Smoothing Step Research Articles

An Efficient and Versatile Variational Method for High-Dimensional Data Classification

High-dimensional data classification is a fundamental task in machine learning and imaging science. In this paper, we propose an efficient and versatile multi-class semi-supervised classification method for classifying high-dimensional data and unstructured point clouds. To begin with, a warm initialization is generated by using a fuzzy classification method such as the standard support vector machine or random labeling. Then an unconstraint convex variational model is proposed to purify and smooth the initialization, followed by a step which is to project the smoothed partition obtained previously to a binary partition. These steps can be repeated, with the latest result as a new initialization, to keep improving the classification quality. We show that the convex model of the smoothing step has a unique solution and can be solved by a specifically designed primal–dual algorithm whose convergence is guaranteed. We test our method and compare it with the state-of-the-art methods on several benchmark data sets. Thorough experimental results demonstrate that our method is superior in both the classification accuracy and computation speed for high-dimensional data and point clouds.

Transforming the Tradition of Discrete Milk Yield Correction Factors: A Continuous One-step DeLorenzo-Wiggans Method

Over the past decades, various methods have been proposed to estimate daily milk yields from partial yields. Many of these methods divide milking interval time into varied classes, assuming that the yield correction factors are constant within classes but vary between classes. The DeLorenzo and Wiggans (D-W) method has been widely used in the United States, typically following a 2-step process. It calculates discrete yield factors for segmented milking interval classes and then refines them through a follow-up smoothing step. Such a 2-step approach is computationally inefficient, and discrete yield correction factors introduce biases. This study explored strategies to integrate continuous yield factors into established methods, exemplified by the D-W method. The renovated method, also called the polynomial-interaction regression (PIR) model, postulates multiplicative yield correction factors as a linear or quadratic function of milking interval time, operating on interactions with partial yields. It utilizes all available data in a single step, exhibiting greater computability efficiency and higher estimation accuracy. A reparameterization leads to a linear model, making estimating the model parameters convenient. We evaluated the performance of the revised methods using a previous data set of milking records from Holstein cows compared with some existing methods. The results showed that the refurbished model gave more accurate estimates of daily milk yields.

Better Understanding Differences in Attribution Methods via Systematic Evaluations.

Deep neural networks are very successful on many vision tasks, but hard to interpret due to their black box nature. To overcome this, various post-hoc attribution methods have been proposed to identify image regions most influential to the models' decisions. Evaluating such methods is challenging since no ground truth attributions exist. We thus propose three novel evaluation schemes to more reliably measure the faithfulness of those methods, to make comparisons between them more fair, and to make visual inspection more systematic. To address faithfulness, we propose a novel evaluation setting (DiFull) in which we carefully control which parts of the input can influence the output in order to distinguish possible from impossible attributions. To address fairness, we note that different methods are applied at different layers, which skews any comparison, and so evaluate all methods on the same layers (ML-Att) and discuss how this impacts their performance on quantitative metrics. For more systematic visualizations, we propose a scheme (AggAtt) to qualitatively evaluate the methods on complete datasets. We use these evaluation schemes to study strengths and shortcomings of some widely used attribution methods over a wide range of models. Finally, we propose a post-processing smoothing step that significantly improves the performance of some attribution methods, and discuss its applicability.

Online Bayesian Optimization of Polynomial-Multigrid Cycles for Flux Reconstruction

In this study, we present a novel strategy for dynamically optimizing polynomial multigrid cycles to accelerate convergence within the dual-time-stepping formulation of the artificial compressibility method. To accomplish this, a Gaussian process model is developed using Bayesian optimization to efficiently sample possible cycles to minimize run-time. To allow the use of conventional optimization methods, we developed fractional smoothing steps, moving the optimization from a discrete space to a continuous space. Initially, a static, offline, approach was developed, and optimal cycles were found for two flow past cylinder test cases with Re=200 and Re=500; however, when exchanging optimal cycles between the different test cases, there was significant degradation in speedup. Toward this, a dynamic, online, approach was developed where cycles are optimized during a simulation. The performance of the resulting optimal cycles gave a similar speedup to the offline approach while achieving a net reduction in run-time. Again testing the optimization strategy on the flow past a cylinder, this yielded candidates with mean speedups of ∼3.0× and ∼2.1×, respectively. Finally, testing online optimization on a turbulent flow past a cylinder at Re=3900 resulted in an overall speedup of ∼1.9×.

A localized subdomain smoothing MMALE particle method for efficient modeling FSI problems

Fluid–structure-interaction (FSI) phenomena with multi-phase flow dynamics and structural damage commonly exist in engineering practice, which however bring great challenges to nowadays numerical FSI algorithms. A novel localized subdomain smoothing MMALE particle method (ls-ALEPM) is proposed in this paper for efficient and accurate simulations of large scale FSI problems. The MMALE method and the MPM are strongly coupled by immersing the MPM particles into the MMALE grid. In order to avoid the spurious strain induced by the mixed FSI velocity field, a decoupled stress updating scheme is proposed to update the stress of solid particles by introducing a virtual velocity field in the vicinity of FSI interface. And specifically, the highly accurate polyhedron intersection based method is employed for its remapping phase, which however is time-consuming. Thus, the localized subdomain smoothing method (LSSM) is put forward to accelerate the remapping phase which only involves the distorted regions of computational grid. The LSSM is composed of a distorted subdomain determination step and a combinated mesh smoothing step. Each iteration of the combinated mesh smoothing step consists of the modified GETMe and the weighted average method, and the transfinite interpolation method is adopted if the quality criteria is still not satisfied after prescribed maximum number of iterations. The validity and efficiency of ls-ALEPM is verified by several benchmark numerical examples and practical engineering simulations.

A Discontinuous Galerkin and Semismooth Newton Approach for the Numerical Solution of Bingham Flow with Variable Density

Abstract This paper is devoted to the study of Bingham flow with variable density. We propose a local bi-viscosity regularization of the stress tensor based on a Huber smoothing step. Next, our computational approach is based on a second-order, divergence-conforming discretization of the Huber regularized Bingham constitutive equations, coupled with a discontinuous Galerkin scheme for the mass density. We take advantage of the properties of divergence-conforming and discontinuous Galerkin formulations to effectively incorporate upwind discretizations, thereby ensuring the stability of the formulation. The stability of the continuous problem and the fully discrete scheme are analyzed. Further, a semismooth Newton method is proposed for solving the obtained fully discretized system of equations at each time step. Finally, several numerical examples that illustrate the main features of the problem and the properties of the numerical scheme are presented.

Difference of anisotropic and isotropic TV for segmentation under blur and Poisson noise

In this paper, we aim to segment an image degraded by blur and Poisson noise. We adopt a smoothing-and-thresholding (SaT) segmentation framework that finds a piecewise-smooth solution, followed by k-means clustering to segment the image. Specifically for the image smoothing step, we replace the least-squares fidelity for Gaussian noise in the Mumford-Shah model with a maximum posterior (MAP) term to deal with Poisson noise and we incorporate the weighted difference of anisotropic and isotropic total variation (AITV) as a regularization to promote the sparsity of image gradients. For such a nonconvex model, we develop a specific splitting scheme and utilize a proximal operator to apply the alternating direction method of multipliers (ADMM). Convergence analysis is provided to validate the efficacy of the ADMM scheme. Numerical experiments on various segmentation scenarios (grayscale/color and multiphase) showcase that our proposed method outperforms a number of segmentation methods, including the original SaT.

A Novel EM-Type Algorithm to Estimate Semi-Parametric Mixtures of Partially Linear Models

Semi- and non-parametric mixture of normal regression models are a flexible class of mixture of regression models. These models assume that the component mixing proportions, regression functions and/or variances are non-parametric functions of the covariates. Among this class of models, the semi-parametric mixture of partially linear models (SPMPLMs) combine the desirable interpretability of a parametric model and the flexibility of a non-parametric model. However, local-likelihood estimation of the non-parametric term poses a computational challenge. Traditional EM optimisation of the local-likelihood functions is not appropriate due to the label-switching problem. Separately applying the EM algorithm on each local-likelihood function will likely result in non-smooth function estimates. This is because the local responsibilities calculated at the E-step of each local EM are not guaranteed to be aligned. To prevent this, the EM algorithm must be modified so that the same (global) responsibilities are used at each local M-step. In this paper, we propose a one-step backfitting EM-type algorithm to estimate the SPMPLMs and effectively address the label-switching problem. The proposed algorithm estimates the non-parametric term using each set of local responsibilities in turn and then incorporates a smoothing step to obtain the smoothest estimate. In addition, to reduce the computational burden imposed by the use of the partial-residuals estimator of the parametric term, we propose a plug-in estimator. The performance and practical usefulness of the proposed methods was tested using a simulated dataset and two real datasets, respectively. Our finite sample analysis revealed that the proposed methods are effective at solving the label-switching problem and producing reasonable and interpretable results in a reasonable amount of time.

A forward-backward filter for estimating mud properties in SBCEX 17

The goal of SBCEX 17 was to investigate properties of the mud layer at the experiment site. We perform geoacoustic inversion for the mud site, integrating data and estimates obtained on a track of a moving source. The transmitted sound signals were LFM pulses in a mid-frequency range. The sound was received at a vertical array comprising 16 phones. Arrival times of multiple paths were extracted from the received signals using particle filtering and a backward-moving smoother: forward filtering and smoothing were applied to the received signals for the estimation of path arrival times generated by sound interacting with the waveguide. The smoothing step corrected for outliers that provided erroneous geoacoustic estimates for some source positions. The forward-backward filter provided accurate arrival times with a significant uncertainty reduction. The obtained arrival times were linked with a ray tracer and linearization for source localization and estimation of other parameters that affect sound propagation such as water column depth and sound speed. Sediment sound speed and thickness were then computed. Inversion was carried out at every source location within the track; the results were combined into a single set of estimates and corresponding probability density functions. [Work supported by ONR.]

A New Algorithm for Convex Biclustering and Its Extension to the Compositional Data

Biclustering is a powerful data mining technique that allows simultaneously clustering rows (observations) and columns (features) in a matrix-format data set, which can provide results in a checkerboard-like pattern for visualization and exploratory analysis in a wide array of domains. Multiple biclustering algorithms have been developed in the past two decades, among which the convex biclustering can guarantee a global optimum by formulating in as a convex optimization problem. On the other hand, the application of biclustering has not progressed in parallel with the algorithm techniques. For example, biclustering for increasingly popular microbiome research data is under-applied possibly due to its compositional constraints for each sample. In this manuscript, we propose a new convex biclustering algorithm, called the bi-ADMM, under general setups based on the ADMM algorithm, which is free of extra smoothing steps to visualize informative biclusters required by existing convex biclustering algorithms. Furthermore, we tailor it to the algorithm named biC-ADMM specifically to tackle compositional constraints confronted in microbiome data. The key step of our methods is to utilize the Sylvester Equation to derive the ADMM algorithm, which is new to the clustering research. The effectiveness of the proposed methods is examined through a variety of numerical experiments and a microbiome data application.

Fast Image Restoration Method Based on the L0, L1, and L2 Gradient Minimization

In this paper, we propose a novel image denoising method by coupling with L0, L1 and L2 gradient minimization. Our proposed method smoothes the gradient difference between image pixels and noise pixels and sharpens the edges by increasing the steepness of transition. We focus on global noise processing rather than local features and adaptively process noise signals with different characteristics. Based on the half-quadratic splitting method, we perform a smoothing step realized by a Poisson approach and two edge-preserving steps through an optimization formulation. This iterative method is fast, simple, and easy to implement. The proposed numerical scheme can be performed to a discrete cosine transform implementation, which can be applied with parallel GPUs computing in a straightforward manner. Various tests are presented, including both qualitative and quantitative tests, to demonstrate that the proposed method is efficient and robust for producing image processing results with good quality.

Arbitrary Lagrangian-Eulerian Remeshing in FE Simulations of Tire Forming

ABSTRACT Tire forming simulation is challenging for Lagrangian finite element method codes due to large changes in the geometry of the tire in the course of molding. This Technical Note briefly describes the use of Arbitrary Lagrangian-Eulerian (ALE) adaptive remeshing in the context of tire molding and curing simulations. The ALE concept generalizes the pure Lagrangian formulation, where the solution within a time step is split into a mesh smoothing step, a history remapping step, and a Lagrangian step. Mesh distortion is reduced in the smoothing step by optimizing the node positions of spatial and material meshes without changing the data structure. The advantage of the ALE approach is demonstrated by a tire forming example.

Planning system for the optimization of electric field delivery using implanted electrodes for brain tumor control.

The use of non-ionizing electric fields from low-intensity voltage sources (<10 V) to control malignant tumor growth is showing increasing potential as a cancer treatment modality. A method of applying these low-intensity electric fields using multiple implanted electrodes within or adjacent to tumor volumes has been termed as intratumoral modulation therapy (IMT). This study explores advancements in the previously established IMT optimization algorithm, and the development of a custom treatment planning system for patient-specific IMT. The practicality of the treatment planning system is demonstrated by implementing the full optimization pipeline on a brain phantom with robotic electrode implantation, postoperative imaging, and treatment stimulation. The integrated planning pipeline in 3D Slicer begins with importing and segmenting patient magnetic resonance images (MRI) or computed tomography (CT) images. The segmentation process is manual, followed by a semi-automatic smoothing step that allows the segmented brain and tumor mesh volumes to be smoothed and simplified by applying selected filters. Electrode trajectories are planned manually on the patient MRI or CT by selecting insertion and tip coordinates for a chosen number of electrodes. The electrode tip positions and stimulation parameters (phase shift and voltage) can then be optimized with the custom semi-automatic IMT optimization algorithm where users can select the prescription electric field, voltage amplitude limit, tissue electrical properties, nearby organs at risk, optimization parameters (electrode tip location, individual contact phase shift and voltage), desired field coverage percent, and field conformity optimization. Tables of optimization results are displayed, and the resulting electric field is visualized as a field-map superimposed on the MR or CT image, with 3D renderings of the brain, tumor, and electrodes. Optimized electrode coordinates are transferred to robotic electrode implantation software to enable planning and subsequent implantation of the electrodes at the desired trajectories. An IMT treatment planning system was developed that incorporates patient-specific MRI or CT, segmentation, volume smoothing, electrode trajectory planning, electrode tip location and stimulation parameter optimization, and results visualization. All previous manual pipeline steps operating on diverse software platforms were coalesced into a single semi-automated 3D Slicer-based user interface. Brain phantom validation of the full system implementation was successful in preoperative planning, robotic electrode implantation, and postoperative treatment planning to adjust stimulation parameters based on actual implant locations. Voltage measurements were obtained in the brain phantom to determine the electrical parameters of the phantom and validate the simulated electric field distribution. A custom treatment planning and implantation system for IMT has been developed in this study and validated on a phantom brain model, providing an essential step in advancing IMT technology toward future clinical safety and efficacy investigations.

A two-grid binary level set method for structural topology optimization

A binary level set method of two-grid type is proposed for structural topology optimization. The method allows both shape and topological changes during evolution with no need for reinitialization. The Galerkin finite element method is used to discretize the linear elasticity equation, the eigenvalue problem in structure and the semi-implicit time discrete level set equation. In order to improve the efficiency of the gradient-type algorithm as well as balance the computational efforts of solvers, a nested two-grid discretization strategy is proposed. The linear elasticity or eigenvalue problem is solved on a coarse mesh, while the level set equation and the smoothing step are both discretized on a fine mesh. A variety of numerical results are given to demonstrate both the efficiency and effectiveness of the algorithm.

Autohighlight: Highlight detection in League of Legends esports broadcasts via crowd-sourced data

Every minute, 500 h of footage is uploaded to Youtube.com, and ∼1900 h of footage is livestreamed on Twitch.tv. It can therefore be challenging for viewers to find the content they are most likely to enjoy. Highlight videos can entertain users who did not watch a broadcast, e.g. due to a lack of awareness, availability, or willingness. Furthermore, livestream content creators can grow their audiences by using highlights as advertisement, while also engaging casual followers who do not watch full broadcasts. However, hand-generating these videos is laborious, thus automatic highlight detection is an active research challenge. We examine automatic highlight detection by focusing on esports broadcasts. Esports are an emerging genre of sport played using a video games. We focus on League of Legends, a popular title with multiple professional leagues. Esports broadcasts are high-quality and professionally produced, mirroring traditional sports. We tackle the problem in a weakly supervised manner, utilising two datasets, one of ‘crowd-sourced’ highlight videos and one of unedited broadcasts. These datasets allow us to leverage massive data while hugely reducing the human cost of data curation and annotation. We propose two novel extensions to state-of-the-art rank-based highlight detection architectures. Firstly, a multimodal hybrid–fusion architecture that enables audio-visual highlight detection, and secondly, a smoothing step to incorporate context into decision making. Both extensions show significant improvement over state-of-the-art ranking models, in places performing nearly twice as well as competing architectures. Additionally, we examine the effectiveness of each modality and compare ranking models with classification based systems.

Bernoulli track‐before‐detect smoothing for maritime radar

Detection and tracking of small targets in sea clutter using a high-resolution radar is a challenging problem as the sea surface constantly moves in a complex manner, with rough seas creating strong target-like returns. Recently, a Bernoulli track-before-detect (TBD) filter has been developed for an airborne scanning radar in the maritime domain. Its purpose is to detect and track short-exposure targets by using the radar in a fast scanning mode. The current paper investigates the potential improvement in detection and tracking performance of the Bernoulli TBD filter by incorporating a backward smoothing step. The developed algorithm, referred to as the Bernoulli TBD forward-backward smoother (FBS) for maritime radar, is making a delayed decision by taking into account multiple future scans of radar data. A numerical analysis of a joint detection and tracking error with a fixed-lag smoothing is presented, as a function of the number of delay lags, signal-to-interference ratio and the sea clutter spikiness.

Smoothing Filter With a Variation of Coefficients for Tracking a Maneuvering Aerodynamic Target

The article offers a new filter for tracking a maneuvering aerodynamic target. During the process of the filter synthesis, three main requirements were considered: the filter must provide a minimum smoothing error in the areas without maneuver; the filter should ensure the minimum possible errors and emissions of smoothing error during the maneuver; filter must not contain additional constants, which take into account, for example, the value of input errors, parameters of target maneuver, period of information modification and so on. In order to meet these requirements a two-fold adjustment (variation) of the coefficients smoothing was used in accordance with the deviation of the coordinate of the newly measured position of the target (mark) from the extrapolated position. The variation is performed in accordance with the selected function, while the smoothing step acquires a certain conditional value. The proposed filter modelling has been performed. Received by modelling values of smoothing errors were compared with smoothing errors of other filters, described in scientific literature. The comparison results demonstrate a significant decrease in smoothing of the root mean square errors of coordinates and velocity in the proposed filter in comparison with other samples; with according to main requirements, any “tunes” in proposed filter were not used.

Extended Rauch–Tung–Striebel Smoother for the State of Charge Estimation of Lithium-Ion Batteries Based on an Enhanced Circuit Model

The state of charge (SOC) of a lithium battery system is critical since it indicates the remaining operating hours, full charge time, and peak power of the battery. This paper recommends an extended Rauch–Tung–Striebel smoother (ERTSS) for estimating SOC. It is implemented based on an improved equivalent circuit model with hysteresis voltage. The smoothing step of ERTSS will reduce the estimation error further. Additionally, the genetic algorithm (GA) is employed for searching the optimal ERTSS’s smoothing time interval. Various dynamic cell tests are conducted to verify the model’s accuracy and error estimation deviation. The test results demonstrate that ERTSS’s SOC estimation error is limited to 4% with an initial error between −25 ∘C and 45 ∘C and that the root mean square error (RMSE) of ERTSS’s SOC estimation is approximately 5% lower than that of extended Kalman filter (EKF). The ERTSS improves the SOC estimation accuracy at all operating temperatures of batteries.

Obstacle Avoidance for UAS in Continuous Action Space Using Deep Reinforcement Learning

Obstacle avoidance for small unmanned aircraft is vital for the safety of future urban air mobility (UAM) and Unmanned Aircraft System (UAS) Traffic Management (UTM). There are a variety of techniques for real-time robust drone guidance, but numerous of them solve in discretized airspace and control, which would require an additional path smoothing step to provide flexible commands for UAS. To deliver safe and computationally efficient guidance for UAS operations, we explore the use of a deep reinforcement learning algorithm based on Proximal Policy Optimization (PPO) to lead autonomous UAS to their destinations while bypassing obstacles through continuous control. The proposed scenario state representation and reward function can map the continuous state space to continuous control for both heading angle and speed. To verify the effectiveness of the proposed learning framework, we conducted numerical experiments with static and moving obstacles. Uncertainties associated with the environments and safety operation bounds are investigated in detail. Results show that the proposed model is able to provide accurate and robust guidance and resolve conflict with a success rate of over 99%.

Detection and Optimization of Traffic Networks Based on Voronoi Diagram

Traffic peak is an important parameter of modern transport systems. It can be used to calculate the indices of road congestion, which has become a common problem worldwide. With accurate information about traffic peaks, transportation administrators can make better decisions to optimize the traffic networks and therefore enhance the performance of transportation systems. We present a traffic peak detection method, which constructs the Voronoi diagram of the input traffic flow data and computes the prominence of candidate peak points using the diagram. Salient peaks are selected based on the prominence. The algorithm takes O(n log n) time and linear space, where n is the size of the input time series. As compared with the existing algorithms, our approach works directly on noisy data and detects salient peaks without a smoothing prestep and thus avoids the dilemma in choosing an appropriate smoothing scale and prevents the occurrence of removing/degrading real peaks during smoothing step. The prominence of candidate peaks offers the subsequent analysis the flexibility to choose peaks at any scale. Experiments illustrated that the proposed method outperforms the existing smoothing-based methods in sensitivity, positive predictivity, and accuracy.