Source-free unsupervised domain adaptation (SF-UDA), which relies only on a pre-trained source model and unlabeled target data, has gained significant attention. Pseudo-labeling, valued for its simplicity and effectiveness, is a key approach in SF-UDA. However, existing methods neglect the consistency priors of anatomical features across samples, leading them fail to revise of high-confidence noise in structurally inconsistent regions, ultimately manifesting as significant discrepancies in pseudo-labeled samples especially in limited source data scenarios. Motivated by this insight, we propose a novel Geometric Correspondence Constrained (GCC) pseudo-labeling framework. GCC first stratifies pseudo-labeled samples into high/low-quality subsets. It then refines low-quality samples by leveraging the anatomical features inherent in high-quality samples while injecting Gaussian perturbation to perturb high-confidence noise towards the decision boundaries. This process effectively mitigates high-confidence noise disruptive effect and preserves critical prior anatomical knowledge, making it particularly powerful for scenarios with limited source data. Experiments on cross-domain fundus image datasets demonstrate that our method achieves state-of-the-art performance.

Fetal MRI is often acquired with thick slices to mitigate motion artifacts, but this leads to partial volume effects and reduced through-plane spatial resolution, limiting precise anatomical analysis. To address this, various super-resolution methods have been proposed to reconstruct high-resolution volumes from thick-slice scans. Current methods face several major challenges: 1) relying on multi-stack paired data makes arbitrary super-resolution ratios difficult to achieve; 2) lacking robustness against voxel coordinate misalignment caused by partial volume effects; 3) failing to fully utilize the high in-plane resolution of MRI images. To address these issues, we propose a dual-consistency guided curriculum learning method based on implicit neural representation, which uses single-stack inputs to achieve arbitrary super-resolution. We introduce progressive consistency and volumetric consistency to mitigate voxel misalignment caused by partial volume effects and ensure smooth transitions during the model's curriculum-based training. Additionally, we design a curriculum-aware multi-scale feature interaction block to fully leverage thick-slice MRI's high in-plane resolution. Comprehensive evaluations on three fetal MRI datasets demonstrate SOTA performance, with particularly outstanding results in high-ratio super-resolution tasks.

Depthwise-separable convolution has emerged as a significant milestone in the lightweight development of Convolutional Neural Networks (CNNs) over the past decade. This technique consists of two key components: depthwise convolution, which captures spatial information, and pointwise convolution, which enhances channel interactions. In this paper, we propose a novel method to lightweight CNNs through the discretization of Ordinary Differential Equations (ODEs). Specifically, we optimize depthwise-separable convolution by replacing the pointwise convolution with a discrete ODE module, termed the \emph{\textbf{C}hannelwise \textbf{O}DE \textbf{S}olver (COS)}. The COS module is constructed by a simple yet efficient direct differentiation Euler algorithm, using learnable increment parameters. This replacement reduces parameters by over $98.36$\% compared to conventional pointwise convolution. By integrating COS into MobileNet, we develop a new extra lightweight network called MobileODE. With carefully designed basic and inverse residual blocks, the resulting MobileODEV1 and MobileODEV2 reduce channel interaction parameters by $71.0$\% and $69.2$\%, respectively, compared to MobileNetV1, while achieving higher accuracy across various tasks, including image classification, object detection, and semantic segmentation. The code is available at {\url{https://github.com/cashily/MobileODE}}.

Semi-supervised semantic segmentation for medical images has evolved through time. While it can leverage the unlabeled data to significantly improve the segmentation performance, it still suffers the problems of intra-class variance and the consequent class-domain distribution misalignment along with costly training. In this paper, a stability-aware dual-head architecture is proposed to synergize prototype-based and Fully Convolutional Network (FCN) methodologies. By integrating prototype-based method for feature consistency and FCN method for spatial detail preservation, our method enforces consistency between different feature representations. It combines the semantic consistency of prototype learning with the precision of dense prediction. A sample-level stability-aware adaptive augmentation strategy is introduced to further mitigate intra-class variance and distribution shifts. The following certainty guided fusion process dynamically refines the pseudo-labels, better utilizing the advantages in different methods. Experiments on BraTS2019 and LA Heart demonstrate State-Of-The-Art (SOTA) performance, achieving significant improvements over the previous SOTA methods on multiple metrics. The framework effectively bridges domain gaps and enhances pseudo-label reliability for medical image analysis. (Code is available at https://github.com/Alfredzly/SDNP).

The performance of medical image segmentation is critical for subsequent analysis and decision-making in clinical practice. Although great successes have been achieved by employing deep neural networks trained with large-scale annotated datasets, the cost of collecting such datasets is usually expensive, which makes the application of these methods challenging. To address this difficulty, we propose a double-branch framework from the perspective of integrating data annotation and model construction. For the data annotation, to preserve more information as well as high efficiency, a dual polygon annotation approach is employed from the view of sparse annotating and multi-rater learning. In the generated dual polygon annotations, a larger annotation contains all the information about the lesion area, while the smaller annotation is inside the lesion area as much as possible and does not contain any background information. For the model construction, to utilize the polygon annotations efficiently, a framework included one encoder and two different decoders is used to learn agreement information between two annotations in an adversarial manner, while facilitating the learning of disagreement information. To evaluate the effectiveness of the proposed method, extensive experiments are conducted on the ISIC2017, ISIC2018, and KvasirSeg datasets. Experimental results demonstrate that the proposed method can achieve comparable or even superior performance than the fully-supervised methods.

Acne detection is a challenging task due to its small size and blurred boundaries. Previous methods are mostly based on traditional object detection models, where the detected objects’ classification scores could not represent the localization regression quality well. The recent ranking loss somewhat alleviates this problem by generating a ranking score to correct the classification score. In this work, we investigate the factors influencing ranking loss and reveal that the key factors are the sampling method and the weights of sample pairs. Based on this observation, two effective sampling methods are proposed for ranking loss by combining the characteristics of acne data. Firstly, the previous sampling method was to sample all the bounding boxes (Bboxes) in the image. The low scores of Bboxes of some ground truths restrict them from participating in sampling as negative samples. So, the Ground-truth-aware (Gt-aware) Sampling is proposed to make more Bboxes participate in training sufficiently. Secondly, the background Bbox accounts for most of the Bbox in acne images, yet previous sampling methods did not use these Bboxes. Hence, we propose Background Sampling (BGS) to make these Bboxes participate in training effectively. Extensive experiments are conducted on the public dataset ACNE04 and AcneSCU, showing that the proposed method can consistently outperform state-of-the-art methods. The code is available at https://github.com/StevenGerrad/acneDet.

The Brainstem-Vermis (BV) and BrainstemTentorium (BT) angles in the fetal head are two essential indicators for determining whether the fetal development is normal. If these two angle values deviate from the norm, there is a high likelihood of potential fetal health issues arising. Traditional manual measurement is not only time-consuming but also prone to errors. Previous CNN-based landmark detection methods have exhibited some effectiveness. However, These methods for angle calculation using landmarks often overlook their inherent directionality, and their network structures struggle to adapt to the significant variations in fetal size observed in medical images. In this paper, we propose a two-layer neural network and heatmaps with anisotropic Gaussian functions. Specifically, the network extracts local and global features and fuse them together. The global feature attends to the more critical regions in the image, thus correcting ambiguous areas within the local features. Moreover, we introduce heatmaps based on anisotropic Gaussian functions to utilize the direction information associated with landmarks to impose directional constraints on the network’s predictions, resulting in enhanced accuracy in angle calculations. We collected a dataset of 493 fetus MRI images to train and evaluate the performance of the proposed model. Experimental results demonstrate that our method achieves state-of-the-art performance.

Gliomas are the most common intracranial primary tumors . Accurate grading of gliomas is crucial in determining treatment options and prognosis. Clinicians conventionally rely on multiple Magnetic Resonance Imaging (MRI) sequences for accurate glioma assessment. Traditional deep learning methods typically utilize the individual MRI sequence with the annotations of Region of Interest (ROIs), incurring substantial manual effort while losing the complementary information provided by other sequences. This task is inherently a standard multi-modal problem. However, existing methods often adopt complex multi-stream networks for feature extraction and fusion, leading to high resource demands and potential feature redundancy. To address the above challenge, a discrepancy-aware self-distillation method is proposed for multi-modal glioma grading, which requires only a single-stream network to concurrently analyze multiple MRI sequences without auxiliary ROIs. The first Modality Discrepancy-aware Fusion (MDF) module considers the MRI imaging differentiation and widens the inter-modal contrasts, allowing the modality-specific features to be highlighted and the modality-invariant features to be diminished. Furthermore, the proposed Class Activation Self-Distillation (CASD) strategy leverages the generated Class Activation Maps (CAMs) as dark knowledge for the distillation process . This guides shallow layers to focus on the category discriminative features specifically within the lesion region. Extensive experiments were conducted on the BraTS2018 and BraTS2019 datasets to evaluate the effectiveness of our method. The results show that our method outperforms other relevant glioma grading and multi-modal fusion methods on both datasets.

Deep neural networks have demonstrated impressive results in medical image analysis, but designing suitable architectures for each specific task is expertise-dependent and time-consuming. Neural architecture search (NAS) offers an effective means of discovering architectures. It has been highly successful in numerous applications, particularly in natural image classification. Yet, medical images possess unique characteristics, such as small regions and a wide variety of lesion sizes, that differentiate them from natural images. Furthermore, most current NAS methods struggle with high computational costs, especially when dealing with high-resolution image datasets. In this paper, we present a novel evolutionary neural architecture search method called Multi-Scale Training-Free Neural Architecture Search to address these challenges. Specifically, to accommodate the broad range of lesion region sizes in disease diagnosis, we develop a new reduction cell search space that enables the search algorithm to explicitly identify the optimal scale combination for multi-scale feature extraction. To overcome the issue of high computational costs, we utilize training-free indicators as performance measures for candidate architectures, which allows us to search for the optimal architecture more efficiently. More specifically, by considering the capability and simplicity of various networks, we formulate a multi-objective optimization problem that involves two training-free indicators and model complexity for candidate architectures. Extensive experiments on a large medical image benchmark and a publicly available breast cancer detection dataset are conducted. The empirical results demonstrate that our MSTF-NAS outperforms both human-designed architectures and current state-of-the-art NAS algorithms on both datasets, indicating the effectiveness of our proposed method.

Medical image segmentation is a fundamental task in many clinical applications, yet current automated segmentation methods rely heavily on manual annotations, which are inherently subjective and prone to annotation bias. Recently, modeling annotator preference has garnered great interest, and several methods have been proposed in the past two years. However, the existing methods completely ignore the potential correlation between annotations, such as complementary and discriminative information. In this work, the Adaptive annotation CorrelaTion based multI-annOtation LearNing (ACTION) method is proposed for calibrated medical image segmentation. ACTION employs consensus feature learning and dynamic adaptive weighting to leverage complementary information across annotations and emphasize discriminative information within each annotation based on their correlations, respectively. Meanwhile, memory accumulation-replay is proposed to accumulate the prior knowledge and integrate it into the model to enable the model to accommodate the multi-annotation setting. Two medical image benchmarks with different modalities are utilized to evaluate the performance of ACTION, and extensive experimental results demonstrate that it achieves superior performance compared to several state-of-the-art methods.

Due to the exorbitant expense of obtaining labeled data in the field of medical image analysis, semi-supervised learning has emerged as a favorable method for the segmentation of anatomical structures. Although semi-supervised learning techniques have shown great potential in this field, existing methods only utilize image-level spatial consistency to impose unsupervised regularization on data in label space. Considering that anatomical structures often possess inherent anatomical properties that have not been focused on in previous works, this study introduces the inherent consistency into semi-supervised anatomical structure segmentation. First, the prediction and the ground-truth are projected into an embedding space to obtain latent representations that encapsulate the inherent anatomical properties of the structures. Then, two inherent consistency constraints are designed to leverage these inherent properties by aligning these latent representations. The proposed method is plug-and-play and can be seamlessly integrated with existing methods, thereby collaborating to improve segmentation performance and enhance the anatomical plausibility of the results. To evaluate the effectiveness of the proposed method, experiments are conducted on three public datasets (ACDC, LA, and Pancreas). Extensive experimental results demonstrate that the proposed method exhibits good generalizability and outperforms several state-of-the-art methods.

Cross-modal retrieval aims to retrieve relevant content of different modalities by giving a query of another modality. The biggest difficulty is how to bridge the heterogeneous gap between different modalities. The commonly-used methods tend to focus on exploiting individual image-text pair and mining the relations of cross-modality data thereof, but ignore the role of multi-sample correlation. Moreover, more global, structural inter-pair knowledge contained by the training dataset will be under-used. To fully exploit graph-structured semantics and mine the semantic information in the dataset for learning discriminative representations, we propose Weighted Graph-structured Semantics Constraint Network (WGSCN), a unified, graph-based, semantic-constrained learning framework, in which GCN is used to mine comprehensive relation information from cross modality data. Our main inspiration is to design a novel two-branch GCN-based Cross-modal Semantic Encoding (GCSE) module to produce semantic embeddings with the both modality-specific and modality-shared correlation. Moreover, a GAN-based dual learning approach is used to further improve the discriminability and model the joint distribution across different modalities. Our proposed GDL uses semantic embeddings as supervisory signal to make the common representation semantically discriminative while adversarial learning and dual learning are used to make the common representation modality-invariant. Through comparative experiments on five commonly used cross-modal datasets, we have shown the superior retrieval accuracy of our WGSCN.

Three-dimensional (3D) medical image segmentation plays a crucial role in medical care applications. Although various two-dimensional (2D) and 3D neural network models have been applied to 3D medical image segmentation and achieved impressive results, a trade-off remains between efficiency and accuracy. To address this issue, a novel mixture convolutional network (MixConvNet) is proposed, in which traditional 2D/3D convolutional blocks are replaced with novel MixConv blocks. In the MixConv block, 3D convolution is decomposed into a mixture of 2D convolutions from different views. Therefore, the MixConv block fully utilizes the advantages of 2D convolution and maintains the learning ability of 3D convolution. It acts as 3D convolutions and thus can process volumetric input directly and learn intra-slice features, which are absent in the traditional 2D convolutional block. By contrast, the proposed MixConv block only contains 2D convolutions; hence, it has significantly fewer trainable parameters and less computation budget than a block containing 3D convolutions. Furthermore, the proposed MixConvNet is pre-trained with small input patches and fine-tuned with large input patches to improve segmentation performance further. In experiments on the Decathlon Heart dataset and Sliver07 dataset, the proposed MixConvNet outperformed the state-of-the-art methods such as UNet3D, VNet, and nnUnet.

Neural Architecture Search (NAS) has recently shown a powerful ability to engineer networks automatically on various tasks. Most current approaches navigate the search direction with the validation performance-based architecture evaluation methodology, which estimates an architecture's quality by training and validating on a specific large dataset. However, for small-scale datasets, the model's performance on the validation set cannot precisely estimate that on the test set. The imprecise architecture evaluation can mislead the search to sub-optima. To address the above problem, we propose an efficient multi-objective evolutionary zero-shot NAS framework by evaluating architectures with zero-cost metrics, which can be calculated with randomly initialized models in a training-free manner. Specifically, a general zero-cost metric design principle is proposed to unify the current metrics and help develop several new metrics. Then, we offer an efficient computational method for multi-zero-cost metrics by calculating them in one forward and backward pass. Finally, comprehensive experiments have been conducted on NAS-Bench-201 and MedMNIST. The results have shown that the proposed method can achieve sufficiently accurate, high-throughput performance on MedMNIST and 20[Formula: see text]faster than the previous best method.

Deep neural network has shown a powerful performance in the medical image analysis of a variety of diseases. However, a number of studies over the past few years have demonstrated that these deep learning systems can be vulnerable to well-designed adversarial attacks, with minor disruptions added to the input. Since both the public and academia have focused on deep learning in the health information economy, these adversarial attacks would prove more important and raise security concerns. In this article, adversarial attacks on deep learning systems in medicine are analyzed from two different points of view: 1) white box and 2) black box. A fast adversarial sample generation method, Feature Space-Restricted Attention Attack is proposed to explore more confusing adversarial samples. It is based on a generative adversarial network with bound classification space to generate perturbations to achieve attacks. Meanwhile, it can employ an attention mechanism to focus this perturbation on the lesion region. This enables the perturbation closely associated with the classification information making the attack more efficient and invisible. The performance and specificity of the proposed attack method are demonstrated by conducting extensive experiments on three different types of medical images. Finally, it is expected that this work can assist practitioners become being of current weaknesses in the deployment of deep learning systems in clinical settings. And, it further investigates domain-specific features of medical deep learning systems to enhance model generalization and resistance to attacks.

Breast cancer was the most commonly diagnosed cancer among women worldwide in 2020. Recently, several deep learning-based classification approaches have been proposed to screen breast cancer in mammograms. However, most of these approaches require additional detection or segmentation annotations. Meanwhile, some other image-level label-based methods often pay insufficient attention to lesion areas, which are critical for diagnosis. This study designs a novel deep-learning method for automatically diagnosing breast cancer in mammography, which focuses on the local lesion areas and only utilizes image-level classification labels. In this study, we propose to select discriminative feature descriptors from feature maps instead of identifying lesion areas using precise annotations. And we design a novel adaptive convolutional feature descriptor selection (AFDS) structure based on the distribution of the deep activation map. Specifically, we adopt the triangle threshold strategy to calculate a specific threshold for guiding the activation map to determine which feature descriptors (local areas) are discriminative. Ablation experiments and visualization analysis indicate that the AFDS structure makes the model easier to learn the difference between malignant and benign/normal lesions. Furthermore, since the AFDS structure can be regarded as a highly efficient pooling structure, it can be easily plugged into most existing convolutional neural networks with negligible effort and time consumption. Experimental results on two publicly available INbreast and CBIS-DDSM datasets indicate that the proposed method performs satisfactorily compared with state-of-the-art methods.

Automated detection of skin lesions offers excellent potential for interpretative diagnosis and precise treatment of acne vulgar. However, the blurry boundary and small size of lesions make it challenging to detect acne lesions with traditional object detection methods. To better understand the acne detection task, we construct a new benchmark dataset named AcneSCU, consisting of 276 facial images with 31777 instance-level annotations from clinical dermatology. To the best of our knowledge, AcneSCU is the first acne dataset with high-resolution imageries, precise annotations, and fine-grained lesion categories, which enables the comprehensive study of acne detection. More importantly, we propose a novel method called Spatial Aware Region Proposal Network (SA-RPN) to improve the proposal quality of two-stage detection methods. Specifically, the representation learning for the classification and localization task is disentangled with a double head component to promote the proposals for hard samples. Then, Normalized Wasserstein Distance of each proposal is predicted to improve the correlation between the classification scores and the proposals' intersection-over-unions (IoUs). SA-RPN can serve as a plug-and-play module to enhance standard two-stage detectors. Extensive experiments are conducted on both AcneSCU and the public dataset ACNE04, and the results show that the proposed method can consistently outperform state-of-the-art methods.

Cross-modal hashing is an effective cross-modal retrieval approach because of its low storage and high efficiency. However, most existing methods mainly utilize pre-trained networks to extract modality-specific features, while ignore the position information and lack information interaction between different modalities. To address those problems, in this paper, we propose a novel approach, named cross-modal generation and pair correlation alignment hashing (CMGCAH), which introduces transformer to exploit position information and utilizes cross-modal generative adversarial networks (GAN) to boost cross-modal information interaction. Concretely, a cross-modal interaction network based on conditional generative adversarial network and pair correlation alignment networks are proposed to generate cross-modal common representations. On the other hand, a transformer-based feature extraction network (TFEN) is designed to exploit position information, which can be propagated to text modality and enforce the common representation to be semantically consistent. Experiments are performed on widely used datasets with text-image modalities, and results show that the proposed method achieved competitive performance compared with many existing methods.

Radiographic attributes of lung nodules remedy the shortcomings of lung cancer computer-assisted diagnosis systems, which provides interpretable diagnostic reference for doctors. However, current studies fail to dedicate multi-label classification of lung nodules using convolutional neural networks (CNNs) and are inferior in exploiting statistical dependency between the labels. In addition, data imbalance is an indispensable problem to be reckoned with when employing CNNs to perform lung nodule classification. It introduces greater challenges especially in the multi-label classification. In this paper, we propose a method called MLSL-Net to discriminate lung nodule characteristics and simultaneously address the challenges. Particularly, the proposal employs multi-label softmax loss (MLSL) as the performance index, aiming to reduce the ranking errors between the labels and within the labels during training, thereby optimizing ranking loss and AUC directly. Such criterions can better evaluate the classifier's performance on the multi-label imbalanced dataset. Furthermore, a scale factor is introduced based on the investigation of the max surrogate function. Different from preceding usages, the small factor is used so that to narrow the discrepancy of gradients produced by different labels. More interestingly, this factor also facilitates the exploit of label dependency. Experimental results on the LIDC-IDRI dataset as well as another akin dataset demonstrate that MLSL-Net can effectively perform multi-label classification despite the imbalance issue. Meanwhile, the results confirm the responsibility of the factor for capturing label correlations, accordingly leading to more accurate predictions.

Patient-specific quality assurance (QA) for Volumetric Modulated Arc Therapy (VMAT) plans is routinely performed in the clinical. However, it is labor-intensive and time-consuming for medical physicists. QA prediction models can address these shortcomings and improve efficiency. Current approaches mainly focus on single cancer and single modality data. They are not applicable to clinical practice. To assess the accuracy of QA results for VMAT plans, this paper presents a new model that learns complementary features from the multi-modal data to predict the gamma passing rate (GPR). According to the characteristics of VMAT plans, a feature-data fusion approach is designed to fuse the features of imaging and non-imaging information in the model. In this study, 690 VMAT plans are collected encompassing more than ten diseases. The model can accurately predict the most VMAT plans at all three gamma criteria: 2%/2 mm, 3%/2 mm and 3%/3 mm. The mean absolute error between the predicted and measured GPR is 2.17%, 1.16% and 0.71%, respectively. The maximum deviation between the predicted and measured GPR is 3.46%, 4.6%, 8.56%, respectively. The proposed model is effective, and the features of the two modalities significantly influence QA results.

Semi-supervised learning reduces overfitting and facilitates medical image segmentation by regularizing the learning of limited well-annotated data with the knowledge provided by a large amount of unlabeled data. However, there are many misuses and underutilization of data in conventional semi-supervised methods. On the one hand, the model will deviate from the empirical distribution under the training of numerous unlabeled data. On the other hand, the model treats labeled and unlabeled data differently and does not consider inter-data information. In this paper, a semi-supervised method is proposed to exploit unlabeled data to further narrow the gap between the semi-supervised model and its fully-supervised counterpart. Specifically, the architecture of the proposed method is based on the mean-teacher framework, and the uncertainty estimation module is improved to impose constraints of consistency and guide the selection of feature representation vectors. Notably, a voxel-level supervised contrastive learning module is devised to establish a contrastive relationship between feature representation vectors, whether from labeled or unlabeled data. The supervised manner ensures that the network learns the correct knowledge, and the dense contrastive relationship further extracts information from unlabeled data. The above overcomes data misuse and underutilization in semi-supervised frameworks. Moreover, it favors the feature representation with intra-class compactness and inter-class separability and gains extra performance. Extensive experimental results on the left atrium dataset from Atrial Segmentation Challenge demonstrate that the proposed method has superior performance over the state-of-the-art methods.

To obtain a well-performed computer-aided detection model for detecting breast cancer, it is usually needed to design an effective and efficient algorithm and a well-labeled dataset to train it. In this paper, first, a multi-instance mammography clinic dataset was constructed. Each case in the dataset includes a different number of instances captured from different views, it is labeled according to the pathological report, and all the instances of one case share one label. Nevertheless, the instances captured from different views may have various levels of contributions to conclude the category of the target case. Motivated by this observation, a feature-sensitive deep convolutional neural network with an end-to-end training manner is proposed to detect breast cancer. The proposed method first uses a pre-train model with some custom layers to extract image features. Then, it adopts a feature fusion module to learn to compute the weight of each feature vector. It makes the different instances of each case have different sensibility on the classifier. Lastly, a classifier module is used to classify the fused features. The experimental results on both our constructed clinic dataset and two public datasets have demonstrated the effectiveness of the proposed method.

3-D radiotherapy is an effective treatment modality for breast cancer. In 3-D radiotherapy, delineation of the clinical target volume (CTV) is an essential step in the establishment of treatment plans. However, manual delineation is subjective and time consuming. In this study, we propose an automated segmentation model based on deep neural networks for the breast cancer CTV in planning computed tomography (CT). Our model is composed of three stages that work in a cascade manner, making it applicable to real-world scenarios. The first stage determines which slices contain CTVs, as not all CT slices include breast lesions. The second stage detects the region of the human body in an entire CT slice, eliminating boundary areas, which may have side effects for the segmentation of the CTV. The third stage delineates the CTV. To permit the network to focus on the breast mass in the slice, a novel dynamically strided convolution operation, which shows better performance than standard convolution, is proposed. To train and evaluate the model, a large dataset containing 455 cases and 50 425 CT slices is constructed. The proposed model achieves an average dice similarity coefficient (DSC) of 0.802 and 0.801 for right-0 and left-sided breast, respectively. Our method shows superior performance to that of previous state-of-the-art approaches.

Identifying position errors for Graves' ophthalmopathy (GO) patients using electronic portal imaging device (EPID) transmission fluence maps is helpful in monitoring treatment. However, most of the existing models only extract features from dose difference maps computed from EPID images, which do not fully characterize all information of the positional errors. In addition, the position error has a three-dimensional spatial nature, which has never been explored in previous work. To address the above problems, a deep neural network (DNN) model with structural similarity difference and orientation-based loss is proposed in this paper, which consists of a feature extraction network and a feature enhancement network. To capture more information, three types of Structural SIMilarity (SSIM) sub-index maps are computed to enhance the luminance, contrast, and structural features of EPID images, respectively. These maps and the dose difference maps are fed into different networks to extract radiomic features. To acquire spatial features of the position errors, an orientation-based loss function is proposed for optimal training. It makes the data distribution more consistent with the realistic 3D space by integrating the error deviations of the predicted values in the left-right, superior-inferior, anterior-posterior directions. Experimental results on a constructed dataset demonstrate the effectiveness of the proposed model, compared with other related models and existing state-of-the-art methods.

Automatic vessel segmentation in the fundus images plays an important role in the screening, diagnosis, treatment, and evaluation of various cardiovascular and ophthalmologic diseases. However, due to the limited well-annotated data, varying size of vessels, and intricate vessel structures, retinal vessel segmentation has become a long-standing challenge. In this paper, a novel deep learning model called AACA-MLA-D-UNet is proposed to fully utilize the low-level detailed information and the complementary information encoded in different layers to accurately distinguish the vessels from the background with low model complexity. The architecture of the proposed model is based on U-Net, and the dropout dense block is proposed to preserve maximum vessel information between convolution layers and mitigate the over-fitting problem. The adaptive atrous channel attention module is embedded in the contracting path to sort the importance of each feature channel automatically. After that, the multi-level attention module is proposed to integrate the multi-level features extracted from the expanding path, and use them to refine the features at each individual layer via attention mechanism. The proposed method has been validated on the three publicly available databases, i.e. the DRIVE, STARE, and CHASE _ DB1. The experimental results demonstrate that the proposed method can achieve better or comparable performance on retinal vessel segmentation with lower model complexity. Furthermore, the proposed method can also deal with some challenging cases and has strong generalization ability.

The early detection and timely treatment of breast cancer can save lives. Mammography is one of the most efficient approaches to screening early breast cancer. An automatic mammographic image classification method could improve the work efficiency of radiologists. Current deep learning-based methods typically use the traditional softmax loss to optimize the feature extraction part, which aims to learn the features of mammographic images. However, previous studies have shown that the feature extraction part cannot learn discriminative features from complex data using the standard softmax loss. In this paper, we design a new architecture and propose respective loss functions. Specifically, we develop a double-classifier network architecture that constrains the extracted features' distribution by changing the classifiers' decision boundaries. Then, we propose the double-classifier constraint loss function to constrain the decision boundaries so that the feature extraction part can learn discriminative features. Furthermore, by taking advantage of the architecture of two classifiers, the neural network can detect the difficult-to-classify samples. We propose a weighted double-classifier constraint method to make the feature extract part pay more attention to learning difficult-to-classify samples' features. Our proposed method can be easily applied to an existing convolutional neural network to improve mammographic image classification performance. We conducted extensive experiments to evaluate our methods on three public benchmark mammographic image datasets. The results showed that our methods outperformed many other similar methods and state-of-the-art methods on the three public medical benchmarks. Our code and weights can be found on GitHub.

Class imbalance is a common problem in real-world image classification problems, some classes are with abundant data, and the other classes are not. In this case, the representations of classifiers are likely to be biased toward the majority classes and it is challenging to learn proper features, leading to unpromising performance. To eliminate this biased feature representation, many algorithm-level methods learn to pay more attention to the minority classes explicitly according to the prior knowledge of the data distribution. In this article, an attention-based approach called deep attention-based imbalanced image classification (DAIIC) is proposed to automatically pay more attention to the minority classes in a data-driven manner. In the proposed method, an attention network and a novel attention augmented logistic regression function are employed to encapsulate as many features, which belongs to the minority classes, as possible into the discriminative feature learning process by assigning the attention for different classes jointly in both the prediction and feature spaces. With the proposed object function, DAIIC can automatically learn the misclassification costs for different classes. Then, the learned misclassification costs can be used to guide the training process to learn more discriminative features using the designed attention networks. Furthermore, the proposed method is applicable to various types of networks and data sets. Experimental results on both single-label and multilabel imbalanced image classification data sets show that the proposed method has good generalizability and outperforms several state-of-the-art methods for imbalanced image classification.

For lesions required segmentation are very similar to other background tissues, existing methods often incorrectly segment these tissues into foregrounds. As the fact that diagnostic descriptions can improve the performance of lesion segmentation, but existing methods do not sufficiently capture the correlations between images and the corresponding diagnostic descriptions. In this paper, we propose a novel cross-modal mutual-aware network which utilizes diagnostic descriptions to guide lesion segmentation. Concretely, the proposed network integrates several mutually aware feature fusion module to learn the co-relationship between visual and linguistic features at multiple levels, yielding the final mask which are more closely to the descriptions. We have carried out experiments on an internal dataset and the experimental results show a significant performance improvement compared to other traditional and cross-modal approaches.

We study and address the cross-modal retrieval problem which lies at the heart of visual-textual processing. Its major challenge lies in how to effectively learn a shared multi-modal feature space where the discrepancies of semantically related pairs, such as images and texts, are minimized regardless of their modalities. Most current methods focus on reasoning about cross-modality semantic relations within individual image-text pair to learn the common representation. However, they overlook more global, structural inter-pair knowledge within the dataset, i.e., the graph-structured semantics within each training batch. In this paper, we introduce a graph-based, semantic-constrained learning framework to comprehensively explore the intra- and inter-modality information for cross-modal retrieval. Our idea is to maximally explore the structures of labeled data in graph latent space, and use them as semantic constraints to enforce feature embeddings from the semantically-matched (image-text) pairs to be more similar and vice versa. It raises a novel graph-constrained common embedding learning paradigm for cross-modal retrieval, which is largely under-explored up to now. Moreover, a GAN-based dual learning approach is used to further improve the discriminability and model the joint distribution across different modalities. Our fully-equipped approach, called Graph-constrained Cross-modal Retrieval (GCR), is able to mine intrinsic structures of training data for model learning and enable reliable cross-modal retrieval. We empirically demonstrate that our GCR can achieve higher accuracy than existing state-of-the-art approaches on Wikipedia, NUS-WIDE-10K, PKU XMedia and Pascal Sentence datasets. Our code will be made publicly available. Code is available at https://github.com/neoscheung/GCR.

Neural Architecture Search (NAS), which aims at automatically designing neural architectures, recently draw a growing research interest. Different from conventional NAS methods, in which a large number of neural architectures need to be trained for evaluation, the one-shot NAS methods only have to train one supernet which synthesizes all the possible candidate architectures. As a result, the search efficiency could be significantly improved by sharing the supernet's weights during the candidate architectures' evaluation. This strategy could greatly speed up the search process but suffer a challenge that the evaluation based on sharing weights is not predictive enough. Recently, pruning the supernet during the search has been proven to be an efficient way to alleviate this problem. However, the pruning direction in complex-structured search space remains unexplored. In this paper, we revisited the role of path dropout strategy, which drops the neural operations instead of the neurons, in supernet training, and several interesting characters of the supernet trained with dropout are found. Based on the observations, a Hierarchically-Ordered Pruning Neural Architecture Search (HOPNAS) algorithm is proposed by dynamically pruning the supernet with a proper pruning direction. Experimental results indicate that our method is competitive with state-of-the-art approaches on CIFAR10 and ImageNet.

Manifold learning has been widely used for dimensionality reduction and feature extraction of data recently. However, in the application of the related algorithms, it often suffers from noisy or unreliable data problems. For example, when the sample data have complex background, occlusions, and/or illuminations, the clustering of data is still a challenging task. To address these issues, we propose a family of novel algorithms for manifold regularized non-negative matrix factorization in this paper. In the algorithms, based on the alpha-beta-divergences, graph regularization with multiple segments is utilized to constrain the data transitivity in data decomposition. By adjusting two tuning parameters, we show that the proposed algorithms can significantly improve the robustness with respect to the images with complex background. The efficiency of the proposed algorithms is confirmed by the experiments on four different datasets. For different initializations and datasets, variations of cost functions and decomposition data elements in the learning are presented to show the convergent properties of the algorithms.

Exploiting label dependence is a widely used approach to boost classification performance for multilabel classification problems. However, most of the traditional label dependence methods have high time complexity, especially when combined with deep neural networks (DNNs). Thus they usually can not be efficiently applied in large-scale data sets. Recent advances in large-scale multilabel classification widely developed pair-wise ranking and structure-driven methods, but label dependence was little exploited. In most of the structure-driven methods, binary relevance (BR) with multiple binary cross-entropy (BCE) loss functions, a simple but effective method, is still the prior solution incorporation with DNNs in large-scale data sets. In this paper, we propose a novel loss function called label dependent cross-entropy (LDCE), which directly introduces label dependence to BCE loss function by data-driven conditional probability. Combined with deep convolutional neural networks (DCNNs), LDCE introduces no extra parameters and induces very little extra computational complexity. Moreover, we develop its tiny variant with sparse label dependence and its learnable version for automatic learning pair-wise label dependence. Within the BR scheme, LDCE outperforms BCE on seven widely used benchmark datasets. We also perform two large-scale multilabel image classification tasks (VOC 2007 and ChestX-ray14) with DCNNs, and LDCE outperforms BCE and achieves comparable results to the state-of-the-art.

Classifying breast cancer histopathological images automatically is an important task in computer assisted pathology analysis. However, extracting informative and non-redundant features for histopathological image classification is challenging due to the appearance variability caused by the heterogeneity of the disease, the tissue preparation, and staining processes. In this paper, we propose a new feature extractor, called deep manifold preserving autoencoder, to learn discriminative features from unlabeled data. Then, we integrate the proposed feature extractor with a softmax classifier to classify breast cancer histopathology images. Specifically, it learns hierarchal features from unlabeled image patches by minimizing the distance between its input and output, and simultaneously preserving the geometric structure of the whole input data set. After the unsupervised training, we connect the encoder layers of the trained deep manifold preserving autoencoder with a softmax classifier to construct a cascade model and fine-tune this deep neural network with labeled training data. The proposed method learns discriminative features by preserving the structure of the input datasets from the manifold learning view and minimizing reconstruction error from the deep learning view from a large amount of unlabeled data. Extensive experiments on the public breast cancer dataset (BreaKHis) demonstrate the effectiveness of the proposed method.

Breast cancer is one of the most frequently diagnosed solid cancers. Mammography is the most commonly used screening technology for detecting breast cancer. Traditional machine learning methods of mammographic image classification or segmentation using manual features require a great quantity of manual segmentation annotation data to train the model and test the results. But manual labeling is expensive, time-consuming, and laborious, and greatly increases the cost of system construction. To reduce this cost and the workload of radiologists, an end-to-end full-image mammogram classification method based on deep neural networks was proposed for classifier building, which can be constructed without bounding boxes or mask ground truth label of training data. The only label required in this method is the classification of mammographic images, which can be relatively easy to collect from diagnostic reports. Because breast lesions usually take up a fraction of the total area visualized in the mammographic image, we propose different pooling structures for convolutional neural networks(CNNs) instead of the common pooling methods, which divide the image into regions and select the few with high probability of malignancy as the representation of the whole mammographic image. The proposed pooling structures can be applied on most CNN-based models, which may greatly improve the models' performance on mammographic image data with the same input. Experimental results on the publicly available INbreast dataset and CBIS dataset indicate that the proposed pooling structures perform satisfactorily on mammographic image data compared with previous state-of-the-art mammographic image classifiers and detection algorithm using segmentation annotations.

In recent years, the State Grid Corporation of China (SGCC) has been building a strong smart grid to improve the security level of the power grid. By implementing the Internet+ strategy, the SGCC comprehensively improves the informatization and intelligence of the power grid and fully utilizes modern information communication technologies and control technologies. Network slicing is not only a technology but also a new business model, which has attracted broad interest of researchers. Base on above background, in this paper, several typical user cases for smart grid are introduced firstly. In addition, we present the E2E business models and steps to implement network slicing for operators. Besides, the Total Cost of Ownership (TCO) and Return on Investment (ROI) of Network Slicing are also analyzed in Smart Grids for Operators.

As you open this January issue of the IEEE Transactions on Neural Networks and Learning Systems (TNNLS), I hope everyone enjoyed a great holiday season and is excited for the new year of 2019. I am very delighted and honored to report several key metrics of IEEE TNNLS to the community.

Connections play a crucial role in neural network (NN) learning because they determine how information flows in NNs. Suitable connection mechanisms may extensively enlarge the learning capability and reduce the negative effect of gradient problems. In this paper, a new delay connection is proposed for Long Short-Term Memory (LSTM) unit to develop a more sophisticated recurrent unit, called Delay Connected LSTM (DCLSTM). The proposed delay connection brings two main merits to DCLSTM with introducing no extra parameters. First, it allows the output of the DCLSTM unit to maintain LSTM, which is absent in the LSTM unit. Second, the proposed delay connection helps to bridge the error signals to previous time steps and allows it to be back-propagated across several layers without vanishing too quickly. To evaluate the performance of the proposed delay connections, the DCLSTM model with and without peephole connections was compared with four state-of-the-art recurrent model on two sequence classification tasks. DCLSTM model outperformed the other models with higher accuracy and F1[Formula: see text]score. Furthermore, the networks with multiple stacked DCLSTM layers and the standard LSTM layer were evaluated on Penn Treebank (PTB) language modeling. The DCLSTM model achieved lower perplexity (PPL)/bit-per-character (BPC) than the standard LSTM model. The experiments demonstrate that the learning of the DCLSTM models is more stable and efficient.

Memory is one of the most important mechanisms in recurrent neural networks (RNNs) learning. It plays a crucial role in practical applications, such as sequence learning. With a good memory mechanism, long term history can be fused with current information, and can thus improve RNNs learning. Developing a suitable memory mechanism is always desirable in the field of RNNs. This paper proposes a novel memory mechanism for RNNs. The main contributions of this paper are: 1) an auxiliary memory unit (AMU) is proposed, which results in a new special RNN model (AMU-RNN), separating the memory and output explicitly and 2) an efficient learning algorithm is developed by employing the technique of error flow truncation. The proposed AMU-RNN model, together with the developed learning algorithm, can learn and maintain stable memory over a long time range. This method overcomes both the learning conflict problem and gradient vanishing problem. Unlike the traditional method, which mixes the memory and output with a single neuron in a recurrent unit, the AMU provides an auxiliary memory neuron to maintain memory in particular. By separating the memory and output in a recurrent unit, the problem of learning conflicts can be eliminated easily. Moreover, by using the technique of error flow truncation, each auxiliary memory neuron ensures constant error flow during the learning process. The experiments demonstrate good performance of the proposed AMU-RNNs and the developed learning algorithm. The method exhibits quite efficient learning performance with stable convergence in the AMU-RNN learning and outperforms the state-of-the-art RNN models in sequence generation and sequence classification tasks.

Neurons in a network can be both active or inactive. Given a subset of neurons in a network, is it possible for the subset of neurons to evolve to form an active oscillator by applying some external periodic stimulus? Furthermore, can these oscillator neurons be observable, that is, is it a stable oscillator? This paper explores such possibility, finding that an important property: any subset of neurons can be intermittently co-activated to form a stable oscillator by applying some external periodic input without any condition. Thus, the existing of intermittently active oscillator neurons is an essential property possessed by the networks. Moreover, this paper shows that, under some conditions, a subset of neurons can be fully co-activated to form a stable oscillator. Such neurons are called selectable oscillator neurons. Necessary and sufficient conditions are established for a subset of neurons to be selectable oscillator neurons in linear threshold recurrent neuron networks. It is proved that a subset of neurons forms selectable oscillator neurons if and only if the real part of each eigenvalue of the associated synaptic connection weight submatrix of the network is not larger than one. This simple condition makes the concept of selectable oscillator neurons tractable. The selectable oscillator neurons can be regarded as memories stored in the synaptic connections of networks, which enables to find a new perspective of memories in neural networks, different from the equilibrium-type attractors.

Motion models have been proved to be a crucial part in the visual tracking process. In recent trackers, particle filter and sliding windows-based motion models have been widely used. Treating motion models as a sequence prediction problem, we can estimate the motion of objects using their trajectories. Moreover, it is possible to transfer the learned knowledge from annotated trajectories to new objects. Inspired by recent advance in deep learning for visual feature extraction and sequence prediction, we propose a trajectory predictor to learn prior knowledge from annotated trajectories and transfer it to predict the motion of target objects. In this predictor, convolutional neural networks extract the visual features of target objects. Long short-term memory model leverages the annotated trajectory priors as well as sequential visual information, which includes the tracked features and center locations of the target object, to predict the motion. Furthermore, to extend this method to videos in which it is difficult to obtain annotated trajectories, a dynamic weighted motion model that combines the proposed trajectory predictor with a random sampler is proposed. To evaluate the transfer performance of the proposed trajectory predictor, we annotated a real-world vehicle dataset. Experiment results on both this real-world vehicle dataset and an online tracker benchmark dataset indicate that the proposed method outperforms several state-of-the-art trackers.

Low rank representation (LRR) is widely used to construct a good affinity matrix to cluster data drawn from the union of multiple linear subspaces. However, it is not easy to solve the LRR problem in a closed form, and augmented Lagrange multiplier method (ALM) is usually applied. ALM takes a relative long time dealing with the real-world data. To solve the LRR problem efficiently, we propose an efficient low rank representation (eLRR) algorithm. Given a contaminated data set, we propose a novel way to solve the LRR of the data. We establish a useful theorem which directly gives an approximate solution to our LRR optimization problem. Thus, we can construct a good affinity matrix for subspace clustering. Experimental results with several public databases verify the efficiency and effectiveness of our method.

-norm-based representation, and have achieved the state-of-the-art performance. However, these methods have suffered from the following two limitations. First, the time complexities of these methods are at least proportional to the cube of the data size, which make those methods inefficient for solving the large-scale problems. Second, they cannot cope with the out-of-sample data that are not used to construct the similarity graph. To cluster each out-of-sample datum, the methods have to recalculate the similarity graph and the cluster membership of the whole data set. In this paper, we propose a unified framework that makes the representation-based subspace clustering algorithms feasible to cluster both the out-of-sample and the large-scale data. Under our framework, the large-scale problem is tackled by converting it as the out-of-sample problem in the manner of sampling, clustering, coding, and classifying. Furthermore, we give an estimation for the error bounds by treating each subspace as a point in a hyperspace. Extensive experimental results on various benchmark data sets show that our methods outperform several recently proposed scalable methods in clustering a large-scale data set.

Recently, considerable attention has been devoted to the prediction problems arising from heterogeneous information networks. In this paper, we present a new prediction task, Neighbor Distribution Prediction (NDP), which aims at predicting the distribution of the labels on neighbors of a given node and is valuable for many different applications in heterogeneous information networks. The challenges of NDP mainly come from three aspects: the infinity of the state space of a neighbor distribution, the sparsity of available data, and how to fairly evaluate the predictions. To address these challenges, we first propose an Evolution Factor Model (EFM) for NDP, which utilizes two new structures proposed in this paper, i.e. Neighbor Distribution Vector (NDV) to represent the state of a given node's neighbors, and Neighbor Label Evolution Matrix (NLEM) to capture the dynamics of a neighbor distribution, respectively. We further propose a learning algorithm for Evolution Factor Model. To overcome the problem of data sparsity, the learning algorithm first clusters all the nodes and learns an NLEM for each cluster instead of for each node. For fairly evaluating the predicting results, we propose a new metric: Virtual Accuracy (VA), which takes into consideration both the absolute accuracy and the predictability of a node. Extensive experiments conducted on three real datasets from different domains validate the effectiveness of our proposed model EFM and metric VA.

We propose a novel unsupervised subspace learning method to optimize graph construction for face recognition called Datum Adaptive Weighted Collaborative Representation (DAWCR). Different from sparsity preserving projection (SPP), a recently proposed linear dimensionality reduction method inspired by sparse representation, where graph is constructed using sparse reconstructive relationship by minimizing a l1-regularization-based objective function, DAWCR aims to optimize the graph construction by incorporating the locality structure and features variance among data elements into a unified framework using regularized linear representation i.e. weighted regularized least square using l2-minimization approach. The neighborhood selection method in DAWCR is datum dependent, moreover neighborhood size for each datum is chosen automatically by considering data distribution probability. Hence the resulting graph is sparse, models the nonlinear geometry of data set, and conveys more discriminate information. The DAWCR problem formulation has the algebraic solution without involving any parameter tuning for optimal neighbors selection, which makes it computationally efficient than SPP. Extensive experiments on several publicly available real-world face and some UCI data sets, are conducted to verify the feasibility and effectiveness of the proposed method. Experimental results show that the proposed method achieves competitive performance with encouraging results.

MapReduce has become one of the most popular framework for building big-data applications. It was originally designed for distributed-computing, and has been extended to various hardware architectures, e.g., multi-core CPUs, GPUs and FPGAs. In this work, we develop the first MapReduce framework on the recently released Intel Xeon Phi coprocessor. We utilize advanced features of the Xeon Phi to achieve high performance. In order to take advantage of the SIMD vector processing units, we propose a vectorization friendly technique to assist the auto-vectorization as well as develop SIMD hash computation algorithms. Furthermore, we utilize MIMD hyper-threading to pipeline the map and reduce phases to improve the resource utilization. We also eliminate multiple local arrays but use low cost atomic operations on the global array for some applications, which can improve the thread scalability and data locality. We conduct comprehensive experiments to compare our optimized MapReduce framework with a state-of-the-art multi-core based MapReduce framework (Phoenix++). By evaluating six real-world applications, the experimental results show that our optimized framework is 1.2X to 38X faster than Phoenix++ for various applications on the Xeon Phi.

In this paper, we address two problems in Sparse Subspace Clustering algorithm (SSC), i.e., scalability issue and out-of-sample problem. SSC constructs a sparse similarity graph for spectral clustering by using l1-minimization based coefficients, has achieved state-of-the-art results for image clustering and motion segmentation. However, the time complexity of SSC is proportion to the cubic of problem size such that it is inefficient to apply SSC into large scale setting. Moreover, SSC does not handle with out-of-sample data that are not used to construct the similarity graph. For each new datum, SSC needs recalculating the cluster membership of the whole data set, which makes SSC is not competitive in fast online clustering. To address the problems, this paper proposes out-of-sample extension of SSC, named as Scalable Sparse Subspace Clustering (SSSC), which makes SSC feasible to cluster large scale data sets. The solution of SSSC adopts a "sampling, clustering, coding, and classifying" strategy. Extensive experimental results on several popular data sets demonstrate the effectiveness and efficiency of our method comparing with the state-of-the-art algorithms.

The concepts of selectable and unselectable sets are proposed to describe some interesting dynamical properties of a class of recurrent neural networks (RNNs) with saturated piecewise linear transfer function. A set of neurons is said to be selectable if it can be co-unsaturated at a stable equilibrium point by some external input. A set of neurons is said to be unselectable if it is not selectable, i.e., such set of neurons can never be co-unsaturated at any stable equilibrium point regardless of what the input is. The importance of such concepts is that they enable a new perspective of the memory in RNNs. Necessary and sufficient conditions for the existence of selectable and unselectable sets of neurons are obtained. As an application, the problem of group selection is discussed by using such concepts. It shows that, under some conditions, each group is a selectable set, and each selectable set is contained in some group. Thus, groups are indicated by selectable sets of the RNNs and can be selected by external inputs. Simulations are carried out to further illustrate the theory.

The concepts of permitted and forbidden sets enable a new perspective of the memory in neural networks. Such concepts exhibit interesting dynamics in recurrent neural networks. This paper studies the basic theories of permitted and forbidden sets of the linear threshold discrete-time recurrent neural networks. The linear threshold transfer function has been regarded as an adequate transfer function for recurrent neural networks. Networks with this transfer function form a class of hybrid analog and digital networks which are especially useful for perceptual computations. Networks in discrete time can directly provide algorithms for efficient implementation in digital hardware. The main contribution of this paper is to establish foundations of permitted and forbidden sets. Necessary and sufficient conditions for the linear threshold discrete-time recurrent neural networks are obtained for complete convergence, existence of permitted and forbidden sets, as well as conditionally multiattractivity, respectively. Simulation studies explore some possible interesting practical applications.

A continuous attractor of a recurrent neural network (RNN) is a set of connected stable equilibrium points. Continuous attractors have been used to describe the encoding of continuous stimuli in neural networks. Dynamic behaviors of continuous attractors of RNNs exhibit interesting properties. This brief desires to derive explicit representations of continuous attractors of RNNs. Representations of continuous attractors of linear RNNs as well as linear-threshold (LT) RNNs are obtained under some conditions. These representations could be looked at as solutions of continuous attractors of the networks. Such results provide clear and complete descriptions to the continuous attractors.

This paper studies multiperiodicity and attractivity for a class of recurrent neural networks (RNNs) with unsaturating piecewise linear transfer functions and variable delays. Using local inhibition, conditions for boundedness and global attractivity are established. These conditions allow coexistence of stable and unstable trajectories. Moreover, multiperiodicity of the network is investigated by using local invariant sets. It shows that under some interesting conditions, there exists one periodic trajectory in each invariant set which exponentially attracts all trajectories in that region correspondingly. Simulations are carried out to illustrate the theories.

This paper studies the output convergence of a class of recurrent neural networks with time-varying inputs. The model of the studied neural networks has different dynamic structure from that in the well known Hopfield model, it does not contain linear terms. Since different structures of differential equations usually result in quite different dynamic behaviors, the convergence of this model is quite different from that of Hopfield model. This class of neural networks has been found many successful applications in solving some optimization problems. Some sufficient conditions to guarantee output convergence of the networks are derived.