arXiv subjects

Feiping Nie

Publications and source records attributed to Feiping Nie.

At least 19 recordsLinked to original sources

arXiv2026

Doubly Stochastic Adaptive Neighbors Clustering via the Marcus Mapping

Clustering is a fundamental task in machine learning and data science, and similarity graph-based clustering is an important approach within this domain. Doubly stochastic symmetric similarity graphs provide numerous benefits for clustering problems and downstream tasks, yet learning such graphs remains a significant challenge. Marcus theorem states that a strictly positive symmetric matrix can be transformed into a doubly stochastic symmetric matrix by diagonal matrices. However, in clustering, learning sparse matrices is crucial for computational efficiency. We extend Marcus theorem by proposing the Marcus mapping, which indicates that certain sparse matrices can also be transformed into doubly stochastic symmetric matrices via diagonal matrices. Additionally, we introduce rank constraints into the clustering problem and propose the Doubly Stochastic Adaptive Neighbors Clustering algorithm based on the Marcus Mapping (ANCMM). This ensures that the learned graph naturally divides into the desired number of clusters. We validate the effectiveness of our algorithm through extensive comparisons with state-of-the-art algorithms. Finally, we explore the relationship between the Marcus mapping and optimal transport. We prove that the Marcus mapping solves a specific type of optimal transport problem.

cs.LG↗

arXiv2026

Achieving More with Less: A Tensor-Optimization-Powered Ensemble Method

Ensemble learning is a method that leverages weak learners to produce a strong learner. However, obtaining a large number of base learners requires substantial time and computational resources. Therefore, it is meaningful to study how to achieve the performance typically obtained with many base learners using only a few. We argue that to achieve this, it is essential to enhance both classification performance and generalization ability during the ensemble process. To increase model accuracy, each weak base learner needs to be more efficiently integrated. It is observed that different base learners exhibit varying levels of accuracy in predicting different classes. To capitalize on this, we introduce confidence tensors $\tilde{\mathbfΘ}$, where $\tilde{\mathbfΘ}_{rst}$ signifies the degree of confidence that the $t$-th base classifier assigns the sample to class $r$ while it actually belongs to class $s$. To the best of our knowledge, this is the first time an evaluation of the performance of base classifiers across different classes has been proposed. The proposed confidence tensor compensates for the strengths and weaknesses of each base classifier in different classes, enabling the method to achieve superior results with a smaller number of base learners. To enhance generalization performance, we design a smooth and partially convex objective function that leverages the concept of margin, making the strong learner more discriminative. Furthermore, it is proved that in the gradient matrix of the loss function, the sum of each column's elements is zero, allowing us to solve a constrained optimization problem using gradient-based methods.

cs.LG↗

arXiv2026

Double-Bounded Nonlinear Optimal Transport for Size Constrained Min Cut Clusterin

Min cut is an important graph partitioning method. However, current solutions to the min cut problem suffer from slow speeds, difficulty in solving, and often converge to simple solutions. To address these issues, we relax the min cut problem into a double-bounded constraint and, for the first time, treat the min cut problem as a double-bounded nonlinear optimal transport problem. Additionally, we develop a method for solving double bounded nonlinear optimal transport based on the Frank-Wolfe method (abbreviated as DNF). We prove that for convex problems satisfying Lipschitz smoothness, the DNF method can achieve a convergence rate of $\mathcal{O}(\frac{1}{t})$. We apply DNF to size-constrained min-cut clustering and evaluate it on eight benchmark datasets. DNF achieves competitive clustering performance and matches or outperforms the compared baselines on several datasets and metrics.

cs.LG↗

arXiv2026

Nora: Normalized Orthogonal Row Alignment for Scalable Matrix Optimizer

Matrix-based optimizers have demonstrated immense potential in training Large Language Models (LLMs), however, designing an ideal optimizer remains a formidable challenge. A superior optimizer must satisfy three core desiderata: efficiency, achieving Muon-like preconditioning to accelerate optimization; stability, strictly adhering to the scale-invariance inherent in neural networks; and speed, minimizing computational overhead. While existing methods address these aspects to varying degrees, they often fail to unify them, either incurring prohibitive computational costs like Muon, or allowing radial jitters that compromise stability like RMNP. To bridge this gap, we propose Nora, an optimizer that rigorously satisfies all three requirements. Nora achieves training stability by explicitly stabilizing weight norms and angular velocities through row-wise momentum projection onto the orthogonal complement of the weights. Simultaneously, by leveraging the block-diagonal dominance of the Transformer Hessian, Nora effectively approximates structured preconditioning while maintaining an optimal computational complexity of $\mathcal{O}(mn)$. Furthermore, we prove that Nora is a scalable optimizer and establish its corresponding scaling theorems. With a streamlined implementation requiring only two lines of code, our preliminary experiments validate Nora as an efficient and highly promising optimizer for large-scale training.

cs.LG↗

arXiv2026

All-weather Multi-Modality Image Fusion: Unified Framework and 100k Benchmark

Multi-modality image fusion (MMIF) combines complementary information from different image modalities to provide a comprehensive and objective interpretation of scenes. However, existing fusion methods cannot resist different weather interferences in real-world scenes, limiting their practical applicability. To bridge this gap, we propose an end-to-end, unified all-weather MMIF model. Rather than focusing solely on pixel-level recovery, our method emphasizes maximizing the representation of key scene information through joint feature fusion and restoration. Specifically, we first decompose images into low-rank and sparse components, enabling effective feature separation for enhanced multi-modality perception. During feature recovery, we introduce a physically-aware clear feature prediction module, inferring variations in light transmission via illumination and reflectance. Clear features generated by the network are used to enhance salient information representation. We also construct a large-scale MMIF dataset with 100,000 image pairs comprehensively across rain, haze, and snow conditions, as well as covering various degradation levels and diverse scenes. Experimental results in both real-world and synthetic scenes demonstrate that the proposed method excels in image fusion and downstream tasks such as object detection, semantic segmentation, and depth estimation. The code is available at https://github.com/ixilai/AWFusion.

cs.CV↗

arXiv2026

TSJNet: A Multi-modality Target and Semantic Awareness Joint-driven Image Fusion Network

This study aims to address the problem of incomplete information in unimodal images for semantic segmentation and object detection tasks. Existing multimodal fusion methods suffer from limited capability in discriminative modeling of multi-scale semantic structures and salient target regions, which further restricts the effective fusion of task-related semantic details and target information across modalities. To tackle these challenges, this paper proposes a novel fusion network termed TSJNet, which leverages the semantic information output by high-level tasks in a joint manner to guide the fusion process. Specifically, we design a multi-dimensional feature extraction module with dual parallel branches to capture multi-scale and salient features. Meanwhile, a data-agnostic spatial attention module embedded in the decoder dynamically calibrates attention allocation across different data domains, significantly enhancing the model's generalization ability. To optimize both fusion and advanced visual tasks, we balance performance by combining fusion loss with semantic losses. Additionally, we have developed a multimodal unmanned aerial vehicle (UAV) dataset covering multiple scenarios (UMS). Extensive experiments demonstrate that TSJNet achieves outstanding performance on five public datasets (MSRS, M\textsuperscript{3}FD, RoadScene, LLVIP, and TNO) and our UMS dataset. The generated fusion results exhibit favorable visual effects, and compared to state-of-the-art methods, the mean average precision (mAP@0.5) and mean intersection over union (mIoU) for object detection and segmentation, respectively, improve by 7.97\% and 10.88\%.The code and the dataset has been publicly released at https://github.com/XylonXu01/TSJNet.

cs.CV↗

arXiv2026

Multi-class Support Vector Machine with Maximizing Minimum Margin

Support Vector Machine (SVM) stands out as a prominent machine learning technique widely applied in practical pattern recognition tasks. It achieves binary classification by maximizing the "margin", which represents the minimum distance between instances and the decision boundary. Although many efforts have been dedicated to expanding SVM for multi-class case through strategies such as one versus one and one versus the rest, satisfactory solutions remain to be developed. In this paper, we propose a novel method for multi-class SVM that incorporates pairwise class loss considerations and maximizes the minimum margin. Adhering to this concept, we embrace a new formulation that imparts heightened flexibility to multi-class SVM. Furthermore, the correlations between the proposed method and multiple forms of multi-class SVM are analyzed. The proposed regularizer, akin to the concept of "margin", can serve as a seamless enhancement over the softmax in deep learning, providing guidance for network parameter learning. Empirical evaluations demonstrate the effectiveness and superiority of our proposed method over existing multi-classification methods.

cs.LG↗

arXiv2025

FusAD: Time-Frequency Fusion with Adaptive Denoising for General Time Series Analysis

Time series analysis plays a vital role in fields such as finance, healthcare, industry, and meteorology, underpinning key tasks including classification, forecasting, and anomaly detection. Although deep learning models have achieved remarkable progress in these areas in recent years, constructing an efficient, multi-task compatible, and generalizable unified framework for time series analysis remains a significant challenge. Existing approaches are often tailored to single tasks or specific data types, making it difficult to simultaneously handle multi-task modeling and effectively integrate information across diverse time series types. Moreover, real-world data are often affected by noise, complex frequency components, and multi-scale dynamic patterns, which further complicate robust feature extraction and analysis. To ameliorate these challenges, we propose FusAD, a unified analysis framework designed for diverse time series tasks. FusAD features an adaptive time-frequency fusion mechanism, integrating both Fourier and Wavelet transforms to efficiently capture global-local and multi-scale dynamic features. With an adaptive denoising mechanism, FusAD automatically senses and filters various types of noise, highlighting crucial sequence variations and enabling robust feature extraction in complex environments. In addition, the framework integrates a general information fusion and decoding structure, combined with masked pre-training, to promote efficient learning and transfer of multi-granularity representations. Extensive experiments demonstrate that FusAD consistently outperforms state-of-the-art models on mainstream time series benchmarks for classification, forecasting, and anomaly detection tasks, while maintaining high efficiency and scalability. Code is available at https://github.com/zhangda1018/FusAD.

cs.LG↗

arXiv2025

UniDiff: A Unified Diffusion Framework for Multimodal Time Series Forecasting

As multimodal data proliferates across diverse real-world applications, leveraging heterogeneous information such as texts and timestamps for accurate time series forecasting (TSF) has become a critical challenge. While diffusion models demonstrate exceptional performance in generation tasks, their application to TSF remains largely confined to modeling single-modality numerical sequences, overlooking the abundant cross-modal signals inherent in complex heterogeneous data. To address this gap, we propose UniDiff, a unified diffusion framework for multimodal time series forecasting. To process the numerical sequence, our framework first tokenizes the time series into patches, preserving local temporal dynamics by mapping each patch to an embedding space via a lightweight MLP. At its core lies a unified and parallel fusion module, where a single cross-attention mechanism adaptively weighs and integrates structural information from timestamps and semantic context from texts in one step, enabling a flexible and efficient interplay between modalities. Furthermore, we introduce a novel classifier-free guidance mechanism designed for multi-source conditioning, allowing for decoupled control over the guidance strength of textual and temporal information during inference, which significantly enhances model robustness. Extensive experiments on real-world benchmark datasets across eight domains demonstrate that the proposed UniDiff model achieves state-of-the-art performance.

cs.LG↗

arXiv2025

FAIM: Frequency-Aware Interactive Mamba for Time Series Classification

Time series classification (TSC) is crucial in numerous real-world applications, such as environmental monitoring, medical diagnosis, and posture recognition. TSC tasks require models to effectively capture discriminative information for accurate class identification. Although deep learning architectures excel at capturing temporal dependencies, they often suffer from high computational cost, sensitivity to noise perturbations, and susceptibility to overfitting on small-scale datasets. To address these challenges, we propose FAIM, a lightweight Frequency-Aware Interactive Mamba model. Specifically, we introduce an Adaptive Filtering Block (AFB) that leverages Fourier Transform to extract frequency-domain features from time series data. The AFB incorporates learnable adaptive thresholds to dynamically suppress noise and employs element-wise coupling of global and local semantic adaptive filtering, enabling in-depth modeling of the synergy among different frequency components. Furthermore, we design an Interactive Mamba Block (IMB) to facilitate efficient multi-granularity information interaction, balancing the extraction of fine-grained discriminative features and comprehensive global contextual information, thereby endowing FAIM with powerful and expressive representations for TSC tasks. Additionally, we incorporate a self-supervised pre-training mechanism to enhance FAIM's understanding of complex temporal patterns and improve its robustness across various domains and high-noise scenarios. Extensive experiments on multiple benchmarks demonstrate that FAIM consistently outperforms existing state-of-the-art (SOTA) methods, achieving a superior trade-off between accuracy and efficiency and exhibits outstanding performance.

cs.LG↗

arXiv2025

Dynamic Programming Techniques for Enhancing Cognitive Representation in Knowledge Tracing

Knowledge Tracing (KT) involves monitoring the changes in a student's knowledge over time by analyzing their past responses, with the goal of predicting future performance. However, most existing methods primarily focus on feature enhancement, while overlooking the deficiencies in cognitive representation and the ability to express cognition-issues often caused by interference from non-cognitive factors such as slipping and guessing. This limitation hampers the ability to capture the continuity and coherence of the student's cognitive process. As a result, many methods may introduce more prediction bias and modeling costs due to their inability to maintain cognitive continuity and coherence. Based on the above discussion, we propose the Cognitive Representation Dynamic Programming based Knowledge Tracing (CRDP-KT) model. This model em ploys a dynamic programming algorithm to optimize cognitive representations based on the difficulty of the questions and the performance intervals between them. This approach ensures that the cognitive representation aligns with the student's cognitive patterns, maintaining overall continuity and coherence. As a result, it provides more accurate and systematic input features for subsequent model training, thereby minimizing distortion in the simulation of cognitive states. Additionally, the CRDP-KT model performs partitioned optimization of cognitive representations to enhance the reliability of the optimization process. Furthermore, it improves its ability to express the student's cognition through a weighted fusion of optimized record representations and re lationships learned from a bipartite graph. Finally, experiments conducted on three public datasets validate the effectiveness of the proposed CRDP-KT model.

cs.AI↗

arXiv2025

Towards Federated Clustering: A Client-wise Private Graph Aggregation Framework

Federated clustering addresses the critical challenge of extracting patterns from decentralized, unlabeled data. However, it is hampered by the flaw that current approaches are forced to accept a compromise between performance and privacy: \textit{transmitting embedding representations risks sensitive data leakage, while sharing only abstract cluster prototypes leads to diminished model accuracy}. To resolve this dilemma, we propose Structural Privacy-Preserving Federated Graph Clustering (SPP-FGC), a novel algorithm that innovatively leverages local structural graphs as the primary medium for privacy-preserving knowledge sharing, thus moving beyond the limitations of conventional techniques. Our framework operates on a clear client-server logic; on the client-side, each participant constructs a private structural graph that captures intrinsic data relationships, which the server then securely aggregates and aligns to form a comprehensive global graph from which a unified clustering structure is derived. The framework offers two distinct modes to suit different needs. SPP-FGC is designed as an efficient one-shot method that completes its task in a single communication round, ideal for rapid analysis. For more complex, unstructured data like images, SPP-FGC+ employs an iterative process where clients and the server collaboratively refine feature representations to achieve superior downstream performance. Extensive experiments demonstrate that our framework achieves state-of-the-art performance, improving clustering accuracy by up to 10\% (NMI) over federated baselines while maintaining provable privacy guarantees.

cs.LG↗

arXiv2025

Dynamic Manipulation of Deformable Objects in 3D: Simulation, Benchmark and Learning Strategy

Goal-conditioned dynamic manipulation is inherently challenging due to complex system dynamics and stringent task constraints, particularly in deformable object scenarios characterized by high degrees of freedom and underactuation. Prior methods often simplify the problem to low-speed or 2D settings, limiting their applicability to real-world 3D tasks. In this work, we explore 3D goal-conditioned rope manipulation as a representative challenge. To mitigate data scarcity, we introduce a novel simulation framework and benchmark grounded in reduced-order dynamics, which enables compact state representation and facilitates efficient policy learning. Building on this, we propose Dynamics Informed Diffusion Policy (DIDP), a framework that integrates imitation pretraining with physics-informed test-time adaptation. First, we design a diffusion policy that learns inverse dynamics within the reduced-order space, enabling imitation learning to move beyond naïve data fitting and capture the underlying physical structure. Second, we propose a physics-informed test-time adaptation scheme that imposes kinematic boundary conditions and structured dynamics priors on the diffusion process, ensuring consistency and reliability in manipulation execution. Extensive experiments validate the proposed approach, demonstrating strong performance in terms of accuracy and robustness in the learned policy.

cs.RO↗

arXiv2025

Riemannian Optimization on Relaxed Indicator Matrix Manifold

The indicator matrix plays an important role in machine learning, but optimizing it is an NP-hard problem. We propose a new relaxation of the indicator matrix and prove that this relaxation forms a manifold, which we call the Relaxed Indicator Matrix Manifold (RIM manifold). Based on Riemannian geometry, we develop a Riemannian toolbox for optimization on the RIM manifold. Specifically, we provide several methods of Retraction, including a fast Retraction method to obtain geodesics. We point out that the RIM manifold is a generalization of the double stochastic manifold, and it is much faster than existing methods on the double stochastic manifold, which has a complexity of $ \mathcal{O}(n^3) $, while RIM manifold optimization is $ \mathcal{O}(n) $ and often yields better results. We conducted extensive experiments, including image denoising, with millions of variables to support our conclusion, and applied the RIM manifold to Ratio Cut, we provide a rigorous convergence proof and achieve clustering results that outperform the state-of-the-art methods. Our Code in \href{https://github.com/Yuan-Jinghui/Riemannian-Optimization-on-Relaxed-Indicator-Matrix-Manifold}{here}.

cs.LG↗

arXiv2024

A Greedy Strategy for Graph Cut

We propose a Greedy strategy to solve the problem of Graph Cut, called GGC. It starts from the state where each data sample is regarded as a cluster and dynamically merges the two clusters which reduces the value of the global objective function the most until the required number of clusters is obtained, and the monotonicity of the sequence of objective function values is proved. To reduce the computational complexity of GGC, only mergers between clusters and their neighbors are considered. Therefore, GGC has a nearly linear computational complexity with respect to the number of samples. Also, unlike other algorithms, due to the greedy strategy, the solution of the proposed algorithm is unique. In other words, its performance is not affected by randomness. We apply the proposed method to solve the problem of normalized cut which is a widely concerned graph cut problem. Extensive experiments show that better solutions can often be achieved compared to the traditional two-stage optimization algorithm (eigendecomposition + k-means), on the normalized cut problem. In addition, the performance of GGC also has advantages compared to several state-of-the-art clustering algorithms.

cs.LG↗

arXiv2024

Clustering Based on Density Propagation and Subcluster Merging

We propose the DPSM method, a density-based node clustering approach that automatically determines the number of clusters and can be applied in both data space and graph space. Unlike traditional density-based clustering methods, which necessitate calculating the distance between any two nodes, our proposed technique determines density through a propagation process, thereby making it suitable for a graph space. In DPSM, nodes are partitioned into small clusters based on propagated density. The partitioning technique has been proved to be sound and complete. We then extend the concept of spectral clustering from individual nodes to these small clusters, while introducing the CluCut measure to guide cluster merging. This measure is modified in various ways to account for cluster properties, thus provides guidance on when to terminate the merging process. Various experiments have validated the effectiveness of DOSM and the accuracy of these conclusions.

cs.LG↗

arXiv2024

Fast Semi-supervised Learning on Large Graphs: An Improved Green-function Method

In the graph-based semi-supervised learning, the Green-function method is a classical method that works by computing the Green's function in the graph space. However, when applied to large graphs, especially those sparse ones, this method performs unstably and unsatisfactorily. We make a detailed analysis on it and propose a novel method from the perspective of optimization. On fully connected graphs, the method is equivalent to the Green-function method and can be seen as another interpretation with physical meanings, while on non-fully connected graphs, it helps to explain why the Green-function method causes a mess on large sparse graphs. To solve this dilemma, we propose a workable approach to improve our proposed method. Unlike the original method, our improved method can also apply two accelerating techniques, Gaussian Elimination, and Anchored Graphs to become more efficient on large graphs. Finally, the extensive experiments prove our conclusions and the efficiency, accuracy, and stability of our improved Green's function method.

cs.LG↗

arXiv2024

A Margin-Maximizing Fine-Grained Ensemble Method

Ensemble learning has achieved remarkable success in machine learning, but its reliance on numerous base learners limits its application in resource-constrained environments. This paper introduces an innovative "Margin-Maximizing Fine-Grained Ensemble Method" that achieves performance surpassing large-scale ensembles by meticulously optimizing a small number of learners and enhancing generalization capability. We propose a novel learnable confidence matrix, quantifying each classifier's confidence for each category, precisely capturing category-specific advantages of individual learners. Furthermore, we design a margin-based loss function, constructing a smooth and partially convex objective using the logsumexp technique. This approach improves optimization, eases convergence, and enables adaptive confidence allocation. Finally, we prove that the loss function is Lipschitz continuous, based on which we develop an efficient gradient optimization algorithm that simultaneously maximizes margins and dynamically adjusts learner weights. Extensive experiments demonstrate that our method outperforms traditional random forests using only one-tenth of the base learners and other state-of-the-art ensemble methods.

cs.LG↗