Related papers: Topological Autoencoders++: Fast and Accurate Cycl…

Anomaly detection without priors of the anomalies is challenging. In the field of unsupervised anomaly detection, traditional auto-encoder (AE) tends to fail based on the assumption that by training only on normal images, the model will not…

Dimensionality reduction methods such as UMAP and t-SNE are central tools for visualising high-dimensional data, but their local-neighborhood objectives can preserve sampling noise while distorting global topology. We show that standard…

We develop Riemannian approaches to variational autoencoders (VAEs) for PDE-type ambient data with regularizing geometric latent dynamics, which we refer to as VAE-DLM, or VAEs with dynamical latent manifolds. We redevelop the VAE framework…

Persistent homology provides information about the lifetime of homology classes along a filtration of cell complexes. Persistence barcode is a graphical representation of such information. A filtration might be determined by time in a set…

Neural networks encode inputs as high-dimensional vectors, known as representations, that capture how models process data by encoding task-relevant structure and semantics. Representation alignment refers to the degree to which different…

Autoencoders (AE) provide a useful method for nonlinear dimensionality reduction but are ill-suited for low data regimes. Conversely, Principal Component Analysis (PCA) is data-efficient but is limited to linear dimensionality reduction,…

The computational cost of traditional Computational Fluid Dynamics-based Aerodynamic Shape Optimization severely restricts design space exploration. This paper introduces TripOptimizer, a fully differentiable deep learning framework for…

This paper presents a new algorithm for the lossy compression of scalar data defined on 2D or 3D regular grids, with topological control. Certain techniques allow users to control the pointwise error induced by the compression. However, in…

This paper presents a practical approach for the optimization of topological simplification, a central pre-processing step for the analysis and visualization of scalar data. Given an input scalar field f and a set of "signal" persistence…

The persistence diagram (PD) is an increasingly popular topological descriptor. By encoding the size and prominence of topological features at varying scales, the PD provides important geometric and topological information about a space.…

Enforcing distributions of latent variables in neural networks is an active subject. It is vital in all kinds of generative models, where we want to be able to interpolate between points in the latent space, or sample from it. Modern…

With the increasing availability of high-dimensional data, analysts often rely on exploratory data analysis to understand complex data sets. A key approach to exploring such data is dimensionality reduction, which embeds high-dimensional…

This paper introduces a hybrid attention and autoencoder (AE) model for unsupervised online anomaly detection in time series. The autoencoder captures local structural patterns in short embeddings, while the attention model learns long-term…

Topological features based on persistent homology capture high-order structural information so as to augment graph neural network methods. However, computing extended persistent homology summaries remains slow for large and dense graphs and…

The geometric constraints of Zhou et al. (2015) are a widely used technique in topology/freeform optimization to impose minimum lengthscales for manufacturability. However, its efficacy degrades as design binarization is increased, and it…

The growing volume of high-resolution Whole Slide Images in digital histopathology poses significant storage, transmission, and computational efficiency challenges. Standard compression methods, such as JPEG, reduce file sizes but often…

The computer vision task of reconstructing 3D images, i.e., shapes, from their single 2D image slices is extremely challenging, more so in the regime of limited data. Deep learning models typically optimize geometric loss functions, which…

Persistent homology (PH) is a method used in topological data analysis (TDA) to study qualitative features of data that persist across multiple scales. It is robust to perturbations of input data, independent of dimensions and coordinates,…

Choosing a suitable filtering function for the Mapper algorithm can be difficult due to its arbitrariness and domain-specific requirements. Finding a general filtering function that can be applied across domains is therefore of interest,…

Reconstructing models from unorganized point clouds presents a significant challenge, especially when the models consist of multiple components represented by their surface point clouds. Such models often involve point clouds with noise…