Distance Regularization Research Articles

Ordinal Classification with Distance Regularization for Robust Brain Age Prediction.

Age is one of the major known risk factors for Alzheimer's Disease (AD). Detecting AD early is crucial for effective treatment and preventing irreversible brain damage. Brain age, a measure derived from brain imaging reflecting structural changes due to aging, may have the potential to identify AD onset, assess disease risk, and plan targeted interventions. Deep learning-based regression techniques to predict brain age from magnetic resonance imaging (MRI) scans have shown great accuracy recently. However, these methods are subject to an inherent regression to the mean effect, which causes a systematic bias resulting in an overestimation of brain age in young subjects and underestimation in old subjects. This weakens the reliability of predicted brain age as a valid biomarker for downstream clinical applications. Here, we reformulate the brain age prediction task from regression to classification to address the issue of systematic bias. Recognizing the importance of preserving ordinal information from ages to understand aging trajectory and monitor aging longitudinally, we propose a novel ORdinal Distance Encoded Regularization (ORDER) loss that incorporates the order of age labels, enhancing the model's ability to capture age-related patterns. Extensive experiments and ablation studies demonstrate that this framework reduces systematic bias, outperforms state-of-art methods by statistically significant margins, and can better capture subtle differences between clinical groups in an independent AD dataset. Our implementation is publicly available at https://github.com/jaygshah/Robust-Brain-Age-Prediction.

PDRLRR: A novel low-rank representation with projection distance regularization via manifold optimization for clustering

The low-rank representation (LRR) method has attracted widespread attention due to its excellent performance in pattern recognition and machine learning. LRR-based variants have been proposed to solve the three existing problems in LRR: (1) the projection matrix is permanently fixed when dimensionality reduction techniques are adopted; (2) LRR fails to capture the local geometric structure; and (3) the solution deviates from the real low-rank solution. To address these problems, this paper proposes a low-rank representation with projection distance regularization (PDRLRR) via manifold optimization for clustering. In detail, we first introduce a low-dimensional projection matrix and a projection distance regularization term to fit the projected data automatically and capture the local structure of the data, respectively. Consequently, the projection matrix and representation matrix are obtained jointly. Then, we obtain a more accurate low-rank solution by minimizing the Schatten-p norm instead of the nuclear norm. Next, the projection matrix is optimized through a generalized Stiefel manifold. Extensive experiments demonstrate that our proposed method outperforms the state-of-the-art methods.

Infrared cluster target detection based on Facet kernel and adaptive distance regularization level set

The acquisition of high signal-to-noise ratio (SNR) detection results for targets in infrared images is of great significance for early warning detection and precision guidance. To address the issue of detecting cluster targets in complex backgrounds, a detection method combining the Facet kernel and adaptive distance regularization level set evolution (ADRLSE) is proposed. Firstly, local order-statistics and mean filters are applied to remove high-brightness noise and smooth the image. Subsequently, the Facet kernel filter is applied to enhance the target while suppress the background. Candidate target pixels are obtained through adaptive threshold segmentation. Additionally, based on the edge characteristics of cluster targets, a novel edge detection function is proposed that adaptively determines the parameters using the contour volume (CV) and peak signal-to-noise ratio (PSNR) as references. The enhanced mapping of the target region is obtained by extracting the cluster target contour using ADRLSE. The ADRLSE map is weighted using the target map obtained from the Facet kernel to further enhance the target, and the target is detected through thresholding operations. Finally, the separation result of a single target within a cluster is obtained through a novel adaptive k-means clustering algorithm. Simulation experiments demonstrate that our method has high detection accuracy for cluster targets and can accomplish detection tasks such as cluster contour extraction and single target division.

Bregman distance regularization for nonsmooth and nonconvex optimization

AbstractSolving a nonsmooth and nonconvex minimization problem can be approached as finding a zero of a set-valued operator. With this perspective, we propose a novel Majorizer–Minimizer technique to find a local minimizer of a nonsmooth and nonconvex function and establish its convergence. Our approach leverages Bregman distances to generalize the classical quadratic regularization. By doing so, we generate a family of regularized problems that encompasses quadratic regularization as a special case. To further demonstrate the effectiveness of our method, we apply it on a lasso regression model, showcasing its performance.

Inverse design of electromagnetically induced transparency metamaterials based on generative adversarial networks

The traditional metamaterial design process usually relies on some knowledge experience and simulation tools to continuously optimize by trial and error, until the simulation results meet the requirements. But this trial-and-error approach could be more unstable and time-consuming, especially when there are too many material parameters or the optimization interval is too large. This paper proposes a multi-prediction model for metamaterials, Improved-StarGan based on StarGan with semi-supervised learning, and use an EIT structure as a validation object. The generator can output various material structures according to the input spectrum extremes, and the discriminator can forward predict the spectrum extremes based on the input material structure parameters. Spectral normalization, gradient penalty, and hidden space distance regularization are also used to increase the diversity of its output data at the expense of sacrificing a part of the accuracy of the generator. During model training, the loss values of the training and validation sets converge normally and end up in a small range. Finally, the data was extracted from the test set for model prediction and simulation comparison. Meanwhile, a sample of one of the predicted structures is tested. All the results show that the model predictions have low error and high confidence. the results demonstrate that the method is effective in both inverse multiple structure and forward prediction of metamaterials, which provides a new design idea for the structural design of metamaterials.

An active contour model based on shadow image and reflection edge for image segmentation

Image segmentation is popular in many applications. Active contour models (ACMs) are very useful methods for image segmentation. However, many existing ACMs have drawbacks, e.g., obtaining poor performance for segmenting images with intensity inhomogeneity, or excessive convolution operations increasing calculation time. To solve these problems, a novel ACM based on shadow image and reflection edge (SIRE) is proposed, which represents the image by an additive model with the shadow image and the reflection edge. The shadow image is calculated with mean filtering, and the reflection edge is calculated by the optimal solution of the data driven term within the energy function. The image energy function is minimized by the level set method (LSM), by which the image segmentation is realized. The difference between the background and the target is adequately reflected by the reflection edge, which drives the evolution of the contour lines to find the target edge correctly. In the level set calculation, the optimized length term and the distance regularization term are used to improve the model robustness. Experimental results demonstrate that the proposed method can effectively segment inhomogeneous images, and that our model outperforms other three ACMs in terms of segmentation speed and accuracy.

A Transformer Model for Coastline Prediction in Weitou Bay, China

The simulation and prediction of coastline changes are of great significance for the development and scientific management of coastal zones. Coastline changes are difficult to capture completely but appear significantly periodic over a long time series. In this paper, the transformer model is used to learn the changing trend of the coastline so as to deduce the position of the coastline in the coming year. First, we use the distance regularization level set evolution (DRLSE) model for instantaneous waterline extraction (IWE) from preprocessed Landsat time-series images from 2010–2020 in Weitou Bay, China. Then, tidal correction (TC) is performed on the extracted instantaneous waterline dataset to obtain coastlines projected to a single reference tidal datum. Finally, the coastline datasets from 2010–2019 are used for model training, and the coastline in 2020 is used for accuracy assessment. Three precision evaluation methods, including receiver operating characteristic curve matching, the mean offset, and the root mean square error, were used to verify the predicted coastline data. The receiver operating characteristic curve was specifically designed and improved to evaluate the accuracy of the obtained coastline. Compared with the support vector regression (SVR) and long–short-term memory (LSTM) methods, the results showed that the coastline predicted by the transformer model was the closest to the accurate extracted coastline. The accuracies of the correct values corresponding to SVR, LSTM, and transformer models were 88.27%, 94.08%, and 98.80%, respectively, which indicated the accuracy of the coastline extraction results. Additionally, the mean offset and root mean square error were 0.32 pixels and 0.57 pixels, respectively. In addition, the experimental results showed that tidal correction is important for coastline prediction. Moreover, through field investigations of coastlines, the predicted results obtained for natural coastlines were more accurate, while the predicted results were relatively poor for some artificial coastlines that were intensely influenced by human activities. This study shows that the transformer model can provide natural coastline changes for coastal management.

CDM: A coupled deformable model for image segmentation with speckle noise and severe intensity inhomogeneity

Speckle noise and intensity inhomogeneity are always challenging issues in the area of image segmentation, especially when both difficulties appear simultaneously. Consequently, the majority of existing deformable models yield inadequate results in this situation. This paper aims to address these issues by combining a bias correction term and a despeckling term into a single variational level set architecture, which not only corrects the severe intensity inhomogeneity but also performs image despeckling and segmentation simultaneously. Specifically, edge and region synergetic terms are defined to correct the severe intensity inhomogeneity during image segmentation that eradicates their shortcomings as well as retains their advantages. Further, a despeckling term is constructed, which effectively suppresses the noise while enhancing image details. Since the lack of thorough investigation on despeckling of images degraded by Rayleigh noise distribution, which usually appear in ultrasound (US) images, so we included it in the coupled deformable model (CDM). Moreover, region-based terms eradicate complex re-initialization and numerical instability during the level set evolution, as a result, no distance regularization term is needed. Additionally, Schauder’s fixed point theorem is used to demonstrate the well-posedness of the present system. Extensive numerical experiments on real and synthetic images with speckle noise and severe inhomogeneous intensity demonstrate that the CDM exhibits superior results compared to classical and some recent deformable models in terms of accuracy, robustness, and various quality measures.

Concurrent topology optimization of multiple components sharing partial design domain based on distance regularized parameterized level set method

AbstractIn this article, the distance regularized parameterized level set method (DRPLSM) is proposed, which introduces a specified energy functional into the level set equation as the distance regularization term. Geometric verification shows that the distance regularization scheme keeps the level set function near the structural boundary as an approximate signed distance function. Based on benchmark example of the cantilever beam, it is verified that the DRPLSM can avoid the re‐initialization of level set function in the optimization process and obtain smooth structural boundary. The DRPLSM is applied to multicomponent concurrent topology optimization with partially shared design domain for the first time. It makes the optimization results have smooth structural boundaries. The optimization objective of this algorithm is to minimize the structural compliance of all components. The sharing domain is divided into different design domains according to the strain energy of elements. The optimality of the proposed algorithm for partitioning the sharing domain is verified using the literature example with known optimal solutions. A symmetric structure example, a main and auxiliary optimization structure example and an example with design‐dependent boundary loads show that the proposed concurrent optimization algorithm has wide applicability.

Incomplete multi-view clustering based on low-rank representation with adaptive graph regularization

Incomplete multi-view clustering has attracted attention due to its ability to deal with clustering problems with incomplete information. However, most existing methods either ignore the local structure of the data or fail to consider the importance of different views. In addition, some methods based on mean filling may easily introduce useless information when the data has a large missing rate. To address these issues, this paper proposes an incomplete multi-view clustering algorithm based on graph regularized low-rank representations without using filling method. Specifically, we combine a distance regularization term and low-rank representation-based non-negativity constraints to directly learn graphs with global and local data structures from raw data. Furthermore, we introduce a novel weighted fusion mechanism in the model to learn a consistent representation of all views, which effectively avoids bad views from affecting the quality of the final fused consensus graph. Experimental results on six incomplete multi-view datasets demonstrate that our proposed method achieves the best performance compared with the existing state-of-the-art methods.

Discovering Community Structure in Multiplex Networks via a Co-Regularized Robust Tensor-Based Spectral Approach

Complex networks arise in various fields, such as biology, sociology and communication, to model interactions among entities. Entities in many real-world systems exhibit different types of interactions, which requires modeling these type of systems properly. Multiplex networks are used to model these systems, as they can reflect the nodes’ pair-wise interactions as multiple distinct types of links across layers. Community detection is a widely studied application in network analysis as it provides insights into the structure and organization of the network. Even though multiple algorithms have been developed in the community detection field, many of them have a limited performance in the presence of noise. In this article, we develop a novel algorithm that combines tensor low-rank representation, spectral clustering and distance regularization to improve the accuracy in discovering communities in multiplex networks. The low-rank representation leads to reducing the noise and errors existing in the network and the optimization of an accurate consensus set of eigenvectors that reveals the communities in the network. Moreover, the proposed approach balances the agreement between the eigenvectors of each layer, i.e., individual subspaces, and the consensus set of eigenvectors, i.e., common subspaces, by minimizing the projection distance between them. The common and individual subspaces are computed efficiently through Tucker decomposition and modified spectral clustering, respectively. Finally, multiple experiments are conducted on real and simulated networks to evaluate the proposed approach and compare it to state-of-the-art algorithms. The proposed approach shows its robustness and efficiency in discovering the communities in multiplex networks.

Deep image and feature prior algorithm based on U-ConformerNet structure

PurposeThe reconstruction performance of the deep image prior (DIP) approach is limited by the conventional convolutional layer structure and it is difficult to enhance its potential. In order to improve the quality of image reconstruction and suppress artifacts, we propose a DIP algorithm with better performance, and verify its superiority in the latest case. MethodsWe construct a new U-ConformerNet structure as the DIP algorithm's network, replacing the traditional convolutional layer-based U-net structure, and introduce the 'lpips' deep network based feature distance regularization method. Our algorithm can switch between supervised and unsupervised modes at will to meet different needs. ResultsThe reconstruction was performed on the low dose CT dataset (LoDoPaB). Our algorithm attained a PSNR of more than 35 dB under unsupervised conditions, and the PSNR under the supervised condition is greater than 36 dB. Both of which are better than the performance of the DIP-TV. Furthermore, the accuracy of this method is positively connected with the quality of the a priori image with the help of deep networks. In terms of noise eradication and artifact suppression, the DIP algorithm with U-ConformerNet structure outperforms the standard DIP method based on convolutional structure. ConclusionsIt is known by experimental verification that, in unsupervised mode, the algorithm improves the output PSNR by at least 2–3 dB when compared to the DIP-TV algorithm (proposed in 2020). In supervised mode, our algorithm approaches that of the state-of-the-art end-to-end deep learning algorithms.

An Improved SVM with Earth Mover’s Distance Regularization and Its Application in Pattern Recognition

A support vector machine (SVM) aims to achieve an optimal hyperplane with a maximum interclass margin and has been widely utilized in pattern recognition. Traditionally, a SVM mainly considers the separability of boundary points (i.e., support vectors), while the underlying data structure information is commonly ignored. In this paper, an improved support vector machine with earth mover’s distance (EMD-SVM) is proposed. It can be regarded as an improved generalization of the standard SVM, and can automatically learn the distribution between the classes. To validate its performance, we discuss the necessity of the structural information of EMD-SVM in the linear and nonlinear cases, respectively. Experimental validation was designed and conducted in different application fields, which have shown its superior and robust performance.

Accurate image segmentation based on adaptive distance regularization level set method

Level set method has been widely applied in the field of image segmentation. However, the level set formulation is inevitably affected by the regularization function, in-homogeneity and weak edge in the process of evolution, which often leads to the instability and inaccuracy of image segmentation results. To solve these problems, a new distance regularization term defined by a double-well potential function is proposed to satisfy more ideal characteristics of signed distance property. In addition, a novel edge indicator function is introduced to segment images with uneven intensity or weak edge. Finally, the adaptive adjustment formulas of distance regularization and area parameters are derived to alleviate the difficulty of parameter adjustment. Experimental results show that the proposed model provides better accuracy and versatility, quantitative experiment on Weizmann segmentation evaluation database achieves mean Dice score (96.87%), IoU (94.38%), Hausdorff distance (3.20[Formula: see text]mm), Recall (97.68%) and Precision (96.32%), respectively.

A Robust Convolutional Neural Network for 6D Object Pose Estimation from RGB Image with Distance Regularization Voting Loss

Six-degree (6D) pose estimation of objects is important for robot manipulation but at the same time challenging when dealing with occluded and textureless objects. To overcome this challenge, the proposed method presents an end-to-end robust network for real-time 6D pose estimation of rigid objects using the RGB image. In this proposed method, a fully convolutional network with a features pyramid is developed that effectively boosts the accuracy of pixelwise labeling and direction unit vector field that take part in the voting process for object keypoints estimation. The network further takes into account measuring the distance between pixel and keypoint, which aims to help select accurate hypotheses in the RANSAC process. This avoids hypothesis deviations caused by the errors due to direction unit vectors in cases of distant pixels from keypoints. A vectorial distance regularization loss function is used to help Perspective-n-Point find 2D-3D correspondences between 3D object keypoints and their estimated corresponding 2D counterparts. Experiments are performed on widely used LINEMOD and occlusion LINEMOD datasets with ADD (-S) and 2D projection evaluation metrics. The results show that our method improves pose estimation performance compared to the state-of-the-art while still achieving real-time efficiency.

Noncritical maps on geodesically complete spaces with curvature bounded above

We define and study the regularity of distance maps on geodesically complete spaces with curvature bounded above. We prove that such a regular map is locally a Hurewicz fibration. This regularity can be regarded as a dual concept of Perelman’s regularity in the geometry of Alexandrov spaces with curvature bounded below. As a corollary, we obtain a sphere theorem for geodesically complete CAT(1) spaces.

Efficient Federated Learning Using Layer-Wise Regulation and Momentum Aggregation

Federated Learning (FL) enables multiple parties to train a global model collaboratively without sharing local data. However, a key challenge of FL is data distribution heterogeneity across participants, which causes model drift in local training and significantly reduces the model performance. To address this challenge, we analyze the inconsistency differences between different model layers of local models and further propose Layer-wise Distance Regularization (LWDR) and Layer-wise Momentum Aggregation (LWMA). The proposed LWDR and LWMA optimize the local training and model aggregation processes, respectively, to improve the convergence performance of FL on data in the nonindependent and identically distributed (Non-IID) scenarios. Our experiments on well-known datasets show that our algorithm significantly outperforms the state-of-the-art FL algorithms in convergence speed, accuracy, and stability in different Non-IID scenarios.

Multi-feature sparse similar representation for person identification

Person identification with a single feature (e.g., face recognition, speaker verification, person re-identification, etc.) has been studied extensively for many years, while few works focus on multi-feature person identification. Though promising performance has been achieved by only using the information of facial images, voice, or pedestrian appearance, it is still challenging to recognize a person with only a single feature in some situations (e.g., a person at a distance or occluded by other objects, and a partial person out of view). In this paper, we present a multi-feature sparse similar representation (MFSSR) method to effectively fuse face features, body features, and global image features for the task of person identification. In MFSSR, we designed a reconstructed deep spatial feature for representing the appearance of human body by using the spatial correlation coding of partial deep spatial features. Then we presented a multi-feature sparse similar representation model for jointly using different features, e.g., face, body, and the global image. Besides, considering that the coding coefficients associated with good samples but not outliers should be more similar among different features, we jointly represent different features by imposing a weighted ℓ1-norm distance regularization, instead of the conventional ℓ2-norm regularization, on the coefficients. Experimental results on several multi-feature person identification databases have clearly shown the superior performance of the proposed model.

Elevational diversity patterns of rodents differ between wet and arid mountains

AbstractAimPatterns of species richness along elevation gradients vary with geographic and environmental factors but evidence for similar variation in functional and phylogenetic diversity remains scarce. Here, we provide the most comprehensive evaluation to date of elevational gradients in taxonomic, functional, and phylogenetic diversity of rodents – one of the most ecologically diverse groups of mammals – and test the effects of latitude and aridity on their variation for the first time.LocationForty‐nine mountains on five continents.Time periodContemporary.Major taxa studiedRodents (Rodentia).MethodsWe compiled elevational distributions of 374 rodent species across 49 elevational gradients. For each gradient, we quantified – in 100‐m elevational bins – rodent species richness and functional and phylogenetic richness, evenness, and dispersion, and their species richness‐corrected equivalents. To assess how rodent diversity varies with elevation, we fitted a series of models that included elevation, average latitude, and aridity of each mountain system while accounting for variation in study design and sampling effort.ResultsA common mid‐elevational peak in species richness among mountains contrasts with functional and phylogenetic diversity pattern variation (model shape and slope) explained by the aridity at a mountain's base. Specifically, we find that functional and phylogenetic richness and dispersion decline with elevation in wet mountain systems but increase with elevation in arid mountains.Main conclusionsIn this first comparative analysis of mammal functional and phylogenetic elevational gradients, we find that the decoupling of each from species richness is particularly pronounced in arid regions. Wet‐mountain lowlands and arid‐mountain highlands harbour the most functionally and phylogenetically diverse rodent communities, indicating that water availability is a strong environmental filter in structuring diversity of small mammals on mountain gradients. High regularity of species distances within assemblages supports a constant role for competition across all elevations and niche expansion in elevations with greater species richness.

The Offset Position Prediction of Light Buoy Based on Grey Optimization Multiplicative Seasonal Model

Light buoy is a navigation aid sign to guide ship navigation, which plays an important role in ensuring the safety of ship navigation. To predict the offset distance of light buoy and provide accurate position information of light buoy for ship navigation safety, and to solve the problem of low prediction accuracy caused by the excessive amplitude of initial training data in the traditional multiplicative seasonal model, a grey optimization multiplicative seasonal model is proposed. By analyzing the characteristics of the time series of the light buoy offset data, as well as the regularity and seasonal characteristics of the light buoy offset distance, an optimization model is established. Based on the real offset distance data of the 1 # light buoy in Meizhou Bay, the model is simulated, and the prediction accuracy of the model is evaluated by MAPE, RMSE, and the Monte Carlo sampling method. The results show that, compared to the traditional multiplicative seasonal model, the average absolute percentage error of the grey optimization multiplicative seasonal model is reduced by 6.66%, and the root mean square error is reduced by 2.96. It shows that the model can effectively deal with the problem that the error of the prediction results caused by the instability of the initial time series of the traditional multiplicative seasonal model is too large, which provides a new idea for the prediction of the offset distance of the light buoy and the navigation safety of the ship.