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Hu Ding

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17 papers

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AAAI Conference 2026 Conference Paper

Sample-and-Search: An Effective Algorithm for Learning-Augmented k-Median Clustering in High Dimensions

Kangke Cheng
Shihong Song
Guanlin Mo
Hu Ding

In this paper, we investigate the learning-augmented k-median clustering problem, which aims to improve the performance of traditional clustering algorithms by preprocessing the point set with a predictor of error rate α ∈ [0,1). This preprocessing step assigns potential labels to the points before clustering. We introduce an algorithm for this problem based on a simple yet effective sampling method, which substantially improves upon the time complexities of existing algorithms. Moreover, we mitigate their exponential dependency on the dimensionality of the Euclidean space. Lastly, we conduct experiments to compare our method with several state-of-the-art learning-augmented k-median clustering methods. The experimental results suggest that our proposed approach can significantly reduce the computational complexity in practice, while achieving a lower clustering cost.

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NeurIPS Conference 2025 Conference Paper

Adaptive and Multi-scale Affinity Alignment for Hierarchical Contrastive Learning

Jiawei Huang
Minming Li
Hu Ding

Contrastive self-supervised learning has emerged as a powerful paradigm for extracting meaningful representations without labels. While effective at capturing broad categorical distinctions, current methods often struggle to preserve the fine-grained and hierarchical relationships inherent in real-world data. From the perspective of semantic alignment, conventional contrastive learning aligns representations to semantic structure at a global level, treating the entire embedding space uniformly and frequently overlooking rich local structural information. In this paper, we propose \emph{Adaptive Multi-scale Affinity alignment (AMA-alignment)}, a framework that introduces localized contrastive objectives and a dynamic multi-scale optimization strategy to adaptively identify and refine poorly aligned regions within the embedding space. Although our model is inherently more complex due to its \emph{multi-scale} and \emph{adaptive} design, we provide the theoretical guarantees indicating that its convergence rate remains comparable to that of standard smooth non-convex optimization. We conduct a set of experiments on diverse benchmarks to show that AMA-alignment can effectively preserve hierarchical structure; moreover, AMA-alignment also outperforms existing contrastive methods on a range of downstream tasks.

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TCS Journal 2025 Journal Article

Bi-criteria sublinear time algorithms for clustering with outliers in high dimensions

Jiawei Huang
Wenjie Liu
Hu Ding

Real-world datasets often contain outliers, and the presence of outliers can make clustering problems be much more challenging. Existing algorithms for clustering with outliers often have high computational complexities. In this paper, we propose a simple yet effective sublinear framework for solving the representative center-based clustering with outliers problems: k -median/means clustering with outliers. Our analysis is fundamentally different from the previous (uniform and non-uniform) sampling based ideas. In particular, our sample complexity is independent of the input size and dimensionality, and thus it is suitable for dealing with large-scale and high-dimensional datasets. We also conduct a set of experiments to evaluate the effectiveness of our proposed method on both synthetic and real datasets.

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NeurIPS Conference 2025 Conference Paper

Bootstrap Your Uncertainty: Adaptive Robust Classification Driven by Optimal-Transport

Jiawei Huang
Minming Li
Hu Ding

Deep learning models often struggle with distribution shifts between training and deployment environments. Distributionally Robust Optimization (DRO) offers a promising framework by optimizing worst-case performance over a set of candidate distributions, which is called as the \emph{uncertainty set}. However, the efficacy of DRO heavily depends on the design of uncertainty set, and existing methods often perform suboptimally due to inappropriate and inflexible uncertainty sets. In this work, we first propose a novel perspective that casts entropy-regularized Wasserstein DRO as a dynamic process of distributional exploration and semantic alignment, both driven by optimal transport (OT). This unified viewpoint yields two key new techniques: \emph{semantic calibration}, which bootstraps semantically meaningful transport costs via inverse OT, and \emph{adaptive refinement}, which adjusts uncertainty set using OT-driven feedback. Together, these components form an exploration-and-feedback system, where the transport costs and uncertainty set evolve jointly during training, enabling the model to better adapt to potential distribution shifts. Moreover, we provide an in-depth analysis on this adaptive process and prove the theoretical convergence guarantee. Finally, we present our experimental results across diverse distribution shift scenarios, which demonstrate that our approach significantly outperforms existing methods, achieving state-of-the-art robustness.

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AAAI Conference 2024 Conference Paper

A Novel Skip Orthogonal List for Dynamic Optimal Transport Problem

Xiaoyang Xu
Hu Ding

Optimal transport is a fundamental topic that has attracted a great amount of attention from the optimization community in the past decades. In this paper, we consider an interesting discrete dynamic optimal transport problem: can we efficiently update the optimal transport plan when the weights or the locations of the data points change? This problem is naturally motivated by several applications in machine learning. For example, we often need to compute the optimal transport cost between two different data sets; if some changes happen to a few data points, should we re-compute the high complexity cost function or update the cost by some efficient dynamic data structure? We are aware that several dynamic maximum flow algorithms have been proposed before, however, the research on dynamic minimum cost flow problem is still quite limited, to the best of our knowledge. We propose a novel 2D Skip Orthogonal List together with some dynamic tree techniques. Although our algorithm is based on the conventional simplex method, it can efficiently find the variable to pivot within expected O(1) time, and complete each pivoting operation within expected O(|V|) time where V is the set of all supply and demand nodes. Since dynamic modifications typically do not introduce significant changes, our algorithm requires only a few simplex iterations in practice. So our algorithm is more efficient than re-computing the optimal transport cost that needs at least one traversal over all |E|=O(|V|^2) variables, where |E| denotes the number of edges in the network. Our experiments demonstrate that our algorithm significantly outperforms existing algorithms in the dynamic scenarios.

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IJCAI Conference 2024 Conference Paper

Approximate Algorithms for k-Sparse Wasserstein Barycenter with Outliers

Qingyuan Yang
Hu Ding

Wasserstein Barycenter (WB) is one of the most fundamental optimization problems in optimal transportation. Given a set of distributions, the goal of WB is to find a new distribution that minimizes the average Wasserstein distance to them. The problem becomes even harder if we restrict the solution to be “k-sparse”. In this paper, we study the k-sparse WB problem in the presence of outliers, which is a more practical setting since real-world data often contains noise. Existing WB algorithms cannot be directly extended to handle the case with outliers, and thus it is urgently needed to develop some novel ideas. First, we investigate the relation between k-sparse WB with outliers and the clustering (with outliers) problems. In particular, we propose a clustering based LP method that yields constant approximation factor for the k-sparse WB with outliers problem. Further, we utilize the coreset technique to achieve the (1+ε)-approximation factor for any ε>0, if the dimensionality is not high. Finally, we conduct the experiments for our proposed algorithms and illustrate their efficiencies in practice.

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NeurIPS Conference 2022 Conference Paper

Coresets for Relational Data and The Applications

Jiaxiang Chen
Qingyuan Yang
Ruomin Huang
Hu Ding

A coreset is a small set that can approximately preserve the structure of the original input data set. Therefore we can run our algorithm on a coreset so as to reduce the total computational complexity. Conventional coreset techniques assume that the input data set is available to process explicitly. However, this assumption may not hold in real-world scenarios. In this paper, we consider the problem of coresets construction over relational data. Namely, the data is decoupled into several relational tables, and it could be very expensive to directly materialize the data matrix by joining the tables. We propose a novel approach called ``aggregation tree with pseudo-cube'' that can build a coreset from bottom to up. Moreover, our approach can neatly circumvent several troublesome issues of relational learning problems [Khamis et al. , PODS 2019]. Under some mild assumptions, we show that our coreset approach can be applied for the machine learning tasks, such as clustering, logistic regression and SVM.

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NeurIPS Conference 2022 Conference Paper

Coresets for Wasserstein Distributionally Robust Optimization Problems

Ruomin Huang
Jiawei Huang
Wenjie Liu
Hu Ding

Wasserstein distributionally robust optimization (\textsf{WDRO}) is a popular model to enhance the robustness of machine learning with ambiguous data. However, the complexity of \textsf{WDRO} can be prohibitive in practice since solving its ``minimax'' formulation requires a great amount of computation. Recently, several fast \textsf{WDRO} training algorithms for some specific machine learning tasks (e. g. , logistic regression) have been developed. However, the research on designing efficient algorithms for general large-scale \textsf{WDRO}s is still quite limited, to the best of our knowledge. \textit{Coreset} is an important tool for compressing large dataset, and thus it has been widely applied to reduce the computational complexities for many optimization problems. In this paper, we introduce a unified framework to construct the $\epsilon$-coreset for the general \textsf{WDRO} problems. Though it is challenging to obtain a conventional coreset for \textsf{WDRO} due to the uncertainty issue of ambiguous data, we show that we can compute a ``dual coreset'' by using the strong duality property of \textsf{WDRO}. Also, the error introduced by the dual coreset can be theoretically guaranteed for the original \textsf{WDRO} objective. To construct the dual coreset, we propose a novel grid sampling approach that is particularly suitable for the dual formulation of \textsf{WDRO}. Finally, we implement our coreset approach and illustrate its effectiveness for several \textsf{WDRO} problems in the experiments. See \href{https: //arxiv. org/abs/2210. 04260}{arXiv: 2210. 04260} for the full version of this paper. The code is available at \url{https: //github. com/h305142/WDRO_coreset}.

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NeurIPS Conference 2021 Conference Paper

Robust and Fully-Dynamic Coreset for Continuous-and-Bounded Learning (With Outliers) Problems

Zixiu Wang
Yiwen Guo
Hu Ding

In many machine learning tasks, a common approach for dealing with large-scale data is to build a small summary, {\em e. g. ,} coreset, that can efficiently represent the original input. However, real-world datasets usually contain outliers and most existing coreset construction methods are not resilient against outliers (in particular, an outlier can be located arbitrarily in the space by an adversarial attacker). In this paper, we propose a novel robust coreset method for the {\em continuous-and-bounded learning} problems (with outliers) which includes a broad range of popular optimization objectives in machine learning, {\em e. g. ,} logistic regression and $ k $-means clustering. Moreover, our robust coreset can be efficiently maintained in fully-dynamic environment. To the best of our knowledge, this is the first robust and fully-dynamic coreset construction method for these optimization problems. Another highlight is that our coreset size can depend on the doubling dimension of the parameter space, rather than the VC dimension of the objective function which could be very large or even challenging to compute. Finally, we conduct the experiments on real-world datasets to evaluate the effectiveness of our proposed robust coreset method.

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NeurIPS Conference 2021 Conference Paper

Solving Soft Clustering Ensemble via $k$-Sparse Discrete Wasserstein Barycenter

Ruizhe Qin
Mengying Li
Hu Ding

Clustering ensemble is one of the most important problems in ensemble learning. Though it has been extensively studied in the past decades, the existing methods often suffer from the issues like high computational complexity and the difficulty on understanding the consensus. In this paper, we study the more general soft clustering ensemble problem where each individual solution is a soft clustering. We connect it to the well-known discrete Wasserstein barycenter problem in geometry. Based on some novel geometric insights in high dimensions, we propose the sampling-based algorithms with provable quality guarantees. We also provide the systematical analysis on the consensus of our model. Finally, we conduct the experiments to evaluate our proposed algorithms.

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TCS Journal 2020 Journal Article

Faster balanced clusterings in high dimension

Hu Ding

The problem of constrained clustering has attracted significant attention in the past decades. In this paper, we study the balanced k-center, k-median, and k-means clustering problems where the size of each cluster is constrained by the given lower and upper bounds. The problems are motivated by the applications in processing large-scale data in high dimension. Existing methods often need to compute complicated matchings (or min cost flows) to satisfy the balance constraint, and thus suffer from high complexities especially in high dimension. We develop an effective framework for the three balanced clustering problems to address this issue, and our method is based on a novel spatial partition idea in geometry. For the balanced k-center clustering, we provide a 4-approximation algorithm that improves the existing approximation factors; for the balanced k-median and k-means clusterings, our algorithms yield constant and ( 1 + ϵ ) -approximation factors with any ϵ > 0. More importantly, our algorithms achieve linear or nearly linear running times when k is a constant, and significantly improve the existing ones. Our results can be easily extended to metric balanced clusterings and the running times are sub-linear in terms of the complexity of n-point metric.

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IJCAI Conference 2020 Conference Paper

On Metric DBSCAN with Low Doubling Dimension

Hu Ding
Fan Yang
Mingyue Wang

The density based clustering method Density-Based Spatial Clustering of Applications with Noise (DBSCAN) is a popular method for outlier recognition and has received tremendous attention from many different areas. A major issue of the original DBSCAN is that the time complexity could be as large as quadratic. Most of existing DBSCAN algorithms focus on developing efficient index structures to speed up the procedure in low-dimensional Euclidean space. However, the research of DBSCAN in high-dimensional Euclidean space or general metric spaces is still quite limited, to the best of our knowledge. In this paper, we consider the metric DBSCAN problem under the assumption that the inliers (excluding the outliers) have a low doubling dimension. We apply a novel randomized k-center clustering idea to reduce the complexity of range query, which is the most time consuming step in the whole DBSCAN procedure. Our proposed algorithms do not need to build any complicated data structures and are easy to implement in practice. The experimental results show that our algorithms can significantly outperform the existing DBSCAN algorithms in terms of running time.

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AAAI Conference 2019 Conference Paper

On Geometric Alignment in Low Doubling Dimension

Hu Ding
Mingquan Ye

In real-world, many problems can be formulated as the alignment between two geometric patterns. Previously, a great amount of research focus on the alignment of 2D or 3D patterns, especially in the field of computer vision. Recently, the alignment of geometric patterns in high dimension finds several novel applications, and has attracted more and more attentions. However, the research is still rather limited in terms of algorithms. To the best of our knowledge, most existing approaches for high dimensional alignment are just simple extensions of their counterparts for 2D and 3D cases, and often suffer from the issues such as high complexities. In this paper, we propose an effective framework to compress the high dimensional geometric patterns and approximately preserve the alignment quality. As a consequence, existing alignment approach can be applied to the compressed geometric patterns and thus the time complexity is significantly reduced. Our idea is inspired by the observation that high dimensional data often has a low intrinsic dimension. We adopt the widely used notion “doubling dimension” to measure the extents of our compression and the resulting approximation. Finally, we test our method on both random and real datasets; the experimental results reveal that running the alignment algorithm on compressed patterns can achieve similar qualities, comparing with the results on the original patterns, but the running times (including the times cost for compression) are substantially lower.

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AAAI Conference 2017 Conference Paper

Novel Geometric Approach for Global Alignment of PPI Networks

Yangwei Liu
Hu Ding
Danyang Chen
Jinhui Xu

In this paper we present a novel geometric method for the problem of global pairwise alignment of protein-protein interaction (PPI) networks. A PPI network can be viewed as a node-edge graph and its alignment often needs to solve some generalized version of the subgraph isomorphism problem which is notoriously challenging and NP-hard. All existing research has focused on designing algorithms with good practical performance. In this paper we propose a two-step algorithm for the global pairwise PPI network alignment which consists of a Geometric Step and an MCMF Step. Our algorithm ﬁrst applies a graph embedding technique that preserves the topological structure of the original PPI networks and maps the problem from graph domain to geometric domain, and computes a rigid transformation for one of the embedded PPI networks so as to minimize its Earth Mover’s Distance (EMD) to the other PPI network. It then solves a Min-Cost Max-Flow problem using the (scaled) inverse of sequence similarity scores as edge weight. By using the ﬂow values from the two steps (i. e. , EMD and Min-Cost Max- Flow) as the matching scores, we are able to combine the two matching results to obtain the desired alignment. Unlike other popular alignment algorithms which are either greedy or incremental, our algorithm globally optimizes the problem to yield an alignment with better quality.

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AAAI Conference 2015 Conference Paper

Random Gradient Descent Tree: A Combinatorial Approach for SVM with Outliers

Hu Ding
Jinhui Xu

Support Vector Machine (SVM) is a fundamental technique in machine learning. A long time challenge facing SVM is how to deal with outliers (caused by mislabeling), as they could make the classes in SVM nonseparable. Existing techniques, such as soft margin SVM, ν-SVM, and Core-SVM, can alleviate the problem to certain extent, but cannot completely resolve the issue. Recently, there are also techniques available for explicit outlier removal. But they suffer from high time complexity and cannot guarantee quality of solution. In this paper, we present a new combinatorial approach, called Random Gradient Descent Tree (or RGD-tree), to explicitly deal with outliers; this results in a new algorithm called RGD-SVM. Our technique yields provably good solution and can be efficiently implemented for practical purpose. The time and space complexities of our approach only linearly depend on the input size and the dimensionality of the space, which are significantly better than existing ones. Experiments on benchmark datasets suggest that our technique considerably outperforms several popular techniques in most of the cases.

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AAAI Conference 2014 Conference Paper

Finding Median Point-Set Using Earth Mover’s Distance

Hu Ding
Jinhui Xu

In this paper, we study a prototype learning problem, called Median Point-Set, whose objective is to construct a prototype for a set of given point-sets so as to minimize the total Earth Mover’s Distances (EMD) between the prototype and the point-sets, where EMD between two point-sets is measured under affine transformation. For this problem, we present the first purely geometric approach. Comparing to existing graph-based approaches (e. g. , median graph, shock graph), our approach has several unique advantages: (1) No encoding and decoding procedures are needed to map between objects and graphs, and therefore avoid errors caused by information losing during the mappings; (2) Staying only in the geometric domain makes our approach computationally more efficient and robust to noise. We evaluate the performance of our technique for prototype reconstruction on a random dataset and a benchmark dataset, handwriting Chinese characters. Experiments suggest that our technique considerably outperforms the existing graph-based methods.

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NeurIPS Conference 2013 Conference Paper

k-Prototype Learning for 3D Rigid Structures

Hu Ding
Ronald Berezney
Jinhui Xu

In this paper, we study the following new variant of prototype learning, called {\em $k$-prototype learning problem for 3D rigid structures}: Given a set of 3D rigid structures, find a set of $k$ rigid structures so that each of them is a prototype for a cluster of the given rigid structures and the total cost (or dissimilarity) is minimized. Prototype learning is a core problem in machine learning and has a wide range of applications in many areas. Existing results on this problem have mainly focused on the graph domain. In this paper, we present the first algorithm for learning multiple prototypes from 3D rigid structures. Our result is based on a number of new insights to rigid structures alignment, clustering, and prototype reconstruction, and is practically efficient with quality guarantee. We validate our approach using two type of data sets, random data and biological data of chromosome territories. Experiments suggest that our approach can effectively learn prototypes in both types of data.

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