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Continuous dynamical systems are cornerstones of many scientific and engineering disciplines. While machine learning offers powerful tools to model these systems from trajectory data, challenges arise when these trajectories are captured as…

Auto-encoders are among the most popular neural network architecture for dimension reduction. They are composed of two parts: the encoder which maps the model distribution to a latent manifold and the decoder which maps the latent manifold…

In this paper, we explore how to use topological tools to compare dimension reduction methods. We first make a brief overview of some of the methods often used dimension reduction such as Isometric Feature Mapping, Laplacian Eigenmaps, Fast…

Leaf-lesion segmentation is topology-sensitive: small merges, splits, or false holes can be biologically meaningful descriptors of biochemical pathways, yet they are weakly penalized by standard pixel-wise losses in Euclidean latents. I…

Dense retrievers encode queries and documents and map them in an embedding space using pre-trained language models. These embeddings need to be high-dimensional to fit training signals and guarantee the retrieval effectiveness of dense…

Node2vec is a graph embedding method that learns a vector representation for each node of a weighted graph while seeking to preserve relative proximity and global structure. Numerical experiments suggest Node2vec struggles to recreate the…

Delineation of curvilinear structures is an important problem in Computer Vision with multiple practical applications. With the advent of Deep Learning, many current approaches on automatic delineation have focused on finding more powerful…

Persistent homology (PH) is a powerful mathematical method to automatically extract relevant insights from images, such as those obtained by high-resolution imaging devices like electron microscopes or new-generation telescopes. However,…

Persistent homology (PH) is a method for generating topology-inspired representations of data. Empirical studies that investigate the properties of PH, such as its sensitivity to perturbations or ability to detect a feature of interest,…

Persistent homology (PH) has been widely applied to graph data to extract topological features. However, little attention has been paid to how different distance functions on a graph affect the resulting persistence barcodes and their…

Within the context of topological data analysis, the problems of identifying topological significance and matching signals across datasets are important and useful inferential tasks in many applications. The limitation of existing solutions…

We present a robust neural watermarking framework for scientific data integrity, targeting high-dimensional fields common in climate modeling and fluid simulations. Using a convolutional autoencoder, binary messages are invisibly embedded…

Existing research highlights the crucial role of topological priors in image segmentation, particularly in preserving essential structures such as connectivity and genus. Accurately capturing these topological features often requires…

The process of tuning the size of the hidden layers for autoencoders has the benefit of providing optimally compressed representations for the input data. However, such hyper-parameter tuning process would take a lot of computation and time…

Topological correctness is critical for segmentation of tubular structures, which pervade in biomedical images. Existing topological segmentation loss functions are primarily based on the persistent homology of the image. They match the…

High-energy large-scale particle colliders produce data at high speed in the order of 1 terabytes per second in nuclear physics and petabytes per second in high-energy physics. Developing real-time data compression algorithms to reduce such…

Unsupervised anomaly detection (AD) is a major topic in the field of Cyber-Physical Production Systems (CPPSs). A closely related concern is dimensionality reduction (DR) which is: 1) often used as a preprocessing step in an AD solution, 2)…

LiDAR scene generation is critical for mitigating real-world LiDAR data collection costs and enhancing the robustness of downstream perception tasks in autonomous driving. However, existing methods commonly struggle to capture geometric…

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…

Cyberattacks on critical infrastructure, particularly water distribution systems, have increased due to rapid digitalization and the integration of IoT devices and industrial control systems (ICS). These cyber-physical systems (CPS)…