Related papers: Topological Autoencoders
In recent years, topological data analysis has been utilized for a wide range of problems to deal with high dimensional noisy data. While text representations are often high dimensional and noisy, there are only a few work on the…
Topological data analysis is becoming increasingly relevant to support the analysis of unstructured data sets. A common assumption in data analysis is that the data set is a sample---not necessarily a uniform one---of some high-dimensional…
Techniques from computational topology, in particular persistent homology, are becoming increasingly relevant for data analysis. Their stable metrics permit the use of many distance-based data analysis methods, such as multidimensional…
Topological loss based on persistent homology has shown promise in various applications. A topological loss enforces the model to achieve certain desired topological property. Despite its empirical success, less is known about the…
Topological Machine Learning (TML) is an emerging field that leverages techniques from algebraic topology to analyze complex data structures in ways that traditional machine learning methods may not capture. This tutorial provides a…
Noting the importance of the latent variables in inference and learning, we propose a novel framework for autoencoders based on the homeomorphic transformation of latent variables, which could reduce the distance between vectors in the…
Evolutionary partial differential equations play a crucial role in many areas of science and engineering. Spatial discretization of these equations leads to a system of ordinary differential equations which can then be solved by numerical…
When doing representation learning on data that lives on a known non-trivial manifold embedded in high dimensional space, it is natural to desire the encoder to be homeomorphic when restricted to the manifold, so that it is bijective and…
Persistent homology probes topological properties from point clouds and functions. By looking at multiple scales simultaneously, one can record the births and deaths of topological features as the scale varies. In this paper we use a…
Vision-language models have shown strong performance, but they often generalize poorly to specialized domains. While semi-supervised vision-language learning mitigates this limitation by leveraging a small set of labeled image-text pairs…
Autoencoders learn data representations (codes) in such a way that the input is reproduced at the output of the network. However, it is not always clear what kind of properties of the input data need to be captured by the codes. Kernel…
Topological methods for data analysis present opportunities for enforcing certain invariances of broad interest in computer vision, including view-point in activity analysis, articulation in shape analysis, and measurement invariance in…
With respect to spatial overlap, CNN-based segmentation of short axis cardiovascular magnetic resonance (CMR) images has achieved a level of performance consistent with inter observer variation. However, conventional training procedures…
Many applications, such as optimization, uncertainty quantification and inverse problems, require repeatedly performing simulations of large-dimensional physical systems for different choices of parameters. This can be prohibitively…
Variational Autoencoders for multimodal data hold promise for many tasks in data analysis, such as representation learning, conditional generation, and imputation. Current architectures either share the encoder output, decoder input, or…
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…
The manifold hypothesis states that many kinds of high-dimensional data are concentrated near a low-dimensional manifold. If the topology of this data manifold is non-trivial, a continuous encoder network cannot embed it in a one-to-one…
Persistent homology is a tool from Topological Data Analysis (TDA) used to summarize the topology underlying data. It can be conveniently represented through persistence diagrams. Observing a noisy signal, common strategies to infer its…
Data living on manifolds commonly appear in many applications. Often this results from an inherently latent low-dimensional system being observed through higher dimensional measurements. We show that under certain conditions, it is possible…
Most existing feature learning methods optimize inflexible handcrafted features and the affinity matrix is constructed by shallow linear embedding methods. Different from these conventional methods, we pretrain a generative neural network…