Federated learning (FL) has become a mainstream decentralized learning paradigm due to its privacy-preserving features. However, the heterogeneity of data in FL can reduce predictive accuracy and complicate the analysis of the generalization properties of FL methods. In this article, we propose efficient federated kernel learning (FedK) algorithms and study their generalization properties. We first devise FedK with random features (FedK-RF), which acquires global information through sharing RF of local data subsets, enhancing predictive capability while protecting privacy. We then propose federated Nyström approximation with RF (FedNK-RF) that reduces errors resulted from RF. Furthermore, using integral operator theory, we derive the excess risk bounds with minimax optimal rates, which illustrate the impacts from data heterogeneity and shared information. Finally, we conduct several experiments that demonstrate the superiority of the proposed FedNK-RF.

Video-text retrieval aims at returning the most semantically relevant videos given a textual query, which is a thriving topic in both computer vision and natural language processing communities. This article focuses on a more challenging task, i.e., Unsupervised Domain Adaptation Video-text Retrieval (UDAVR), wherein training and testing data come from different distributions. Previous approaches are mostly derived from classification-based domain adaptation methods, which are neither multi-modal nor suitable for retrieval tasks. They merely alleviate the domain shift while overlooking the pairwise misalignment issue in the target domain, i.e., there exist no semantic relationships between target videos and texts. While Foundation Models like CLIP perform well in in-domain video-text retrieval, their effectiveness significantly drops during domain shifts due to this lack of alignment. To tackle this, we propose a novel method named D ual A lignment D omain A daptation ( DADA ++). Specifically, we first introduce cross-modal semantic embedding to generate discriminative source features in a joint embedding space. Besides, we utilize cross-modal domain adaptations to balance the minimization of domain shift in a smooth manner. Furthermore, we empirically identify the pairwise misalignment in the target domain, and thus propose the i ntegrated D ual A lignment C onsistency (iDAC). The proposed iDAC adaptively aligns the video-text pairs, which are more likely to be relevant in the target domain, by verifying their cross-modal semantic proximity reciprocally in both hard and soft manners. This enables positive pairs to increase progressively while potentially aligning noisy pairs throughout the training procedure. We also provide insights into the functionality of DADA ++ through the lens of Foundation Models, explaining its superiority in a theoretical way. Compared with state-of-the-art methods, DADA ++ achieves 9.4% and 8.5% relative improvements on R@1 under the settings of TGIF \(\rightarrow\) MSR-VTT and TGIF \(\rightarrow\) MSVD, respectively, demonstrating its superior performance.

Multi-sensor fusion models play a crucial role in autonomous driving perception, particularly in tasks like 3D object detection and HD map construction. These models provide essential and comprehensive static environmental information for autonomous driving systems. While camera-LiDAR fusion methods have shown promising results by integrating data from both modalities, they often depend on complete sensor inputs. This reliance can lead to low robustness and potential failures when sensors are corrupted or missing, raising significant safety concerns. To tackle this challenge, we introduce the Multi-Sensor Corruption Benchmark (MSC-Bench), the first comprehensive benchmark aimed at evaluating the robustness of multi-sensor autonomous driving perception models against various sensor corruptions. Our benchmark includes 16 combinations of corruption types that disrupt both camera and LiDAR inputs, either individually or concurrently. Extensive evaluations of six 3D object detection models and four HD map construction models reveal substantial performance degradation under adverse weather conditions and sensor failures, underscoring critical safety issues. The benchmark toolkit and affiliated code and model checkpoints have been made publicly accessible. Project website: MSC-Bench.

Robust high-definition (HD) map construction is vital for autonomous driving, yet existing methods often struggle with incomplete multi-view camera data. This paper presents SafeMap, a novel framework specifically designed to ensure accuracy even when certain camera views are missing. SafeMap integrates two key components: the Gaussian-based Perspective View Reconstruction (G-PVR) module and the Distillation-based Bird’s-Eye-View (BEV) Correction (D-BEVC) module. G-PVR leverages prior knowledge of view importance to dynamically prioritize the most informative regions based on the relationships among available camera views. Furthermore, D-BEVC utilizes panoramic BEV features to correct the BEV representations derived from incomplete observations. Together, these components facilitate comprehensive data reconstruction and robust HD map generation. SafeMap is easy to implement and integrates seamlessly into existing systems, offering a plug-and-play solution for enhanced robustness. Experimental results demonstrate that SafeMap significantly outperforms previous methods in both complete and incomplete scenarios, highlighting its superior performance and resilience.

Large Language Models (LLMs) excel in mathematical reasoning due to their extensive parameters and training data, but their high computational demands hinder deployment. Distilling LLM reasoning into Smaller Language Models (SLMs, ≤ 1B parameters) is a potential solution, yet these models often struggle with calculation and semantic errors. Previous work introduced Program-of-Thought Distillation (PoTD) to reduce calculation mistakes. To tackle semantic errors, we propose Key-Point-Driven Mathematical Reasoning Distillation (KPDD), which improves SLM reasoning by splitting the problem-solving process into Key Points Extraction and Step-by-Step Solution. KPDD includes KPDD-CoT, generating Chain-of-Thought rationales, and KPDD-PoT, producing Program-of-Thought rationales. Experiments show KPDD-CoT enhances reasoning capabilities, while KPDD-PoT achieves state-of-the-art performance in mathematical tasks, effectively reducing misunderstanding errors and promoting the deployment of efficient, capable SLMs.

Large Language Models (LLMs) demonstrate exceptional reasoning capabilities, often achieving state-of-the-art performance in various tasks. However, their substantial computational and memory demands, due to billions of parameters, hinder deployment in resource-constrained environments. A promising solution is knowledge distillation, where LLMs transfer reasoning capabilities to Small Language Models (SLMs, ≤ 1B parameters), enabling wider deployment on low-resource devices. Existing methods primarily focus on generating high-quality reasoning rationales for distillation datasets but often neglect the critical role of data quantity and quality. To address these challenges, we propose a Feedback-Driven Distillation (FDD) framework to enhance SLMs’ mathematical reasoning capabilities. In the initialization stage, a distillation dataset is constructed by prompting LLMs to pair mathematical problems with corresponding reasoning rationales. We classify problems into easy and hard categories based on SLM performance. For easy problems, LLMs generate more complex variations, while for hard problems, new questions of similar complexity are synthesized. In addition, we propose a multi-round distillation paradigm to iteratively enrich the distillation datasets, thereby progressively improving the mathematical reasoning abilities of SLMs. Experimental results demonstrate that our method can make SLMs achieve SOTA mathematical reasoning performance.

High-definition (HD) map construction methods are crucial for providing precise and comprehensive static environmental information, which is essential for autonomous driving systems. While Camera-LiDAR fusion techniques have shown promising results by integrating data from both modalities, existing approaches primarily focus on improving model accuracy, often neglecting the robustness of perception models—a critical aspect for real-world applications. In this paper, we explore strategies to enhance the robustness of multi-modal fusion methods for HD map construction while maintaining high accuracy. We propose three key components: data augmentation, a novel multi-modal fusion module, and a modality dropout training strategy. These components are evaluated on a challenging dataset containing 13 types of multi-sensor corruption. Experimental results demonstrate that our proposed modules significantly enhance the robustness of baseline methods. Furthermore, our approach achieves state-of-the-art performance on the clean validation set of the NuScenes dataset. Our findings provide valuable insights for developing more robust and reliable HD map construction models, advancing their applicability in real-world autonomous driving scenarios. Project website: https://robomap-123.github.io/.

Large-scale pre-trained models have revolutionized Natural Language Processing (NLP) and Computer Vision (CV), showcasing remarkable cross-domain generalization abilities. However, in graph learning, models are typically trained on individual graph datasets, limiting their capacity to transfer knowledge across different graphs and tasks. This approach also heavily relies on large volumes of annotated data, which presents a significant challenge in resource-constrained settings. Unlike NLP and CV, graph-structured data presents unique challenges due to its inherent heterogeneity, including domain-specific feature spaces and structural diversity across various applications. To address these challenges, we propose a novel structure-aware self-supervised learning method for Text-Attributed Graphs (SSTAG). By leveraging text as a unified representation medium for graph learning, SSTAG bridges the gap between the semantic reasoning of Large Language Models (LLMs) and the structural modeling capabilities of Graph Neural Networks (GNNs). Our approach introduces a dual knowledge distillation framework that co-distills both LLMs and GNNs into structure-aware multilayer perceptrons (MLPs), enhancing the scalability of large-scale TAGs. Additionally, we introduce an in-memory mechanism that stores typical graph representations, aligning them with memory anchors in an in-memory repository to integrate invariant knowledge, thereby improving the model’s generalization ability. Extensive experiments demonstrate that SSTAG outperforms state-of-the-art models on cross-domain transfer learning tasks, achieves exceptional scalability, and reduces inference costs while maintaining competitive performance.

Accurate extraction of molecular representations is a critical step in the drug discovery process. In recent years, significant progress has been made in molecular representation learning methods, among which multi-modal molecular representation methods based on images, and 2D/3D topologies have become increasingly mainstream. However, existing these multi-modal approaches often directly fuse information from different modalities, overlooking the potential of intermodal interactions and failing to adequately capture the complex higher-order relationships and invariant features between molecules. To overcome these challenges, we propose a structure-awareness-based multi-modal self-supervised molecular representation pre-training framework (MMSA) designed to enhance molecular graph representations by leveraging invariant knowledge between molecules. The framework consists of two main modules: the multi-modal molecular representation learning module and the structure-awareness module. The multi-modal molecular representation learning module collaboratively processes information from different modalities of the same molecule to overcome intermodal differences and generate a unified molecular embedding. Subsequently, the structure-awareness module enhances the molecular representation by constructing a hypergraph structure to model higher-order correlations between molecules. This module also introduces a memory mechanism for storing typical molecular representations, aligning them with memory anchors in the memory bank to integrate invariant knowledge, thereby improving the model's generalization ability. Compared to existing multi-modal approaches, MMSA can be seamlessly integrated with any graph-based method and supports multiple molecular data modalities, ensuring both versatility and compatibility. Extensive experiments have demonstrated the effectiveness of MMSA, which achieves state-of-the-art performance on the MoleculeNet benchmark, with average ROC-AUC improvements ranging from 1.8% to 9.6% over baseline methods.

Graph Contrastive Learning (GCL) has emerged as the foremost approach for self-supervised learning on graph-structured data. GCL reduces reliance on labeled data by learning robust representations from various augmented views. However, existing GCL methods typically depend on consistent stochastic augmentations, which overlook their impact on the intrinsic structure of the spectral domain, thereby limiting the model's ability to generalize effectively. To address these limitations, we propose a novel paradigm called AS-GCL that incorporates asymmetric spectral augmentation for graph contrastive learning. A typical GCL framework consists of three key components: graph data augmentation, view encoding, and contrastive loss. Our method introduces significant enhancements to each of these components. Specifically, for data augmentation, we apply spectral-based augmentation to minimize spectral variations, strengthen structural invariance, and reduce noise. With respect to encoding, we employ parameter-sharing encoders with distinct diffusion operators to generate diverse, noise-resistant graph views. For contrastive loss, we introduce an upper-bound loss function that promotes generalization by maintaining a balanced distribution of intra- and inter-class distance. To our knowledge, we are the first to encode augmentation views of the spectral domain using asymmetric encoders. Extensive experiments on eight benchmark datasets across various node-level tasks demonstrate the advantages of the proposed method.

Graph Comparative Learning (GCL) is a self-supervised method that combines the advantages of Graph Convolutional Networks (GCNs) and comparative learning, making it promising for learning node representations. However, the GCN encoders used in these methods rely on the Fourier transform to learn fixed graph representations, which is inherently limited by the uncertainty principle involving spatial and spectral localization trade-offs. To overcome the inflexibility of existing methods and the computationally expensive eigen-decomposition and dense matrix multiplication, this paper proposes an Adaptive Spectral Wavelet Transform-based Self-Supervised Graph Neural Network (ASWT-SGNN). The proposed method employs spectral adaptive polynomials to approximate the filter function and optimize the wavelet using contrast loss. This design enables the creation of local filters in both spectral and spatial domains, allowing flexible aggregation of neighborhood information at various scales and facilitating controlled transformation between local and global information. Compared to existing methods, the proposed approach reduces computational complexity and addresses the limitation of graph convolutional neural networks, which are constrained by graph size and lack flexible control over the neighborhood aspect. Extensive experiments on eight benchmark datasets demonstrate that ASWT-SGNN accurately approximates the filter function in high-density spectral regions, avoiding costly eigen-decomposition. Furthermore, ASWT-SGNN achieves comparable performance to state-of-the-art models in node classification tasks.

Continual graph learning (CGL) is an important and challenging task that aims to extend static GNNs to dynamic task flow scenarios. As one of the mainstream CGL methods, the experience replay (ER) method receives widespread attention due to its superior performance. However, existing ER methods focus on identifying samples by feature significance or topological relevance, which limits their utilization of comprehensive graph data. In addition, the topology-based ER methods only consider local topological information and add neighboring nodes to the buffer, which ignores the global topological information and increases memory overhead. To bridge these gaps, we propose a novel method called Feature-Topology Fusion-based Experience Replay (FTF-ER) to effectively mitigate the catastrophic forgetting issue with enhanced efficiency. Specifically, from an overall perspective to maximize the utilization of the entire graph data, we propose a highly complementary approach including both feature and global topological information, which can significantly improve the effectiveness of the sampled nodes. Moreover, to further utilize global topological information, we propose Hodge Potential Score (HPS) as a novel module to calculate the topological importance of nodes. HPS derives a global node ranking via Hodge decomposition on graphs, providing more accurate global topological information compared to neighbor sampling. By excluding neighbor sampling, HPS significantly reduces buffer storage costs for acquiring topological information and simultaneously decreases training time. Compared with state-of-the-art methods, FTF-ER achieves a significant improvement of 3.6% in AA and 7.1% in AF on the OGB-Arxiv dataset, demonstrating its superior performance in the class-incremental learning setting.

Kernel$k$-means is a fundamental unsupervised learning in data mining. Its computational requirements are typically at least quadratic in the number of data, which are prohibitive for large-scale scenarios. To address these issues, we propose a novel randomized sketching approach SKK based on the circulant matrix. SKK projects the kernel matrix left and right according to the proposed sketch matrices to obtain a smaller one and accelerates the matrix-matrix product by the fast Fourier transform based on the circulant matrix, which can greatly reduce the computational requirements of the approximate kernel$k$-means estimator with the same generalization bound as the exact kernel$k$-means in the statistical setting. In particular, theoretical analysis shows that taking the sketch dimension of$\sqrt{n}$is sufficient for SKK to achieve the optimal excess risk bound with only a fraction of computations, where$n$is the number of data. The extensive experiments verify our theoretical analysis, and SKK achieves the state-of-the-art performances on 12 real-world datasets. To the best of our knowledge, in randomized sketching, this is the first time that unsupervised learning makes such a significant breakthrough.

We investigate the statistical and computational requirements for distributed kernel ridge regression with randomized sketching (DKRR-RS) and successfully achieve the optimal learning rates with only a fraction of computations. More precisely, the proposed DKRR-RS combines sparse randomized sketching, divide-and-conquer and KRR to scale up kernel methods and successfully derives the same learning rate as the exact KRR with greatly reducing computational costs in expectation, at the basic setting, which outperforms previous state of the art solutions. Then, for the sake of the gap between theory and experiments, we derive the optimal learning rate in probability for DKRR-RS to reflect its generalization performance. Finally, to further improve the learning performance, we construct an efficient communication strategy for DKRR-RS and demonstrate the power of communications via theoretical assessment. An extensive experiment validates the effectiveness of DKRR-RS and the communication strategy on real datasets.

Kernel $k$-means is arguably one of the most common approaches to clustering. In this paper, we investigate the efficiency of kernel $k$-means combined with randomized sketches in terms of both statistical analysis and computational requirements. More precisely, we propose a unified randomized sketches framework to kernel $k$-means and investigate its excess risk bounds, obtaining the state-of-the-art risk bound with only a fraction of computations. Indeed, we prove that it suffices to choose the sketch dimension $\Omega(\sqrt{n})$ to obtain the same accuracy of exact kernel $k$-means with greatly reducing the computational costs, for sub-Gaussian sketches, the randomized orthogonal system (ROS) sketches, and Nystr\"{o}m kernel $k$-means, where $n$ is the number of samples. To the best of our knowledge, this is the first result of this kind for unsupervised learning. Finally, the numerical experiments on simulated data and real-world datasets validate our theoretical analysis.

Triangles are the basic substructure of networks and triangle counting (TC) has been a fundamental graph computing problem in numerous fields such as social network analysis. Nevertheless, like other graph computing problems, due to the high memory-computation ratio and random memory access pattern, TC involves a large amount of data transfers thus suffers from the bandwidth bottleneck in the traditional Von-Neumann architecture. To overcome this challenge, in this paper, we propose to accelerate TC with the emerging processing-in-memory (PIM) architecture through an algorithm-architecture co-optimization manner. To enable the efficient in-memory implementations, we come up to reformulate TC with bitwise logic operations (such as AND), and develop customized graph compression and mapping techniques for efficient data flow management. With the emerging computational Spin-Transfer Torque Magnetic RAM (STT-MRAM) array, which is one of the most promising PIM enabling techniques, the device-to-architecture co-simulation results demonstrate that the proposed TC in-memory accelerator outperforms the state-of-the-art GPU and FPGA accelerations by 12.2x and 31.8x, respectively, and achieves a 34x energy efficiency improvement over the FPGA accelerator.

We study the statistical performance for distributed kernel ridge regression with Nyström (DKRR-NY) and with Nyström and iterative solvers (DKRR-NY-PCG) and successfully derive the optimal learning rates, which can improve the ranges of the number of local processors $p$ to the optimal in existing state-of-art bounds. More precisely, our theoretical analysis show that DKRR-NY and DKRR-NY-PCG achieve the same learning rates as the exact KRR requiring essentially $\mathcal{O}(|D|^{1.5})$ time and $\mathcal{O}(|D|)$ memory with relaxing the restriction on $p$ in expectation, where $|D|$ is the number of data, which exhibits the average effectiveness of multiple trials. Furthermore, for showing the generalization performance in a single trial, we deduce the learning rates for DKRR-NY and DKRR-NY-PCG in probability. Finally, we propose a novel algorithm DKRR-NY-CM based on DKRR-NY, which employs a communication strategy to further improve the learning performance, whose effectiveness of communications is validated in theoretical and experimental analysis.

Kernel Regularized Least Squares (KRLS) is a fundamental learner in machine learning. However, due to the high time and space requirements, it has no capability to large scale scenarios. Therefore, we propose DC-NY, a novel algorithm that combines divide-and-conquer method, Nyström, conjugate gradient, and preconditioning to scale up KRLS, has the same accuracy of exact KRLS and the minimum time and space complexity compared to the state-of-the-art approximate KRLS estimates. We present a theoretical analysis of DC-NY, including a novel error decomposition with the optimal statistical accuracy guarantees. Extensive experimental results on several real-world large-scale datasets containing up to 1M data points show that DC-NY significantly outperforms the state-of-the-art approximate KRLS estimates.

Dimension reduction is a fundamental data mining task. However, it has limited applicability in high-dimensional scenarios because of stringent computational requirements. To address these issues, we propose ESE, an extremely sparse Johnson-Lindenstrauss transform, which takes a substantial step in dimension reduction. The projection matrix of ESE is an extremely sparse matrix, which has only k nonzero elements by employing the hash functions, where k is the embedded dimension. Theoretical analysis shows that ESE has a smaller time complexity than the existing projection algorithms and keeps the best accuracy (1+ε) for the general case, where 0 <; ε ≪ 1. In particular, the optimal statistical accuracy is achieved requiring log(n)log(d)/ε embedded dimension, where n is the number of data, d is the dimension of data. The extensive experiments verify that ESE has a significant advantage in time with satisfactory accuracy, compared to the state-of-the-art dimension reduction algorithms.

) , respectively, which are prohibitive for large-scale data sets, where n is the number of data. In this article, we propose a novel random sketch technique based on the circulant matrix that achieves savings in storage space and accelerates the solution of the KRR approximation. The circulant matrix has the following advantages: It can save time complexity by using the fast Fourier transform (FFT) to compute the product of matrix and vector, its space complexity is linear, and the circulant matrix, whose entries in the first column are independent of each other and obey the Gaussian distribution, is almost as effective as the i.i.d. Gaussian random matrix for approximating KRR. Combining the characteristics of the circulant matrix and our careful design, theoretical analysis and experimental results demonstrate that our proposed sketch method, making the estimate kernel methods scalable and practical for large-scale data problems, outperforms the state-of-the-art KRR estimates in time complexity while retaining similar accuracies. Meanwhile, our sketch method provides the theoretical bound that keeps the optimal convergence rate for approximating KRR.

In this paper, we investigate the generalization performance of multi-class classification, for which we obtain a shaper error bound by using the notion of local Rademacher complexity and additional unlabeled samples, substantially improving the state-of-the-art bounds in existing multi-class learning methods. The statistical learning motivates us to devise an efficient multi-class learning framework with the local Rademacher complexity and Laplacian regularization. Coinciding with the theoretical analysis, experimental results demonstrate that the stated approach achieves better performance.

Graph-based semi-supervised learning is one of the most popular and successful semi-supervised learning approaches. Unfortunately, it suffers from high time and space complexity, at least quadratic with the number of training samples. In this paper, we propose an efficient graph-based semi-supervised algorithm with a sound theoretical guarantee. The proposed method combines Nystrom subsampling and preconditioned conjugate gradient descent, substantially improving computational efficiency and reducing memory requirements. Extensive empirical results reveal that our method achieves the state-of-the-art performance in a short time even with limited computing resources.

In this paper, we study the generalization performance of multi-class classification and obtain a shaper data-dependent generalization error bound with fast convergence rate, substantially improving the state-of-art bounds in the existing data-dependent generalization analysis. The theoretical analysis motivates us to devise two effective multi-class kernel learning algorithms with statistical guarantees. Experimental results show that our proposed methods can significantly outperform the existing multi-class classification methods.

Communication technologies, involving fieldbus network, Wireless Sensor Network (WSN) and industrial Ethernet, are mainly applied to complex industrial applications like continuous casting field, in order to transmit information. However, there're still some shortcomings exposed and certain higher requirements such as compatibility, expansibility, and transmission distance and speed have been put forward. Accordingly, this paper proposed a design scheme of embedded multi-protocol gateway with wire and wireless communication methods integrated. A communication model of embedded multi-protocol gateway is established, taking example by the principle of protocol conversion and the architecture of heterogeneous network integration based on Open System Interconnection Reference Model (OSI/RM). In addition, the intercommunication of such a network combining WSN, CAN bus, 3G network, WLAN, and Ethernet is realized, taking data heterogeneous and command message conflicting into consideration. Moreover, the use of modular and hierarchical design method made it possible for subnet communication interface to expand to different monitoring equipment and data acquisition equipment. The proposed model provides solution of heterogeneous network integration and real-time data service of high speed and wide coverage for the MRO online monitoring system.

In the research area of community detection which aims at detecting some highly cohesive vertex subsets in social network, there mainly exist some problems, such as the algorithms with comparatively excellent quality of the final partitioning usually have high time complexity and some other fast algorithms often result in low quality of partitioning or other disadvantages. Nowadays, the increasing demands for community detection in large-scale social networks necessitate the use of distributed and scalable methods to detect communities in an effective and efficient manner. Label propagation algorithm (LPA), whose time complexity is O (m) on a network with m edges, is a near linear time algorithm to detect community effectively. Besides, owing to having good scalability, the parallel version of LPA (DLPA) is suitable for community detection in large-scale social networks. However, DLPA synchronously updates the vertices labels, which usually brings about label oscillations and results in low quality of partitioning. In this paper, we analyze the drawbacks of DLPA and propose a novel method C-DLPA, which combines DLPA with the notion of maximal cliques and at the same time utilizes a new updating mechanism that updating each node' label by probability of its adjacent nodes, to make final partitioning become more accurate and to avoid oscillations effectively. The experimental results show that C-DLPA has better performance is not only low time cost by as much to avoid oscillations but its community detection accuracy compared with DLPA.

Image segmentation in the big data context is a hot topic in the field of image understanding. Contrary to traditional computing paradigm with precise description of problems, Granular Computing (GrC) is studied by utilizing the toleration of imprecise, incomplete, uncertain and mass information to make systems manageable, robust, low-cost and harmonious. Thus it is an efficient measure to simplify calculation. In this paper, a multi-feature fusion approach based on quadtree and Grc was presented in accordance with the mechanism of human vision. In this technique, firstly original images are reduced into gray images, binary images and quadtree-segmented images, then features are extracted with different granularities from the reduced images respectively, and finally original images are partitioned precisely by the fusion of features according to quotient space theory (QST). Based on the technique of granularity hierarchical and synthesis, this paper gives the example and validation of color image segmentation. Experimental results demonstrate that the algorithm is valid for image segmentation with both speed and accuracy obviously approved compared with common segmentation methods.