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Topological Data Analysis (TDA), an emerging field in investment sciences, harnesses mathematical methods to extract data features based on shape, offering a promising alternative to classical portfolio selection methodologies. We utilize…

Visual simultaneous localization and mapping (VSLAM) has broad applications, with state-of-the-art methods leveraging deep neural networks for better robustness and applicability. However, there is a lack of research in fusing these…

Topological Data Analysis (TDA) has emerged as a powerful framework for extracting robust, multiscale, and interpretable features from complex molecular data for artificial intelligence (AI) modeling and topological deep learning (TDL).…

Multivariate spatial data plays an important role in computational science and engineering simulations. The potential features and hidden relationships in multivariate data can assist scientists to gain an in-depth understanding of a…

Deformable object manipulation (DOM) with point clouds has great potential as non-rigid 3D shapes can be measured without detecting and tracking image features. However, robotic shape control of deformable objects with point clouds is…

This paper considers the problem of nonlinear dimensionality reduction. Unlike existing methods, such as LLE, ISOMAP, which attempt to unfold the true manifold in the low dimensional space, our algorithm tries to preserve the nonlinear…

We introduce multi-frequency vector diffusion maps (MFVDM), a new framework for organizing and analyzing high dimensional datasets. The new method is a mathematical and algorithmic generalization of vector diffusion maps (VDM) and other…

Unstructured data(e.g., images, videos, PDF files, etc.) contain semantic information, for example, the facial feature of a person and the plate number of a vehicle. There could be semantic relationships between data items which are not…

Topological Data Analysis (TDA) is a rapidly growing field, which studies methods for learning underlying topological structures present in complex data representations. TDA methods have found recent success in extracting useful geometric…

There is a growing need for unbiased clustering methods, ideally automated. We have developed a topology-based analysis tool called Two-Tier Mapper (TTMap) to detect subgroups in global gene expression datasets and identify their…

In computer vision and medical imaging, the problem of matching structures finds numerous applications from automatic annotation to data reconstruction. The data however, while corresponding to the same anatomy, are often very different in…

Data augmentation is widely used to train deep learning models to address data scarcity. However, traditional data augmentation (TDA) typically relies on simple geometric transformation, such as random rotation and rescaling, resulting in…

Document layout analysis (DLA) is the task of detecting the distinct, semantic content within a document and correctly classifying these items into an appropriate category (e.g., text, title, figure). DLA pipelines enable users to convert…

Topological clustering, and its main algorithm ToMATo, is a clustering method from Topological Data Analysis (TDA) which has been applied successfully in several applications during the last few years. This is due to its high versatility,…

Topological data analysis (TDA) is a rising field in the intersection of mathematics, statistics, and computer science/data science. The cornerstone of TDA is persistent homology, which produces a summary of topological information called a…

We address the problem of data augmentation in a rotating turbulence set-up, a paradigmatic challenge in geophysical applications. The goal is to reconstruct information in two-dimensional (2D) cuts of the three-dimensional flow fields,…

Nowadays, as data becomes increasingly complex and distributed, data analyses often involve several related datasets that are stored on different servers and probably owned by different stakeholders. While there is an emerging need to…

Automated visualization recommendation facilitates the rapid creation of effective visualizations, which is especially beneficial for users with limited time and limited knowledge of data visualization. There is an increasing trend in…

The rapid development of modern technology facilitates the appearance of numerous unprecedented complex data which do not satisfy the axioms of Euclidean geometry, while most of the statistical hypothesis tests are available in Euclidean or…

Experimental materials data are heterogeneous and include a variety of metadata for processing and characterization conditions, making the implementation of data-driven approaches for developing novel materials difficult. In this paper, we…