Related papers: Learning Topology-Preserving Data Representations

We present a novel, domain-agnostic, model-independent, unsupervised, and universally applicable Machine Learning approach for dimensionality reduction based on the principles of algorithmic complexity. Specifically, but without loss of…

Many important problems in science and engineering require solving the so-called parametric partial differential equations (PDEs), i.e., PDEs with different physical parameters, boundary conditions, shapes of computational domains, etc.…

The application of the context-adaptive entropy model significantly improves the rate-distortion (R-D) performance, in which hyperpriors and autoregressive models are jointly utilized to effectively capture the spatial redundancy of the…

Linear discriminant analysis (LDA) is a widely used algorithm in machine learning to extract a low-dimensional representation of high-dimensional data, it features to find the orthogonal discriminant projection subspace by using the Fisher…

Manifold reconstruction has been extensively studied for the last decade or so, especially in two and three dimensions. Recently, significant improvements were made in higher dimensions, leading to new methods to reconstruct large classes…

Learning rich representation from data is an important task for deep generative models such as variational auto-encoder (VAE). However, by extracting high-level abstractions in the bottom-up inference process, the goal of preserving all…

Manifold learning (ML) aims to seek low-dimensional embedding from high-dimensional data. The problem is challenging on real-world datasets, especially with under-sampling data, and we find that previous methods perform poorly in this case.…

Nonlinear dimensionality reduction methods provide a valuable means to visualize and interpret high-dimensional data. However, many popular methods can fail dramatically, even on simple two-dimensional manifolds, due to problems such as…

Empirically, Deep Learning (DL) has demonstrated unprecedented success in practical applications. However, DL remains by and large a mysterious "black-box", spurring recent theoretical research to build its mathematical foundations. In this…

Manifold learning-based encoders have been playing important roles in nonlinear dimensionality reduction (NLDR) for data exploration. However, existing methods can often fail to preserve geometric, topological and/or distributional…

We study the problem of learning representations with controllable connectivity properties. This is beneficial in situations when the imposed structure can be leveraged upstream. In particular, we control the connectivity of an…

Dimensionality reduction can distort vector space properties such as orthogonality and linear independence, which are critical for tasks including cross-modal retrieval, clustering, and classification. We propose a Relationship Preserving…

Topological data analysis (TDA) is a relatively new field that is gaining rapid adoption due to its robustness and ability to effectively describe complex datasets by quantifying geometric information. In imaging contexts, TDA typically…

Practical Imitation Learning (IL) systems rely on large human demonstration datasets for successful policy learning. However, challenges lie in maintaining the quality of collected data and addressing the suboptimal nature of some…

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…

In this work we use the persistent homology method, a technique in topological data analysis (TDA), to extract essential topological features from the data space and combine them with deep learning features for classification tasks. In TDA,…

Variational Autoencoder (VAE) and its variations are classic generative models by learning a low-dimensional latent representation to satisfy some prior distribution (e.g., Gaussian distribution). Their advantages over GAN are that they can…

Classical unsupervised learning methods like clustering and linear dimensionality reduction parametrize large-scale geometry when it is discrete or linear, while more modern methods from manifold learning find low dimensional representation…

Modern representation learning increasingly relies on unsupervised and self-supervised methods trained on large-scale unlabeled data. While these approaches achieve impressive generalization across tasks and domains, evaluating embedding…

Multidimensional Projection is a fundamental tool for high-dimensional data analytics and visualization. With very few exceptions, projection techniques are designed to map data from a high-dimensional space to a visual space so as to…