This paper proposes CFMD-i, a communication-efficient clustered federated multi-domain learning framework for intrusion anomaly detection in heterogeneous Internet-of-Things (IoT) environments. In such settings, multi-source data are typically non-independent and identically distributed (Non-IID), highly imbalanced, and distributed across resource-constrained edge devices, which poses challenges to both model robustness and training efficiency. CFMD-i addresses these issues from both modeling and system perspectives. First, a federated multi-domain optimization objective is formulated to enhance cross-domain robustness through shared representation learning and adversarial domain weighting. Second, a dynamic hierarchical clustered mechanism is introduced to group clients according to model discrepancy, measured by cosine similarity, output divergence, and intra-cluster compactness, enabling a balance between global knowledge sharing and domain-aware personalization. Third, a communication-efficient optimization scheme is developed by integrating parameter-difference transmission, adaptive leapfrog communication, and quantized error-feedback updates, thereby reducing redundant communication under heterogeneous conditions. Experiments on five intrusion detection datasets demonstrate that CFMD-i consistently outperforms representative federated baselines, including Fedavg, Dis-DAGMM, DIOT, and ZeKoC. The proposed framework consistently improves F1 score across multiple attack domains while reducing communication volume by over 95%, and remains operational under packet loss rates of up to 12%, although performance degradation becomes evident under severe communication impairment.

Using image-level weakly supervised semantic segmentation (WSSS) techniques to segment tissue regions in giga-pixel histopathological whole slide images (WSI) has garnered widespread attention, as it can reduce many annotation workloads for pathologists. Most recent studies are based on class activation mapping (CAM) to generate pseudo masks, which are then used to train segmentation model in a fully supervised manner. However, it is still a challenge to accurately segment non-predominant tissue categories due to the existence of long-tailed and inter-class homogeneity matters. For these matters, we propose three designs to solve them: 1) Diffusion-based Data Generation to synthesis new images of tail class to expand data distribution; 2) Feature Recalibration to reassign the logits in CAM to narrow the feature-level prediction gap between predominant and non-predominant classes; 3) Grade-skip Learning to correct the under-fitting tendency of hard samples during the segmentation phase. Moreover, we also design a powerful pipeline LoHo for histopathology tissue segmentation. Extensive experiments demonstrate that our method not only achieves new state-of-the-art performances but also significantly improves segmentation of tail classes. In addition, our methods are plug-and-play, making it easily integrable into many mainstream WSSS frameworks.

Weakly supervised learning based on image-level labels can effectively reduce annotation costs, making it a popular choice for histopathological tissue segmentation. However, this pattern still face some challenges: 1) inaccurate class activation maps (CAM) make pseudo masks quality insufficient; 2) noisy pixels in pseudo masks will mislead the segmentation model's decision-making. To deal with these problems, we propose a novel weakly supervised semantic segmentation (WSSS) framework. First, we introduce Local Spatial Affine Perturbation to strengthen the model's utilization of weak supervision signals and improve its robustness to noisy regions within CAM. Second, we propose Wave-aware Dynamic Feature Aggregation to adaptively enhance the information-aware representation of target regions to obtain fine-grained pseudo masks enriched with positive semantic information. Third, we train a segmentation model with a noise-suppression scheme called Cross-scale Logits Distillation to reduce the inevitable false positive pixels in pseudo masks. We conduct extensive experiments to validate our method and set new state-of-the-art segmentation performances on five histopathological tissue segmentation datasets. Moreover, we will introduce a new dataset, GCSS-WSSS for gastric cancer, to promote the diversification for the research community of computational pathology. Code and data will be released at: https://github.com/director87/WaWeHis.

Cancer is a leading cause of death worldwide due to its aggressive nature and complex variability. Accurate prognosis is therefore challenging but essential for guiding personalized treatment and follow-up. Previous research often relied on single data sources, missing the opportunity to combine various types of patient information for more comprehensive survival predictions. To address these challenges, we propose a two-stage fusion method named Cross-Attention and Multimodal Low-Rank Interaction Fusion Framework (CA-MLIF). In the first stage, we propose a CA mechanism for real-time feature updates and cross-modal mutual learning to capture rich semantic information. In the second stage, we design a novel multimodal low-rank interaction fusion method for survival prediction. Specifically, we present modal attention mechanism (MAM) for feature filtration, low-rank multimodal fusion (LMF) for model complexity reduction, and optimal weight concatenation (OWC) for maximizing feature integration. Extensive experiments on two public datasets TCGA-GBMLGG and TCGA-KIRC, as well as a multi-center in-house lung adenocarcinoma (LUAD) dataset validate the effectiveness of CA-MLIF, which demonstrate that our method outperforms existing approaches in survival prediction under both pathology-gene fusion and CT-pathology fusion scenarios.

Image-level weakly supervised semantic segmentation (WSSS) reduces the dependence on high-quality data annotation, which plays a crucial role in computational pathology. Benefit from the ability to localize the objects with only binary labels, Class Activation Map (CAM) is a widely used method to initial pseudo masks. However, due to the low contrast among different tissues in histopathological images, most existing CAM-based methods perform poorly in gland segmentation. We retrospect this process and find that class consistency and semantic consistency can guide the network to effectively distinguish confusing pixels and generate fine-grained pseudo masks. Specifically, for class consistency, we propose Consistency Correlation Attention (CCA) to encourage the network to focus on the contribution of class features to semantic dependencies. For semantic consistency, we propose Multi-scale Pyramid Fusion Pooling (MPFP) to aggregate coarse-to-fine global semantic information from CAMs at multiple spatial resolutions, thus identifying class localization. Additionally, we introduce a Purified Labels Filtration (PLF) strategy during the segmentation phase to mitigate the noisy supervision signal and improve the segmentation quality of the model. Extensive experiments show that the our method achieves new state-of-the-art results on three publicly available gland datasets. Furthermore, our method demonstrates impressive domain adaptation capability, achieving satisfactory results with only a small portion of samples when faced with unseen domain data.

Deep learning models for medical image segmentation often encounter difficulties when there is a lack of annotated data. While current few-shot segmentation methods have reduced these challenges, they frequently fail to fully utilize the information in the limited samples available. Additionally, they typically depend on large quantities of unlabeled data with pseudo-labels for domain adaptation. In response to these issues, we propose RE-SAM2, a novel framework for fewshot medical image segmentation that combines reinforcement learning with ensemble learning. The central concept involves retaining the reward model from reinforcement learning after training and integrating it into the model through ensemble learning techniques. Unlike previous methods, RE-SAM2 does not require extra unlabeled data and achieves notable improvements in segmentation accuracy with limited supervision. Experiments conducted on benchmark datasets reveal that RE-SAM2 surpasses current leading approaches. The code is available at the link https://github.com/zzzzz37/RE-SAM2.

Detecting objects in foggy scenes remains a persistent challenge, as detectors trained for fair weather often struggle with foggy data due to blurring effects. Previous methods based on domain adaptation, multi-task learning, etc. try to tackle this challenge, but they often fail to achieve an optimal balance between model complexity and accuracy. Hence, we propose a multi-branch pooling information fusion (MPIF) module, which combines local and global information to enhance feature representation with minimal computational overhead. We also design a lightweight multi-scale dehazing network (LMDNet) and utilize the multi-task learning strategy to adaptively incorporate dehazing feature information into the object detection network. Leveraging these core modules with additional design optimizations, we construct a novel real-time object detection framework, called RDFNet, for foggy images. Extensive experiments demonstrate that RDFNet outperforms SOTA detection methods for foggy scenes while enjoying less complexity and faster detection speeds. The source code will be released at https://github.com/PolarisFTL/RDFNet.

To improve the overall survival rate of cancer patients, we propose an innovative approach named Multimodal Fusion Framework based on Low-rank Interaction (MF2LI), which aims to overcome the current limitations of relying solely on single-modal data prediction and the excessive complexity of fusion. By harnessing low-rank multimodal fusion (LMF) and optimal weight integration (OWI), MF2LI maximizes the integration of pathological images and genomic data. The model incorporates a parallel decomposition strategy, reducing complexity and facilitating fusion based on the contributions of each component. We validate our method using the GBMLGG and KIRC datasets from The Cancer Genome Atlas (TCGA). The C-index of the proposed model stands at $0.895 \pm 0.007$ and $0.728 \pm 0.030$ for the two datasets, respectively, outperforming existing methods. Furthermore, we generate visualizations of the risk ratios, which demonstrate a strong alignment with the actual grade classifications. Extensive experiments have shown that our model improves the prognosis prediction of tumor patients and has considerable clinical value.

Object detection methods using deep convolutional neural networks (CNNs) have derived major advances in normal images. However, such success is hardly achieved with adverse weather due to a lack of visibility . To tackle this problem, we propose a Multi-scale Adaptive Sampling Fusion Network, named MASFNet. In this paper, we design a Feature Adaptive Enhancement Network (FAENet) consisting of three modules to adaptively perform feature enhancement on feature maps in adverse scenarios. These modules in FAENet are integrated by the Laplace pyramid, which can perform receptive field fusion, attention perception, and affine transformation for image feature enhancement. To improve the detection performance, we propose a Multi-scale Sampling Fusion Pyramid Network (MSFNet), which is capable of fusing different scale features to improve the semantic information. Experimental results demonstrate that MASFNet achieves 73.68% and 30.95% mAP on the real scene fog dataset (RTTS) and foggy driving dataset (FDD) respectively. Additionally, on the real-world scenario low illumination dataset (ExDark), MASFNet attains a substantial mAP of 63.80%, surpassing current state-of-the-art object detectors while retaining lightweight and high-speed. The source code will be released at https://github.com/PolarisFTL/MASFNet.

Most existing super-resolution (SR) methods assume that the degradation is fixed (e.g., bicubic downsampling), whereas their performance would be degraded if the actual degradation differs from this assumption. To deal with unknown degradations, existing unknown SR methods are committed to learning degradation representation to generate high-resolution images. Nevertheless, they ignore that the impact of degradations on images is related to image content, or they learn degradation representations without any constraints. In this article, we propose a degradation maps extractor for unknown SR. Specifically, we learn degradation maps and condense them into a one-dimensional representation space to distinguish various degradations, which obtains distinguishable degradation maps and preserves the connection with the image contents. Furthermore, we propose a degradation map-guided SR (DMGSR) network, in which the degradation maps adaptively influence the SR process by applying channel attention and spatial attention to middle features. With the cooperation of the degradation maps extractor and the degradation maps-guided SR network, our network can flexibly handle various degradations. Experimental results show that our model achieves state-of-the-art performance in quantitative and qualitative metrics for the unknown SR task.

In partial label learning, each training sample corresponds to a set of candidate labels. The ground-truth label, hidden within this set, cannot be directly obtained during the training phase. The key to solving the partial label learning problem is to obtain ground-truth labels through label disambiguation. Existing works often rely on the label averaging assumption and do not fully investigate the class imbalance. Tail ground-truth labels are often overwhelmed by head pseudo-labels. The incorrectly identified labels could have contagiously negative impacts on the final predictions. In this paper, we propose a cost-guided retraining strategy, which achieves guidance and correction of disambiguation results, and provides instance-based class imbalance concerns for candidate labels. This approach significantly enhances the algorithm’s ability to handle class imbalance problems. The superiority of our method is demonstrated using 8 real-world datasets and 5 evaluation metrics. Code is available at https://github.com/DerrickZzyR/PL-CGR

Nuclei segmentation is a fundamental and critical step in digital pathological image analysis. Fully supervised nuclei segmentation requires a lot of pixel-by-pixel manual annotation by pathologists, which is very time-consuming and laborious. To minimize the labeling burden of pathologists, this paper uses only point annotations of nuclei data for weakly supervised learning. Specifically, a two-stage model named EOFD-Net with feature denoising and edge optimization is proposed. In the first stage, three weak labels (K-means cluster labels, Voronoi labels, and superpixel labels) with complementary information are used to train the encoder-decoder network to achieve coarse segmentation of nuclei. A feature denoising module(FDM) is designed in the encoder part, which can effectively reduce noise interference. In the second stage, we designed an edge optimization strategy using the prior knowledge of the trained model in the first stage. Confident learning is employed to denoise pseudo-label and rectify the mislabel. These optimized labels are input into the second stage to obtain the final segmentation results. The performance of our method outperforms current state-of-the-art methods on two publicly nuclei segmentation datasets, MoNuSeg and TNBC.

Accurate and automated gland segmentation on pathological images can assist pathologists in diagnosing the malignancy of colorectal adenocarcinoma. However, due to various gland shapes, severe deformation of malignant glands, and overlapping adhesions between glands. Gland segmentation has always been very challenging. To address these problems, we propose a DEA model. This model consists of two branches: the backbone encoding and decoding network and the local semantic extraction network. The backbone encoding and decoding network extracts advanced Semantic features, uses the proposed feature decoder to restore feature space information, and then enhances the boundary features of the gland through boundary enhancement attention. The local semantic extraction network uses the pre-trained DeepLabv3+ as a Local semantic-guided encoder to realize the extraction of edge features. Experimental results on two public datasets, GlaS and CRAG, confirm that the performance of our method is better than other gland segmentation methods.

Images captured under low-light conditions suffer from inevitable degradation leading to the missing global structure and detailed local texture. However, existing methods consider these two components as a single entity or perform a similar convolutional operation, which can yield suboptimal results. In this letter, we propose a dual-branch structure-texture awareness feature interaction network named DFINet to tackle the above problems. First, we generate structure and texture components through the Gaussian operator. Subsequently, we conduct CNN-based and Transformer-based branches to cope with the texture and structure components separately. Among them, we design a Feature Interaction Block that leverages local-global information to enrich features in the encoding phase. Then, we generate queries with the potential structural-texture cues for the Transformer blocks in the decoding phase. Finally, we develop a Fusion Block to progressively integrate cross-layer features from two branches for the reconstruction. Our extensive experiment indicates the proposed method outperforms several representative methods in terms of both visual quality and objective assessment.

Single traffic image deraining technology based on deep learning is a vital branch of image preprocessing, which is of great help to intelligent monitoring systems and driving navigation system. It is well understood that established deraining methods are derived based on one specific imaging model, neglecting the underlying correlations between different weather models and thereby limiting the applicability of these standard methods in real scenarios. To ameliorate this issue, in this work, we first explore the inherent relationship between a rain model and the haze one established up to date. We discover that these two models experience similar degradations in the low-frequency components (i.e., similarity) but diverse degradations in the high-frequency areas (i.e., diversity). Based on these observations, we develop a Similarity-Diversity model to describe these characteristics. Afterwards, we introduce a novel deep neural network to restore the rain-free background embedding the similarity-diversity model, namely deep similarity-diversity network (DSDNet). Extensive experiments have been conducted to evaluate our proposed method that outperforms the other state of the art deraining techniques. On the other hand, we deploy the proposed algorithm with Google Vision API for object recognition, which also obtains satisfactory results both qualitatively and quantitatively.

Abstract Lowlight images with low brightness and contrast, blurry details usually bring us an uncomfortable visual experience. To promote the quality of these deviation images, this paper presents a new and efficient approach, named MFMR, for enhancing lowlight images in the hue‐saturation‐value (HSV) colour space. Concretely, the multi‐angle filter is first applied to estimate the artifact‐free illumination and reflection component of the V‐channel. Afterward, the adaptive bi‐interval histogram with human visual characteristics and morphological operations is employed to process the former, adaptive gamma correction to process the latter for generating various feature maps. In the end, these feature maps are united via adaptive multi‐scale fusion strategy to reconstruct high‐quality images, which are characterized by high contrast and brightness, vivid colour, and clearer details. Extensive experiments show that this method is a well‐proven low‐light image enhancement approach, which outperforms the state‐of‐the‐art comparison methods. Furthermore, the proposed method also can yield satisfying images in the heavy foggy, yellow sand, underwater, and other severe conditions.

Due to their low storage capacity and fast retrieval speed, hashing techniques have received much attention in cross-modal retrieval. However, there are some issues that need to be further explored. First, some existing hashing methods use the labels to construct the semantic similarity matrix between pairwise data, ignoring the potential manifold structure between heterogeneous data. Second, some existing methods underestimate the importance of multi-label and the gaps between different class labels, making the learned hash codes less discriminative. Third, few of them embed both manifold and balanced structures within the same model, and the relaxation of discrete constraints will lead to an increasing quantization error. To mitigate these problems, this paper proposes a novel supervised hashing method, termed Label Guided Discrete Hashing (LGDH), which simultaneously preserves the comprehensive manifold structure and discriminative balanced codes that are both constructed by label information into Hamming space. We develop a local category distribution of the nearest neighbors, to excavate the underlying manifold structure of heterogeneous data. To maximize the gaps of different categories, a balanced matrix is constructed by labels to generate hash codes with balanced bits. For multi-label data, we also design a novel multi-label manifold and balanced structure matrix to adapt the real-world scenarios. An effective discrete optimization method is used to optimize our proposed objective function instead of the relaxation one. Extensive experiments on three benchmark datasets verify the effectiveness of LGDH. The comparison results demonstrat that LGDH achieves about 2% and 3% improved to different cross-modal tasks on average.

Unsupervised hashing has attracted much attention for binary representation learning due to the requirement of economical storage and efficiency of binary codes. It aims to encode high-dimensional features in the Hamming space with similarity preservation between instances. However, most existing methods learn hash functions in manifold-based approaches. Those methods capture the local geometric structures (i.e., pairwise relationships) of data, and lack satisfactory performance in dealing with real-world scenarios that produce similar features (e.g., color and shape) with different semantic information. To address this challenge, in this work, we propose an effective unsupervised method, namely, Jointly Personalized Sparse Hashing (JPSH), for binary representation learning. To be specific, first, we propose a novel personalized hashing module, i.e., Personalized Sparse Hashing (PSH). Different personalized subspaces are constructed to reflect category-specific attributes for different clusters, adaptively mapping instances within the same cluster to the same Hamming space. In addition, we deploy sparse constraints for different personalized subspaces to select important features. We also collect the strengths of the other clusters to build the PSH module with avoiding over-fitting. Then, to simultaneously preserve semantic and pairwise similarities in our proposed JPSH, we incorporate the proposed PSH and manifold-based hash learning into the seamless formulation. As such, JPSH not only distinguishes the instances from different clusters but also preserves local neighborhood structures within the cluster. Finally, an alternating optimization algorithm is adopted to iteratively capture analytical solutions of the JPSH model. We apply the proposed representation learning algorithm JPSH to the similarity search task. Extensive experiments on four benchmark datasets verify that the proposed JPSH outperforms several state-of-the-art unsupervised hashing algorithms.

Recently, deep convolutional neural networks (CNNs) have been successfully applied to the single-image super-resolution (SISR) task with great improvement in terms of both peak signal-to-noise ratio (PSNR) and structural similarity (SSIM). However, most of the existing CNN-based SR models require high computing power, which considerably limits their real-world applications. In addition, most CNN-based methods rarely explore the intermediate features that are helpful for final image recovery. To address these issues, in this article, we propose a dense lightweight network, called MADNet, for stronger multiscale feature expression and feature correlation learning. Specifically, a residual multiscale module with an attention mechanism (RMAM) is developed to enhance the informative multiscale feature representation ability. Furthermore, we present a dual residual-path block (DRPB) that utilizes the hierarchical features from original low-resolution images. To take advantage of the multilevel features, dense connections are employed among blocks. The comparative results demonstrate the superior performance of our MADNet model while employing considerably fewer multiadds and parameters.

Deep convolutional neural networks (CNNs) have contributed to the significant progress of the single-image super-resolution (SISR) field. However, the majority of existing CNN-based models maintain high performance with massive parameters and exceedingly deeper structures. Moreover, several algorithms essentially have underused the low-level features, thus causing relatively low performance. In this article, we address these problems by exploring two strategies based on novel local wider residual blocks (LWRBs) to effectively extract the image features for SISR. We propose a cascading residual network (CRN) that contains several locally sharing groups (LSGs), in which the cascading mechanism not only promotes the propagation of features and the gradient but also eases the model training. Besides, we present another enhanced residual network (ERN) for image resolution enhancement. ERN employs a dual global pathway structure that incorporates nonlocal operations to catch long-distance spatial features from the the original low-resolution (LR) input. To obtain the feature representation of the input at different scales, we further introduce a multiscale block (MSB) to directly detect low-level features from the LR image. The experimental results on four benchmark datasets have demonstrated that our models outperform most of the advanced methods while still retaining a reasonable number of parameters.

In this article, a simple yet effective method, called a two-phase learning-based swarm optimizer (TPLSO), is proposed for large-scale optimization. Inspired by the cooperative learning behavior in human society, mass learning and elite learning are involved in TPLSO. In the mass learning phase, TPLSO randomly selects three particles to form a study group and then adopts a competitive mechanism to update the members of the study group. Then, we sort all of the particles in the swarm and pick out the elite particles that have better fitness values. In the elite learning phase, the elite particles learn from each other to further search for more promising areas. The theoretical analysis of TPLSO exploration and exploitation abilities is performed and compared with several popular particle swarm optimizers. Comparative experiments on two widely used large-scale benchmark datasets demonstrate that the proposed TPLSO achieves better performance on diverse large-scale problems than several state-of-the-art algorithms.

Alzheimer's disease (AD) is one of the most common progressive neurodegenerative diseases. Structural magnetic resonance imaging (MRI) would provide abundant information on the anatomical structure of human organs. Fluorodeoxy‐glucose positron emission tomography (PET) obtains the metabolic activity of the brain. Previous studies have demonstrated that multi‐modality images could contribute to improve diagnosis of AD. However, these methods need to extract the handcrafted features that demand domain specific knowledge and image processing stage is time consuming. In order to tackle these problems, in this study, the authors propose a novel framework that ensembles three state‐of‐the‐art deep convolutional neural networks (DCNNs) with multi‐modality images for AD classification. In detail, they extract some slices from each subject of each modality, and every DCNN generates a probabilistic score for the input slices. Furthermore, a ‘dropout’ mechanism is introduced to discard low discrimination slices of the category probabilities. Then average reserved slices of each subject are acquired as a new feature. Finally, they train the Adaboost ensemble classifier based on single decision tree classifier with the MRI and PET probabilistic scores of each DCNN. Evaluations on Alzheimer's Disease Neuroimaging Initiative database show that the proposed algorithm has better performance compared to existing method, the algorithm proposed in this study significantly improved the classification accuracy.

Collaborative representation is an effective way to design classifiers for many practical applications. In this paper, we propose a novel classifier, called the prior knowledge-based probabilistic collaborative representation-based classifier (PKPCRC), for visual recognition. Compared with existing classifiers which use the collaborative representation strategy, the proposed PKPCRC further includes characteristics of training samples of each class as prior knowledge. Four types of prior knowledge are developed from the perspectives of image distance and representation capacity. They adaptively accommodate the contribution of each class and result in an accurate representation to classify a query sample. Experiments and comparisons on four challenging databases demonstrate that PKPCRC outperforms several state-of-the-art classifiers.

Ray-casting algorithm is an important volume rendering algorithm, which is widely used in medical image processing. Aiming to address the shortcomings of the current ray-casting algorithms in 3D reconstruction of medical images, such as slow rendering speed and low sampling efficiency, an improved algorithm based on dynamic adaptive sampling is proposed. By using the central difference gradient method, the corresponding sampling interval is obtained dynamically according to the different sampling points. Meanwhile, a new rendering operator is proposed based on the color value and opacity changes before and after the ray enters the volume element, and the resistance luminosity. Compared with the state of other algorithms, experimental results show that the method proposed in this paper has a faster rendering speed while ensuring the quality of the generated image.

In recent years, deep convolutional neural network (DCNN) has achieved impressive performance in image denoising. However, the existing CNN-based methods cannot work very well on those images with high-level noise. In order to solve this problem, we propose a novel method, named enhanced deep convolution neural network (EDCNN), for image de-noising in this work. Compared with existing models, ED-CNN adopts the residual learning in both global and local manners. In particular, we further apply a residual excitation strategy that enables a short path to be built directly from the input image to output layer. The final model, composed of 52 weight layers, is much deeper than existing ones. Experimental results on standard test images have demonstrated that the proposed method outperforms several state-of-the-art de-noising algorithms in terms of both quantitative measure and visual perception quality.

This paper presents a novel fast algorithm for digital convolutions. It is able to compute arbitrary-length convolutions more efficiently via transforming the convolution into a first-order moment. Although many additions are required, the proposed algorithm has some advantages such as the avoidance of multiplications, simple computation structure, and only integer additions. These advantages contribute to this algorithm being so easy that it can compute convolutions rapidly. Based on the proposed algorithm a very simple and scalable systolic array without multipliers and ROM has been developed leading to more efficient VLSI implementation of convolutions.

Geometric methods are very intuitive and provide a theoretical foundation to many optimization problems in the fields of pattern recognition and machine learning. In this brief, the notion of scaled convex hull (SCH) is defined and a set of theoretical results are exploited to support it. These results allow the existing nearest point algorithms to be directly applied to solve both the separable and nonseparable classification problems successfully and efficiently. Then, the popular S-K algorithm has been presented to solve the nonseparable problems in the context of the SCH framework. The theoretical analysis and some experiments show that the proposed method may achieve better performance than the state-of-the-art methods in terms of the number of kernel evaluations and the execution time.