vision for due to small visual differences among inter-subcategories, but, large intra-class variations. Deep learning methods have achieved remarkable success in…

This paper introduces advanced techniques of Topological Data Analysis (TDA) for unsupervised anomaly detection and customer segmentation in banking data. Using the Mapper algorithm and persistent homology, we develop unsupervised…

To enhance the robustness of the Light Gradient Boosting Machine (LightGBM) algorithm for image classification, a topological data analysis (TDA)-based robustness optimization algorithm for LightGBM, TDA-LightGBM, is proposed to address the…

This research uses deep learning to estimate the topology of manifolds represented by sparse, unordered point cloud scenes in 3D. A new labelled dataset was synthesised to train neural networks and evaluate their ability to estimate the…

Persistent Homology is a powerful tool in Topological Data Analysis (TDA) to capture topological properties of data succinctly at different spatial resolutions. For graphical data, shape, and structure of the neighborhood of individual data…