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Ya-Wei Eileen Lin

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5 papers

2 author rows

NeurIPS Conference 2025 Conference Paper

Joint Hierarchical Representation Learning of Samples and Features via Informed Tree-Wasserstein Distance

Ya-Wei Eileen Lin
Ronald Coifman
Gal Mishne
Ronen Talmon

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 unsupervised method for jointly learning hierarchical representations of samples and features via Tree-Wasserstein Distance (TWD). Our method alternates between the two data modes. It first constructs a tree for one mode, then computes a TWD for the other mode based on that tree, and finally uses the resulting TWD to build the second mode’s tree. By repeatedly alternating through these steps, the method gradually refines both trees and the corresponding TWDs, capturing meaningful hierarchical representations of the data. We provide a theoretical analysis showing that our method converges. We show that our method can be integrated into hyperbolic graph convolutional networks as a pre-processing technique, improving performance in link prediction and node classification tasks. In addition, our method outperforms baselines in sparse approximation and unsupervised Wasserstein distance learning tasks on word-document and single-cell RNA-sequencing datasets.

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ICLR Conference 2025 Conference Paper

Tree-Wasserstein Distance for High Dimensional Data with a Latent Feature Hierarchy

Ya-Wei Eileen Lin
Ronald R. Coifman
Gal Mishne
Ronen Talmon

Finding meaningful distances between high-dimensional data samples is an important scientific task. To this end, we propose a new tree-Wasserstein distance (TWD) for high-dimensional data with two key aspects. First, our TWD is specifically designed for data with a latent feature hierarchy, i.e., the features lie in a hierarchical space, in contrast to the usual focus on embedding samples in hyperbolic space. Second, while the conventional use of TWD is to speed up the computation of the Wasserstein distance, we use its inherent tree as a means to learn the latent feature hierarchy. The key idea of our method is to embed the features into a multi-scale hyperbolic space using diffusion geometry and then present a new tree decoding method by establishing analogies between the hyperbolic embedding and trees. We show that our TWD computed based on data observations provably recovers the TWD defined with the latent feature hierarchy and that its computation is efficient and scalable. We showcase the usefulness of the proposed TWD in applications to word-document and single-cell RNA-sequencing datasets, demonstrating its advantages over existing TWDs and methods based on pre-trained models.

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NeurIPS Conference 2024 Conference Paper

Equivariant Machine Learning on Graphs with Nonlinear Spectral Filters

Ya-Wei Eileen Lin
Ronen Talmon
Ron Levie

Equivariant machine learning is an approach for designing deep learning models that respect the symmetries of the problem, with the aim of reducing model complexity and improving generalization. In this paper, we focus on an extension of shift equivariance, which is the basis of convolution networks on images, to general graphs. Unlike images, graphs do not have a natural notion of domain translation. Therefore, we consider the graph functional shifts as the symmetry group: the unitary operators that commute with the graph shift operator. Notably, such symmetries operate in the signal space rather than directly in the spatial space. We remark that each linear filter layer of a standard spectral graph neural network (GNN) commutes with graph functional shifts, but the activation function breaks this symmetry. Instead, we propose nonlinear spectral filters (NLSFs) that are fully equivariant to graph functional shifts and show that they have universal approximation properties. The proposed NLSFs are based on a new form of spectral domain that is transferable between graphs. We demonstrate the superior performance of NLSFs over existing spectral GNNs in node and graph classification benchmarks.

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ICML Conference 2023 Conference Paper

Hyperbolic Diffusion Embedding and Distance for Hierarchical Representation Learning

Ya-Wei Eileen Lin
Ronald R. Coifman
Gal Mishne
Ronen Talmon

Finding meaningful representations and distances of hierarchical data is important in many fields. This paper presents a new method for hierarchical data embedding and distance. Our method relies on combining diffusion geometry, a central approach to manifold learning, and hyperbolic geometry. Specifically, using diffusion geometry, we build multi-scale densities on the data, aimed to reveal their hierarchical structure, and then embed them into a product of hyperbolic spaces. We show theoretically that our embedding and distance recover the underlying hierarchical structure. In addition, we demonstrate the efficacy of the proposed method and its advantages compared to existing methods on graph embedding benchmarks and hierarchical datasets.

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NeurIPS Conference 2021 Conference Paper

Hyperbolic Procrustes Analysis Using Riemannian Geometry

Ya-Wei Eileen Lin
Yuval Kluger
Ronen Talmon

Label-free alignment between datasets collected at different times, locations, or by different instruments is a fundamental scientific task. Hyperbolic spaces have recently provided a fruitful foundation for the development of informative representations of hierarchical data. Here, we take a purely geometric approach for label-free alignment of hierarchical datasets and introduce hyperbolic Procrustes analysis (HPA). HPA consists of new implementations of the three prototypical Procrustes analysis components: translation, scaling, and rotation, based on the Riemannian geometry of the Lorentz model of hyperbolic space. We analyze the proposed components, highlighting their useful properties for alignment. The efficacy of HPA, its theoretical properties, stability and computational efficiency are demonstrated in simulations. In addition, we showcase its performance on three batch correction tasks involving gene expression and mass cytometry data. Specifically, we demonstrate high-quality unsupervised batch effect removal from data acquired at different sites and with different technologies that outperforms recent methods for label-free alignment in hyperbolic spaces.

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