相关论文: Learning Topology-Preserving Data Representations

Topological Data Analysis (TDA) is a rising field of computational topology in which the topological structure of a data set can be observed by persistent homology. By considering a sequence of sublevel sets, one obtains a filtration that…

This paper proposes a deep representation learning using an information-theoretic loss with an aim to increase the inter-class distances as well as within-class similarity in the embedded space. Tasks such as anomaly and out-of-distribution…

Automatic evaluation of the goodness of Generative Adversarial Networks (GANs) has been a challenge for the field of machine learning. In this work, we propose a distance complementary to existing measures: Topology Distance (TD), the main…

Manifold learning approaches seek the intrinsic, low-dimensional data structure within a high-dimensional space. Mainstream manifold learning algorithms, such as Isomap, UMAP, $t$-SNE, Diffusion Map, and Laplacian Eigenmaps do not use data…

Disentanglement is a useful property in representation learning which increases the interpretability of generative models such as Variational autoencoders (VAE), Generative Adversarial Models, and their many variants. Typically in such…

During the last decades, we have witnessed a surge of interests of learning a low-dimensional space with discriminative information from one single view. Even though most of them can achieve satisfactory performance in some certain…

This paper presents a generalization of the Wasserstein distance for both persistence diagrams and merge trees [20], [66] that takes advantage of the regions of their topological features in the input domain. Specifically, we redefine the…

While high-dimensional embedding vectors are being increasingly employed in various tasks like Retrieval-Augmented Generation and Recommendation Systems, popular dimensionality reduction (DR) methods such as PCA and UMAP have rarely been…

Deep auto-encoders (DAEs) have achieved great success in learning data representations via the powerful representability of neural networks. But most DAEs only focus on the most dominant structures which are able to reconstruct the data…

Image segmentation is to extract meaningful objects from a given image. For degraded images due to occlusions, obscurities or noises, the accuracy of the segmentation result can be severely affected. To alleviate this problem, prior…

We introduce a linear dimensionality reduction technique preserving topological features via persistent homology. The method is designed to find linear projection $L$ which preserves the persistent diagram of a point cloud $\mathbb{X}$ via…

Unsupervised feature learning often finds low-dimensional embeddings that capture the structure of complex data. For tasks for which prior expert topological knowledge is available, incorporating this into the learned representation may…

Representing graph data in a low-dimensional space for subsequent tasks is the purpose of attributed graph embedding. Most existing neural network approaches learn latent representations by minimizing reconstruction errors. Rare work…

High-dimensional data often exhibit hierarchical structures in both modes: samples and features. Yet, most existing approaches for hierarchical representation learning consider only one mode at a time. In this work, we propose an…

The world is moving towards clean and renewable energy sources, such as wind energy, in an attempt to reduce greenhouse gas emissions that contribute to global warming. To enhance the analysis and storage of wind data, we introduce a deep…

In many scenarios, especially biomedical applications, the correct delineation of complex fine-scaled structures such as neurons, tissues, and vessels is critical for downstream analysis. Despite the strong predictive power of deep learning…

Robust topology optimization (RTO), as a class of topology optimization problems, identifies a design with the best average performance while reducing the response sensitivity to input uncertainties, e.g. load uncertainty. Solving RTO is…

We propose a novel probabilistic dimensionality reduction framework that can naturally integrate the generative model and the locality information of data. Based on this framework, we present a new model, which is able to learn a smooth…

The quest for simplification in physics drives the exploration of concise mathematical representations for complex systems. This Dissertation focuses on the concept of dimensionality reduction as a means to obtain low-dimensional…

Data augmentation is a widely used technique and an essential ingredient in the recent advance in self-supervised representation learning. By preserving the similarity between augmented data, the resulting data representation can improve…