Ce Ju

AIJ Journal 2025 Journal Article

Deep optimal transport for domain adaptation on SPD manifolds

• Ce Ju
• Cuntai Guan

NeurIPS Conference 2025 Conference Paper

Riemannian Flow Matching for Brain Connectivity Matrices via Pullback Geometry

• Antoine Collas
• Ce Ju
• Nicolas Salvy
• Bertrand Thirion

Generating realistic brain connectivity matrices is key to analyzing population heterogeneity in brain organization, understanding disease, and augmenting data in challenging classification problems. Functional connectivity matrices lie in constrained spaces—such as the set of symmetric positive definite or correlation matrices—that can be modeled as Riemannian manifolds. However, using Riemannian tools typically requires redefining core operations (geodesics, norms, integration), making generative modeling computationally inefficient. In this work, we propose DiffeoCFM, an approach that enables conditional flow matching (CFM) on matrix manifolds by exploiting pullback metrics induced by global diffeomorphisms on Euclidean spaces. We show that Riemannian CFM with such metrics is equivalent to applying standard CFM after data transformation. This equivalence allows efficient vector field learning, and fast sampling with standard ODE solvers. We instantiate DiffeoCFM with two different settings: the matrix logarithm for covariance matrices and the normalized Cholesky decomposition for correlation matrices. We evaluate DiffeoCFM on three large-scale fMRI datasets with more than $4600$ scans from $2800$ subjects (ADNI, ABIDE, OASIS‑3) and two EEG motor imagery datasets with over $30000$ trials from $26$ subjects (BNCI2014‑002 and BNCI2015‑001). It enables fast training and achieves state-of-the-art performance, all while preserving manifold constraints. Code: https: //github. com/antoinecollas/DiffeoCFM

ICLR Conference 2024 Conference Paper

Deep Geodesic Canonical Correlation Analysis for Covariance-Based Neuroimaging Data

• Ce Ju
• Reinmar J. Kobler
• Liyao Tang
• Cuntai Guan
• Motoaki Kawanabe

In human neuroimaging, multi-modal imaging techniques are frequently combined to enhance our comprehension of whole-brain dynamics and improve diagnosis in clinical practice. Modalities like electroencephalography and functional magnetic resonance imaging provide distinct views to the brain dynamics due to diametral spatiotemporal sensitivities and underlying neurophysiological coupling mechanisms. These distinct views pose a considerable challenge to learning a shared representation space, especially when dealing with covariance-based data characterized by their geometric structure. To capitalize on the geometric structure, we introduce a measure called geodesic correlation which expands traditional correlation consistency to covariance-based data on the symmetric positive definite (SPD) manifold. This measure is derived from classical canonical correlation analysis and serves to evaluate the consistency of latent representations obtained from paired views. For multi-view, self-supervised learning where one or both latent views are SPD we propose an innovative geometric deep learning framework termed DeepGeoCCA. Its primary objective is to enhance the geodesic correlation of unlabeled, paired data, thereby generating novel representations while retaining the geometric structures. In simulations and experiments with multi-view and multi-modal human neuroimaging data, we find that DeepGeoCCA learns latent representations with high geodesic correlation for unseen data while retaining relevant information for downstream tasks.

IJCAI Conference 2020 Conference Paper

Deep Polarized Network for Supervised Learning of Accurate Binary Hashing Codes

• Lixin Fan
• Kam Woh Ng
• Ce Ju
• Tianyu Zhang
• Chee Seng Chan

This paper proposes a novel deep polarized network (DPN) for learning to hash, in which each channel in the network outputs is pushed far away from zero by employing a differentiable bit-wise hinge-like loss which is dubbed as polarization loss. Reformulated within a generic Hamming Distance Metric Learning framework [Norouzi et al. , 2012], the proposed polarization loss bypasses the requirement to prepare pairwise labels for (dis-)similar items and, yet, the proposed loss strictly bounds from above the pairwise Hamming Distance based losses. The intrinsic connection between pairwise and pointwise label information, as disclosed in this paper, brings about the following methodological improvements: (a) we may directly employ the proposed differentiable polarization loss with no large deviations incurred from the target Hamming distance based loss; and (b) the subtask of assigning binary codes becomes extremely simple --- even random codes assigned to each class suffice to result in state-of-the-art performances, as demonstrated in CIFAR10, NUS-WIDE and ImageNet100 datasets.