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Nan Wu

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6 papers

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JBHI Journal 2026 Journal Article

HP-DIL: Deep heterogeneity profiling with graph-informed disentangled interaction learning for MRI-based liver fibrosis staging

Nan Wu
Yutao Wang
Jinhao Huo
Jian Zhang
Qianjiang Ding
Wei Jin

Liver fibrosis staging (LFS) informs treatment decisions and prognostic assessment in liver disease. Multiparametric MRI enables non-invasive, quantitative characterization of fibrosis-related tissue changes across the whole liver. Although deep-learning-based MRI analysis has advanced automated LFS, two bottlenecks remain: (i) etiology- and tissue-level heterogeneities reduce feature consistency across patients and liver regions; (ii) the lack of explicit modeling of inter-regional and inter-biomarker interactions biases models toward isolated imaging cues, leading to spurious correlations and limited generalizability. Here, we introduce a deep heterogeneity profiling framework with graph-informed disentangled interaction learning (HP-DIL) to enable accurate and interpretable LFS. HP-DIL first performs a biologically inspired, unsupervised subregion discovery stage, which fuses multiparametric MRI signals, spatial-texture coherence, and anatomical priors to construct subject-level graphs for heterogeneity profiling while preserving hepatic morphology. Within each subject, identified subregions are encoded as graph nodes carrying spatial coordinates, geometry, and multiparametric MRI attributes, forming a spatial-semantic interaction graph. A global-local graph transformer subsequently captures higher-order interactions among node-level representations within the constructed graph. Based on causal inference principles, we introduce a disentangled interaction mechanism (DIM) that decouples representative node-level features from whole-graph embeddings. An information-theoretic optimization is adopted to preserve disease-relevant signals while mitigating spurious correlations. Experiments on two external test cohorts from three external multi-vendor centers demonstrate that HP-DIL achieves competitive accuracy and cross-center generalizability. Moreover, we clarify the imaging relevance of the subregions identified by HP-DIL, with qualitative analysis showing close agreement between DIM-highlighted regions and radiological assessment. These findings support HP-DIL's potential for reliable clinical deployment in non-invasive LFS.

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AAAI Conference 2025 Conference Paper

SPAC: Sparse Partitioning and Adaptive Core Tensor Pruning Model for Knowledge Graph Completion

Chuhong Yang
Bin Li
Nan Wu

Tensor decomposition (TD) models are promising solutions for knowledge graph completion due to their simple structures but powerful representation capacities. The TD models typically adopt Tucker decomposition with a structured core tensor. Some models with a sparse core tensor, such as DistMult and ComplEx, are too simple and thus limit the interaction between embedding components, while other models with a dense core tensor are too complex and may lead to significant overfitting. To address these issues, we propose a new TD model called SPAC (Sparse Partitioning and Adaptive Core tensor pruning) model for knowledge graph completion. Specifically, SPAC captures coarse and fine-grained semantic information using a hybrid core tensor, where auxiliary cores are used to model sparse interactions and main cores for dense interactions. Moreover, SPAC introduces a gating mechanism to control the output of intermediate variables, enhancing the interaction between different partition groups. Furthermore, SPAC employs an adaptive pruning approach to dynamically adjust the shape of the core tensor. Due to the elaborate model design, the proposed TD model enhances expressive capacity and reduces the number of parameters in the core tensor. Experiments are conducted on datasets FB15k-237, WN18RR, and YAGO3-10. The results demonstrate that SPAC outperforms state-of-the-art tensor decomposition models, including MEIM and Tucker models. A series of ablation studies show that the gating mechanism and adaptive pruning strategy in SPAC are crucial for the performance improvement.

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JBHI Journal 2023 Journal Article

A Multi-Modal Heterogeneous Graph Forest to Predict Lymph Node Metastasis of Non-Small Cell Lung Cancer

Danqing Hu
Shaolei Li
Nan Wu
Xudong Lu

Lymph node metastasis (LNM) is critical for treatment decision-making for cancer patients, but it is difficult to diagnose accurately before surgery. Machine learning can learn nontrivial knowledge from multi-modal data to support accurate diagnosis. In this paper, we proposed a Multi-modal Heterogeneous Graph Forest (MHGF) approach to extract the deep representations of LNM from multi-modal data. Specifically, we first extracted the deep image features from CT images to represent the pathological anatomic extent of the primary tumor (pathological T stage) using a ResNet-Trans network. And then, a heterogeneous graph with six vertices and seven bi-directional relations was defined by medical experts to describe the possible relations between the clinical and image features. After that, we proposed a graph forest approach to construct the sub-graphs by removing each vertex in the complete graph iteratively. Finally, we used graph neural networks to learn the representations of each sub-graph in the forest to predict LNM and averaged all the prediction results as final results. We conducted experiments on 681 patients' multi-modal data. The proposed MHGF achieves the best performances with a 0. 806 AUC value and 0. 513 AP value compared with state-of-art machine learning and deep learning methods. The results indicate that the graph method can explore the relations between different types of features to learn effective deep representations for LNM prediction. Moreover, we found that the deep image features about the pathological anatomic extent of the primary tumor are useful for LNM prediction. And the graph forest approach can further improve the generalization ability and stability of the LNM prediction model.

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JMLR Journal 2023 Journal Article

When Locally Linear Embedding Hits Boundary

Hau-Tieng Wu
Nan Wu

Based on the Riemannian manifold model, we study the asymptotic behavior of a widely applied unsupervised learning algorithm, locally linear embedding (LLE), when the point cloud is sampled from a compact, smooth manifold with boundary. We show several peculiar behaviors of LLE near the boundary that are different from those diffusion-based algorithms. In particular, we show that LLE pointwisely converges to a mixed-type differential operator with degeneracy and we calculate the convergence rate. The impact of the hyperbolic part of the operator is discussed and we propose a clipped LLE algorithm which is a potential approach to recover the Dirichlet Laplace-Beltrami operator. [abs] [ pdf ][ bib ] &copy JMLR 2023. ( edit, beta )

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NeurIPS Conference 2022 Conference Paper

Unsupervised Learning for Combinatorial Optimization with Principled Objective Relaxation

Haoyu Peter Wang
Nan Wu
Hang Yang
Cong Hao
Pan Li

Using machine learning to solve combinatorial optimization (CO) problems is challenging, especially when the data is unlabeled. This work proposes an unsupervised learning framework for CO problems. Our framework follows the standard relaxation-plus-rounding approach and adopts neural networks to parameterize the relaxed solutions so that simple back-propagation can train them end-to-end. Our key contribution is the observation that if the relaxed objective satisfies entry-wise concavity, a low optimization loss guarantees the quality of the obtained integral solutions. This observation significantly generalizes the applicability of the previous framework inspired by Erdos' probabilistic method (Karalias & Loukas, 2020). Our framework is particularly suitable to guide the design of objective models in the applications where the objectives are not given explicitly while requiring being modeled and learned first. We evaluate our framework by solving a synthetic graph optimization problem, and two real-world applications including resource allocation in circuit design and approximate computing. Our framework largely outperforms the baselines based on reinforcement learning and Gumbel-softmax tricks.

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AIIM Journal 2020 Journal Article

Predicting postoperative non-small cell lung cancer prognosis via long short-term relational regularization

Danqing Hu
Shaolei Li
Zhengxing Huang
Nan Wu
Xudong Lu

Objectives Lung cancer is the leading cause of cancer death worldwide. Prognosis of lung cancer plays a crucial role in the clinical decision-making process to optimize the treatment for patients. Most of the existing data-driven prognostic prediction models explore the relations between patient’s characteristics and outcomes at a specific time interval. Although valuable, they neglect the relations between long-term and short-term prognoses and thus may limit the prediction performance. Methods In this study, we present a novel prognostic prediction approach for postoperative NSCLC patients. Specifically, we formulate the learning objective function by exploiting the relations between long-term and short-term prognoses via a long short-term relational regularization. The regularization term is composed of two parts, i. e. , the similarities between prognoses measured by patients’ outcomes and the L 2 -norms between the corresponding prognoses’ weight vectors. Based on this regularization, the proposed method can extract critical risk factors that comprehensively consider the long-term and short-term prognoses to facilitate the estimation of clinical risks. Results We evaluate the proposed model on a clinical dataset containing 693 consecutive postoperative NSCLC patients with more than 5-year follow-up from 2006 to 2015. Our best models achieve 0. 743, 0. 709, and 0. 746 AUCs for 1-year, 3-year, and 5-year survival prediction, 0. 696, 0. 724, and 0. 736 AUCs for 1-year, 3-year, and 5-year recurrence prediction, respectively. The experimental results show the efficiency of our proposed model in improving the performances on 1-year prognostic prediction in comparison with benchmark models. By comparing with the model without the long short-term relational regularization, the proposed model extracts more consistent critical risk factors for both long-term and short-term prognoses and contains fewer unreasonable risk factors under the clinician’s review. Conclusions We conclude that the proposed model can effectively exploit the relations between long-term and short-term prognoses. And the risk factors recognized by the proposed model have the potentials for further prognostic prediction of postoperative non-small cell lung cancer patients.

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