Laplacian Smoothing Research Articles

Filtering Useful App Reviews Using Naïve Bayes—Which Naïve Bayes?

App reviews provide crucial feedback for software maintenance and evolution, but manually extracting useful reviews from vast volumes is time-consuming and challenging. This study investigates the effectiveness of six Naïve Bayes variants for automatically filtering useful app reviews. We evaluated these variants on datasets from five popular apps, comparing their performance in terms of accuracy, precision, recall, F-measure, and processing time. Our results show that Expectation Maximization-Multinomial Naïve Bayes with Laplace smoothing performed best overall, achieving up to 89.2% accuracy and 0.89 F-measure. Complement Naïve Bayes with Laplace smoothing demonstrated particular effectiveness for imbalanced datasets. Generally, incorporating Laplace smoothing and Expectation Maximization improved performance, albeit with increased processing time. This study also examined the impact of data imbalance on classification performance. Our findings suggest that these advanced Naïve Bayes variants hold promise for filtering useful app reviews, especially when dealing with limited labeled data or imbalanced datasets. This research contributes to the body of evidence around app review mining and provides insights for enhancing software maintenance and evolution processes.

Grid Optimization of Free-Form Spatial Structures Considering the Mechanical Properties

In recent years, the application of free-form surface spatial grid structures in large public buildings has become increasingly common. The layouts of grids are important factors that affect both the mechanical performance and aesthetic appeal of such structures. To achieve a triangular grid with good mechanical performance and uniformity on free-form surfaces, this study proposes a new method called the “strain energy gradient optimization method”. The grid topology is optimized to maximize the overall stiffness, by analyzing the sensitivity of nodal coordinates to the overall strain energy. The results indicate that the overall strain energy of the optimized grid has decreased, indicating an improvement in the structural stiffness. Specifically, compared to the initial grid, the optimized grid has a 30% decrease in strain energy and a 43.3% decrease in maximum nodal displacement. To optimize the smoothness of the grid, the study further applies the Laplacian grid smoothing method. Compared to the mechanically adjusted grid, the structural mechanical performance does not significantly change after smoothing, while the geometric indicators are noticeably improved, with smoother lines and regular shapes. On the other hand, compared to the initial grid, the smoothed grid has a 21.4% decrease in strain energy and a 28.3% decrease in maximum nodal displacement.

Application of Surface-Based Smoothing Methods for Topology Optimization Results

Topology optimization (TO) is becoming an essential part of designing new or modifying current parts to improve their properties. A typical problem of TO in structural applications is minimizing compliance with volume (mass) constraints. TO is often complemented by additive manufacturing which allows the printing of complex geometries. Resulting geometries are dependent on the used method, most of the time it is the finite element method. The exported geometry from the optimization procedure, however, tends to have a lot of sharp edges, which causes problems with stress distribution, aesthetics and manufacturing (even if it is additive manufactured). The aim of this paper is to review, apply smoothing techniques on the surface of bodies, Laplacian and Taubin smoothing, and compare the results of smoothing. To fulfill this aim, we developed a smoothing procedure and evaluated the criteria of smoothed-out polymer geometries.

Feedrate-preserved motion planning for five-axis directed energy deposition of freeform metal parts

Laser-powder DED (LP-DED) has been investigated extensively for the rapid prototype of complex and customized metallic parts and in-situ repairing tasks. However, unlike the material extrusion type which allows a relatively large overhang angle, the conventional 2.5-axis LP-DED faces a severe overhang issue that deteriorates the printing stability and quality. While five-axis LP-DED is able to effectively resolve the overhang problem, it however introduces new kinematic issues and limited nozzle orientation range due to physical restrictions of DED. The existing computer numerical control systems are mainly designed for machining, where the above issues can be mostly solved by feedrate scheduling, which, however, is not applicable for LP-DED processes, as the feedrate must be preserved as programmed lest deposition height would be altered since in most cases it is not practical to vary the powder flow rate in real-time. In this paper, a feedrate-preserved motion planning method is proposed to optimize the rotational angles of the machine tool in the machine coordinate system (MCS) under the constraints of MCS and workpiece coordinate system (WCS). Given a five-axis DED path as well as its accompanying initial nozzle orientation in WCS, we first map them via inverse kinematics to MCS, which is represented by a cylindrical coordinate system. Then, the motion path in the cylindrical coordinate system is optimized to avoid the singularity. Finally, the physical constraint of nozzle orientation in WCS is introduced into the time-weighted constrained Laplacian smoothing in MCS with the axial speed limits upheld. The experimental results confirm that the actual feedrate is successfully preserved as the theoretical one under the constraints of the axial kinematic limits, while the singularity is avoided.

An unsupervised deep global–local views model for anomaly detection in attributed networks

An attribute network is a form of data that contains rich semantic information. Many real scenarios can be modeled as attributed networks, such as social media, citations, and traffic networks. Anomaly detection in attributed networks is an interesting research topic owing to its potential in various practical applications, including spam, network intrusion, and financial fraud detection. However, attributed networks exhibit many anomaly patterns, such as structural, attribute, local, and global anomalies, making anomaly detection in attributed networks a challenging task. To address these difficulties, we designed DeepGL, a novel unsupervised deep global–local view model, for anomaly detection in attributed networks. Our model is an encoder–decoder framework with multiple views that capture node attributes and network structure information from both global and local views. Specifically, our model contains two encoders and four decoders. The two encoders are used to capture network features from local and global views, and the four decoders are used to reconstruct the local node attribute information, local structure information, global node attribute information, and global structure information. To the encoders and decoders, we applied Laplacian sharpening and smoothing techniques to maintain the integrity of normal node features while diminishing the conspicuousness of anomalous nodes in the reconstructed information, thereby facilitating the calculation of reconstruction errors. Extensive experiments on four real-world attributed network datasets demonstrate the excellent performance of the proposed method.

Differentially private federated learning with Laplacian smoothing

Federated learning aims to protect data privacy by collaboratively learning a model without sharing private data among users. However, an adversary may still be able to infer the private training data by attacking the released model. Differential privacy provides a statistical protection against such attacks at the price of significantly degrading the accuracy or utility of the trained models. In this paper, we investigate a utility enhancement scheme based on Laplacian smoothing for differentially private federated learning (DP-Fed-LS), to improve the statistical precision of parameter aggregation with injected Gaussian noise without losing privacy budget. Our key observation is that the aggregated gradients in federated learning often enjoy a type of smoothness, i.e. sparsity in a graph Fourier basis with polynomial decays of Fourier coefficients as frequency grows, which can be exploited by the Laplacian smoothing efficiently. Under a prescribed differential privacy budget, convergence error bounds with tight rates are provided for DP-Fed-LS with uniform subsampling of heterogeneous non-iid data, revealing possible utility improvement of Laplacian smoothing in effective dimensionality and variance reduction, among others. Experiments over MNIST, SVHN, and Shakespeare datasets show that the proposed method can improve model accuracy with DP-guarantee and membership privacy under both uniform and Poisson subsampling mechanisms.

Generated realistic noise and rotation-equivariant models for data-driven mesh denoising

3D mesh denoising is a crucial pre-processing step in many graphics applications. However, existing data-driven mesh denoising models, primarily trained on synthetic white noise, are less effective when applied to real-world meshes with the noise of complex intensities and distributions. Moreover, how to comprehensively capture information from input meshes and apply suitable denoising models for feature-preserving mesh denoising remains a critical and unresolved challenge. This paper presents a rotation-Equivariant model-based Mesh Denoising (EMD) model and a Realistic Mesh Noise Generation (RMNG) model to address these issues. Our EMD model leverages rotation-equivariant features and self-attention weights of geodesic patches for more effective feature extraction, thereby achieving SOTA denoising results. The RMNG model, based on the Generative Adversarial Networks (GANs) architecture, generates massive amounts of realistic noisy and noiseless mesh pairs data for data-driven mesh denoising model training, significantly benefiting real-world denoising tasks. To address the smooth degradation and loss of sharp edges commonly observed in captured meshes, we further introduce varying levels of Laplacian smoothing to input meshes during the paired training data generation, endowing the trained denoising model with feature recovery capabilities. Experimental results demonstrate the superior performance of our proposed method in preserving fine-grained features while removing noise on real-world captured meshes.

An Updated Fault Coupling Model Along Major Block‐Bounding Faults on the Eastern and Northeastern Tibetan Plateau From a Stress‐Constrained Inversion of GPS and InSAR Data

AbstractLarge block‐bounding faults on the Tibetan plateau are significant geological structures that accommodate tectonic movements and accumulate stress, leading to large earthquakes. Quantifying the interseismic slip deficit rate helps to better assess the earthquake potential. We combine available InSAR (2015–2020) and interseismic GPS data to determine fault coupling along 14 major block‐bounding faults. Spatially dense InSAR measurements remarkably improve the resolution of the coupling model. Combined with a GPS‐constrained block model, we examine the performance of the inversion approach with the stress constraint and the common Laplacian smoothing based on both synthetic tests and real data. We suggest that, for continental strike‐slip faults, adding the stress constraint can mitigate unphysical coupling distributions due to unreasonable assumptions or modeling artifacts, reducing the model uncertainty and improving the accuracy of the coupling model. This is particularly useful for segments featured by a highly heterogeneous distribution of coupling along the transition zone from locking to creeping region, partially‐coupling segment, and junction zone between main and subsidiary faults. We present a large‐scale fault coupling map along the major block‐bounding faults on the northeastern and eastern Tibetan plateau, highlighting the distinct degrees of fault coupling and lateral variations. The collage of coupling maps along different faults demonstrates the kinematic features over a broad time scale during earthquake cycles ranging from early to late interseismic phases, such as the segments ruptured during the 2001 Kokoxili earthquake and the 1920 Haiyuan earthquake.

Establishment and preliminary application of personalized three-dimensional reconstruction of thyroid gland with automatic detection of thyroid nodules based on ultrasound videos.

A well display of the spatial location of thyroid nodules in the thyroid is important for surgical path planning and surgeon-patient communication. The aim of this study was to establish a three-dimensional (3D) reconstruction method of the thyroid gland, thyroid nodule, and carotid artery with automatic detection based on two-dimensional (2D) ultrasound videos, and to evaluate its clinical value. Ultrasound videos, including the thyroid gland with nodule, isthmus of thyroid gland, and ipsilateral carotid artery, were recorded. BC-UNet, MTN-Net, and RDPA-U-Net network models were innovatively employed for segmentation of the thyroid glands, the thyroid nodules, and the carotid artery respectively. Marching Cubes algorithm was used for reconstruction, while Laplacian smoothing algorithm was employed to smooth the 3D model surface. Using this model, 20 patients and 15 surgeons completed surveys on the effectiveness of this model for the pre-surgery demonstration of nodule location as well as surgeon-patient communication. The thyroid gland with nodule, isthmus of gland, and carotid artery were reconstructed and displayed. With the 3D model, the understanding of the spatial location of thyroid nodules improved in all three surgeon groups, eliminating the influence of professional levels. In the patient survey, the patients' understanding of the thyroid nodule location and procedure for surgery were significantly improved. In addition, with the 3D model, the time for doctors to explain to patients was significantly reduced (16.75 vs. 8.85min, p=0.001). To our knowledge, this is the first report of constructing a 3D thyroid model using a deep learning technique for personalized thyroid segmentation based on 2D ultrasound videos. The preliminary clinical application showed that it was conducive to the comprehension of the location of thyroid nodules for surgeons and patients, with significant improvement on the efficiency of surgeon-patient communication.

Towards Fine-Grained HBOE with Rendered Orientation Set and Laplace Smoothing

Human body orientation estimation (HBOE) aims to estimate the orientation of a human body relative to the camera’s frontal view. Despite recent advancements in this field, there still exist limitations in achieving fine-grained results. We identify certain defects and propose corresponding approaches as follows: 1). Existing datasets suffer from non-uniform angle distributions, resulting in sparse image data for certain angles. To provide comprehensive and high-quality data, we introduce RMOS (Rendered Model Orientation Set), a rendered dataset comprising 150K accurately labeled human instances with a wide range of orientations. 2). Directly using one-hot vector as labels may overlook the similarity between angle labels, leading to poor supervision. And converting the predictions from radians to degrees enlarges the regression error. To enhance supervision, we employ Laplace smoothing to vectorize the label, which contains more information. For fine-grained predictions, we adopt weighted Smooth-L1-loss to align predictions with the smoothed-label, thus providing robust supervision. 3). Previous works ignore body-part-specific information, resulting in coarse predictions. By employing local-window self-attention, our model could utilize different body part information for more precise orientation estimations. We validate the effectiveness of our method in the benchmarks with extensive experiments and show that our method outperforms state-of-the-art. Project is available at: https://github.com/Whalesong-zrs/Towards-Fine-grained-HBOE.

HybridOctree_Hex: Hybrid octree-based adaptive all-hexahedral mesh generation with Jacobian control

We present a new software package, “HybridOctree_Hex,” for adaptive all-hexahedral mesh generation based on hybrid octree and quality improvement with Jacobian control. The proposed HybridOctree_Hex begins by detecting curvatures and narrow regions of the input boundary to identify key surface features and initialize an octree structure. Subsequently, a strongly balanced octree is constructed using the balancing and pairing rules. Inspired by our earlier preliminary hybrid octree-based work, templates are designed to guarantee an all-hexahedral dual mesh generation directly from the strongly balanced octree. With these pre-defined templates, the sophisticated hybrid octree construction step is skipped to achieve an efficient implementation. After that, elements outside and around the boundary are removed to create a core mesh. The boundary points of the core mesh are connected to their corresponding closest points on the surface to fill the buffer zone and build the final mesh. Coupled with smart Laplacian smoothing, HybridOctree_Hex takes advantage of a delicate optimization-based quality improvement method considering geometric fitting, Jacobian and scaled Jacobian, to achieve a minimum scaled Jacobian that is higher than 0.5. We empirically verify the robustness and efficiency of our method by running the HybridOctree_Hex software on dozens of complex 3D models without any manual intervention or parameter adjustment. We provide the HybridOctree_Hex source code, along with comprehensive results encompassing the input and output files and statistical data in the following repository: https://github.com/CMU-CBML/HybridOctree_Hex.

A new strain-based pentagonal membrane finite element for solid mechanics problems

Polygonal finite elements remain an attractive option in finite element analysis due to their flexibility in modeling arbitrary shapes compared to triangles. In this study, a pentagonal membrane element was developed with the strain approach for the first time. The element possesses invariance, and the equilibrium constraint was applied to the assumed strain field using corrective coefficients. Inspired by the advancing front technique, a pentagonal mesh was generated, and the mesh quality was enhanced with Laplacian smoothing. The performance of the developed pentagonal element was assessed in a few numerical tests, and the results revealed its suitability in modeling the bending of beams. Besides, the numerical results are enhanced when pentagonal elements are used in mesh transitions along boundaries to smoothen curved edges and capture distributed loads.

Imbalance Dataset in Aspect-Based Sentiment Analysis on Game Genshin Impact Review

Sentiment analysis was commonly used to determine the polarity of the review text. However, there is a problem if some reviews have more than one aspect with different polarities, so the reviews have more than one polarity. That has happened in some reviews on the game Genshin Impact. Not merely that, the number of sentiments contained in a review is not always the same as other reviews will cause imbalanced data. So, this study will handle imbalance data with Random Under-Sampling and Random Over-Sampling on aspect-based-sentiment-analysis of Genshin Impact Review with Multinomial Naïve-Bayes, so that the classification prediction does not ignore the minority class due to the dominance of the majority class. The classification process used K-Fold Cross Validation (k=10) validation method and the Laplace smoothing technique on Multinomial Naïve Bayes. As a result, the conclusion is that Random Oversampling had better accuracy than Random Undersampling in handling imbalanced data on aspect-based sentiment analysis of Genshin Impact game Review in Indonesian with Naïve Bayes Multinomial, with the highest accuracy of 85.55%.

Formation and evolution of vortex breakdown consequent to post design flow increase in a Francis turbine

Draft tube flow instability encountered under off-design operating conditions in hydraulic turbines significantly limits their operational flexibility. The instability arises consequent to a higher than threshold swirl content in the runner outflow and leads to vortex breakdown phenomenon in the draft tube cone. At high load condition, the phenomenon presents as an enlarged vortex core counter-rotating with respect to the runner. The flow situation is known to compromise the turbine efficiency besides the generation of unwanted effects such as power swings and large-scale pressure fluctuations. The present paper is the first to encapsulate a thorough numerical investigation on the formation and evolution of the enlarged vortex core alongside the consequent effects. A transient operating sequence between best efficiency and high load operating points in a model Francis turbine is simulated. Turbulence closure has been attained using the shear stress transport-scale adaptive simulations turbulence model. Dynamic meshing based on a Laplacian smoothing scheme has been used to account for mesh deformation arising from guide vane motion during load change. The pressure and velocity fields have been determined and analyzed to elucidate the physics of vortex breakdown, the phenomenon underlying the formation of the enlarged vortex core. Furthermore, pressure fluctuations at salient points in the domain have been analyzed using Fourier and short-time Fourier transforms. Finally, the enlarged vortex core formed in the draft tube has been visualized through the λ2 criterion. The core takes the shape of a cork-screw like compactly wound spiral structure extending up to the draft tube elbow.

An extended Laplacian smoothing for boundary element analysis of 3D bubble dynamics

Frequently, smoothing techniques have to be applied to tackle the numerical instability and mesh distortion in modelling bubble dynamics using the boundary element method (BEM). Laplacian smoothing (LS) and its variants have been commonly used in the literature due to their ease of implementation and computational efficiency. Nevertheless, these methods are prone to inducing shrinking and oversmoothing effects. To address this issue, an efficient smoothing technique, called the Extended LS (ELS) method, is devised based on the LS method to accurately capture the salient features of the liquid jet of a collapsing bubble near complex boundaries. The efficacy of the ELS method is demonstrated through its application to various test cases for which theoretical, numerical, or experimental data are available in the literature. The ELS method is then used to simulate intricate bubble dynamics, including the oscillation of a 3D gas bubble near two rigid, fixed spherical particles. The influence of the dimensionless distance d∗ between the bubble and the particles on the dynamics of the bubble is thoroughly examined. As d∗ decreases, the bubble moves closer to the particles, causing its lower side surface to change from concave to convex.

Eligibility Classification of Aid Recipients Hope Family Program in Cinta Rakyat Village Using the Method Weighted Naive Bayes with Laplace Smoothing

The Indonesian government sometimes faces difficulties in dealing with poverty problems. The Indonesian government utilizes a number of programs and stimulants to overcome the problem of poverty. The government's PKH program offers conditional assistance to low-income families who have been designated as PKH recipient households. PKH provision is still below optimal standards, this may be because the data used is not updated frequently. To assist village officials in determining which residents are eligible to receive PKH assistance, this research tries to classify the eligibility of recipient residents in Cinta Rakyat Village. With the Weighted Naive Bayes method, classification calculations are not only based on probability distributions but also by adding weights to each attribute to the class. Assisted with Laplace Smoothing to avoid a probability value of 0. As a result, there are eight factors that determine a person's eligibility to receive PKH assistance, including age, occupation, income, number of family members, number of dependent school children, quality of house, type of floor, and type of walls. As well as classification into eligible and non-eligible groups. And obtained test results using the Confusion Matrix with an accuracy value of 95.65%, error rate of 4.34%, sensitivity of 100% and specificity of 94.74%. To identify village communities who deserve PKH assistance, Cinta Rakyat Village administrators can use the findings of this research.

Performance-Based Analysis of Mesh Smoothing Methods Combining Topology Optimization and Additive Manufacturing

Most design-to-manufacturing frameworks combining topology optimization (TO) and additive manufacturing (AM) integrate mesh smoothing methods as post-processing techniques to remove discrete irregularities of optimized topologies. Notably, a design framework is proposed incorporating all the CAD development stages within the design phase providing smooth and ready-to-print topologies. The Laplacian-based smoothing algorithms have demonstrated a high capacity in removing surface noise. This study focuses on investigating the smoothing capacity of both HC Laplacian and Taubin methods using mesh quality metrics to assess on their performance in terms of geometric preservation and volume shrinkage. Taubin method was found to produce high-quality smooth meshes with less volume shrinkage compared to HC Laplacian. The Taubin model exhibited an increase of 15.06% in mesh volume whereas the HC Laplacian model had a volume shrinkage of 28.14%. Additionally, finite element analyses of the three-point bending test using ANSYS is set to measure the flexural stiffness of an optimized MBB beam under both HC Laplacian and Taubin smoothing methods. Overall, the flexural stiffness of Taubin is nearly two times the original model with a surplus of 46.91% whereas HC Laplacian exhibited a flexural stiffness that is less with 72.07% than the original model.

Adaptive Smoothing for Visual Improvement of Image Quality via the p(x)-Laplacian Operator Effects of the p(x)-Laplacian Smoothing Operator on Digital Image Restoration: Contribution to an Adaptive Control Criterion

This article concerns the improvement of digital image quality using mathematical tools such as nonlinear partial differential operators. In this paper, to perform smoothing on digital images, we propose to use the p(x)-Laplacian operator. Its smoothing power plays a main role in the restoration process. This enables us to dynamically process certain areas of an image. We used a mathematical model of image regularisation that is described by a nonlinear diffusion Equation (this diffusion is modelled by the p(x)-Laplacian operator). We implemented the continuous model in order to observe the steps of the regularisation process to understand the effects of the different parameters of the model on an image. This will enable parameters to be used and adapted in order to provide a proposed solution.

Dynamic personalized graph neural network with linear complexity for multivariate time series forecasting

Spatio-temporal graph neural networks (GNN) that model inter-variable dependencies with learned graph structures for multivariate time series forecasting have received attention due to their superior performance. However, existing methods exhibit quadratic complexity, limiting the GNN’s capability to handle a large number of variables. Moreover, the message-passing mechanism employed by spatio-temporal GNNs can be seen as a type of Laplacian smoothing, which weakens the inherent evolution patterns of nodes and overlooks the dynamic impact of a node’s own information and that of its neighbors on future outcomes. In this paper, we propose a novel approach called the Dynamic Personalized Graph Neural Network (DPGNN), which presents a graph learning framework with linear complexity. To facilitate linearization, we conceptualize the spatio-temporal GNN as an information flow from the source (raw node features) to the sink (new node features). And the flow conservation principle is employed to generate the information attention mechanism to effectively model the dependency between variables. To address the second issue, inspired by PageRank, we design a dynamic personalized graph convolution scheme that explicitly quantifies the impact of each node on the subsequent results based on the dynamic graph signals at each propagation step. Experimental results on six benchmark datasets showcase the superiority of our approach over state-of-the-art methods, including both pre-defined graph structures and graph learning techniques.

Graph Clustering with High-Order Contrastive Learning.

Graph clustering is a fundamental and challenging task in unsupervised learning. It has achieved great progress due to contrastive learning. However, we find that there are two problems that need to be addressed: (1) The augmentations in most graph contrastive clustering methods are manual, which can result in semantic drift. (2) Contrastive learning is usually implemented on the feature level, ignoring the structure level, which can lead to sub-optimal performance. In this work, we propose a method termed Graph Clustering with High-Order Contrastive Learning (GCHCL) to solve these problems. First, we construct two views by Laplacian smoothing raw features with different normalizations and design a structure alignment loss to force these two views to be mapped into the same space. Second, we build a contrastive similarity matrix with two structure-based similarity matrices and force it to align with an identity matrix. In this way, our designed contrastive learning encompasses a larger neighborhood, enabling our model to learn clustering-friendly embeddings without the need for an extra clustering module. In addition, our model can be trained on a large dataset. Extensive experiments on five datasets validate the effectiveness of our model. For example, compared to the second-best baselines on four small and medium datasets, our model achieved an average improvement of 3% in accuracy. For the largest dataset, our model achieved an accuracy score of 81.92%, whereas the compared baselines encountered out-of-memory issues.