Sparse Set Research Articles

Reconstructing Curves from Sparse Samples on Riemannian Manifolds

AbstractReconstructing 2D curves from sample points has long been a critical challenge in computer graphics, finding essential applications in vector graphics. The design and editing of curves on surfaces has only recently begun to receive attention, primarily relying on human assistance, and where not, limited by very strict sampling conditions. In this work, we formally improve on the state‐of‐the‐art requirements and introduce an innovative algorithm capable of reconstructing closed curves directly on surfaces from a given sparse set of sample points. We extend and adapt a state‐of‐the‐art planar curve reconstruction method to the realm of surfaces while dealing with the challenges arising from working on non‐Euclidean domains. We demonstrate the robustness of our method by reconstructing multiple curves on various surface meshes. We explore novel potential applications of our approach, allowing for automated reconstruction of curves on Riemannian manifolds.

A point mapping strategy-based sparse grid integration method for statistical moments estimation and structural reliability analysis

The high-order moment-based method is an attractive non-intrusive approach for structural reliability analysis, while it remains a challenge to strike a balance between accuracy, efficiency, and versatility in estimating statistical moments of performance functions. In this paper, a point mapping strategy-based sparse grid integration (SGI) method is proposed for statistical moment estimation and structural reliability analysis, with improved efficiency while ensuring the accuracy. Firstly, a point mapping strategy (PMS) is developed based on the adaptive high dimensional model representation (HDMR), by which the traditional SGI is reconstructed as a sum of multiple integrations over the sparse grid point sets with different effective dimensions. With this new form of SGI, the estimation of statistical moments only requires the evaluation of the performance function at a small number of necessary reference points, once the effects of some interaction terms are negligible. The validity and feasibility of the proposed PMS-based SGI method for statistical moments estimation are verified by several numerical examples. Then, the proposed method is applied to structural reliability analysis with the aid of an improved maximum entropy method. Two engineering examples are investigated, including the strength failure problem of tubular tower K-shape connection joints and the fatigue failure problem of a marine riser resulting from the vortex-induced vibration (VIV). The results indicate that the proposed method provides a better trade-off between accuracy and efficiency in evaluating the first four order statistical moments and structural failure probability compared to conventional methods.

3Doodle: Compact Abstraction of Objects with 3D Strokes

While free-hand sketching has long served as an efficient representation to convey characteristics of an object, they are often subjective, deviating significantly from realistic representations. Moreover, sketches are not consistent for arbitrary viewpoints, making it hard to catch 3D shapes. We propose 3Dooole, generating descriptive and view-consistent sketch images given multi-view images of the target object. Our method is based on the idea that a set of 3D strokes can efficiently represent 3D structural information and render view-consistent 2D sketches. We express 2D sketches as a union of view-independent and view-dependent components. 3D cubic Bézier curves indicate view-independent 3D feature lines, while contours of superquadrics express a smooth outline of the volume of varying viewpoints. Our pipeline directly optimizes the parameters of 3D stroke primitives to minimize perceptual losses in a fully differentiable manner. The resulting sparse set of 3D strokes can be rendered as abstract sketches containing essential 3D characteristic shapes of various objects. We demonstrate that 3Doodle can faithfully express concepts of the original images compared with recent sketch generation approaches. 1

Generative subgoal oriented multi-agent reinforcement learning through potential field

Multi-agent reinforcement learning (MARL) effectively improves the learning speed of agents in sparse reward tasks with the guide of subgoals. However, existing works sever the consistency of the learning objectives of the subgoal generation and subgoal reached stages, thereby significantly inhibiting the effectiveness of subgoal learning. To address this problem, we propose a novel Potential field Subgoal-based Multi-Agent reinforcement learning (PSMA) method, which introduces the potential field (PF) to unify the two-stage learning objectives. Specifically, we design a state-to-PF representation model that describes agents’ states as potential fields, allowing easy measurement of the interaction effect for both allied and enemy agents. With the PF representation, a subgoal selector is designed to automatically generate multiple subgoals for each agent, drawn from the experience replay buffer that contains both individual and total PF values. Based on the determined subgoals, we define an intrinsic reward function to guide the agent to reach their respective subgoals while maximizing the joint action-value. Experimental results show that our method outperforms the state-of-the-art MARL method on both StarCraft II micro-management (SMAC) and Google Research Football (GRF) tasks with sparse reward settings.

Validating and speeding up x-ray tomographic inversions in tokamak plasmas

X-ray tomography is a precious tool in tokamaks that provides rich information about the core plasma, such as local impurity concentration, electron temperature and density as well as magnetic equilibrium (ME) and magnetohydrodynamic activity. Nevertheless, inferring the local plasma emissivity from a sparse set of line-integrated measurements is an ill-posed problem that requires dedicated regularization and validation methods. Besides, speeding up the inversion algorithm in order to be compatible with real-time control systems is a challenging task with traditional approaches. In this contribution, in a first part we introduce tools aiming at validating and speeding up the x-ray tomographic inversions based on Tikhonov regularization, including ME constraint and parameter optimization, taking the WEST geometry as an example. In a second part, an alternative approach compatible with real-time, based on a set of neural networks is proposed and compared with the Tikhonov approach for an experimental case.

Keyframe Control of Music-Driven 3D Dance Generation.

For 3D animators, choreography with artificial intelligence has attracted more attention recently. However, most existing deep learning methods mainly rely on music for dance generation and lack sufficient control over generated dance motions. To address this issue, we introduce the idea of keyframe interpolation for music-driven dance generation and present a novel transition generation technique for choreography. Specifically, this technique synthesizes visually diverse and plausible dance motions by using normalizing flows to learn the probability distribution of dance motions conditioned on a piece of music and a sparse set of key poses. Thus, the generated dance motions respect both the input musical beats and the key poses. To achieve a robust transition of varying lengths between the key poses, we introduce a time embedding at each timestep as an additional condition. Extensive experiments show that our model generates more realistic, diverse, and beat-matching dance motions than the compared state-of-the-art methods, both qualitatively and quantitatively. Our experimental results demonstrate the superiority of the keyframe-based control for improving the diversity of the generated dance motions.

Prediction of glass transition temperature of oxide glasses based on interpretable machine learning and sparse data sets

The glass transition temperature (Tg) is a crucial characteristic of oxide glasses, exerting significant influence on their properties and applications. In this study, we utilized a sparse dataset and machine learning techniques to establish a predictive model for the relationship between the composition of oxide glasses and Tg. Among four machine learning algorithms compared, the Extreme Tree Regressor (ETR) algorithm demonstrated superior performance, exhibiting robust generalization capabilities on the validation set. We performed feature selection on the original features using Pearson Correlation Coefficient (PCC) and Maximal Information Coefficient (MIC), resulting in a subset of 38 dimensions. Subsequently, we employed Sparse Principal Component Analysis (PCA) and Recursive Feature Elimination (RFE) for dimensionality reduction, yielding a final subset of 12 dimensions. Introducing SHapley Additive exPlanations (SHAP) values for interpretability analysis of the predictive model, we obtained important feature rankings and analyzed how variations in features affect the target variable. Finally, using the CaO-SiO2-Al2O3 system as an example, we demonstrated how the model predicts Tg based on composition, facilitating rational design of oxide glass compositions.

Deep self-reconstruction driven joint nonnegative matrix factorization model for identifying multiple genomic imaging associations in complex diseases

ObjectiveComprehensive analysis of histopathology images and transcriptomics data enables the identification of candidate biomarkers and multimodal association patterns. Most existing multimodal data association studies are derived from extensions of the joint nonnegative matrix factorization model for identifying complex data associations, which can make full use of clinical prior information. However, the raw data were usually taken as the input without considering the underlying complex multi-subspace structure, influencing the subsequent integration analysis results. MethodsThis study proposed a deep-self reconstructed joint nonnegative matrix factorization (DSRJNMF) model to use self-expressive properties to reconstruct the raw data to characterize the similarity structure associated with clinical labels. Then, the sparsity, orthogonality, and regularization constraints constructed from prior information are added to the DSRJNMF model to determine the sparse set of biologically relevant features across modalities. ResultsThe algorithm has been applied to identify the imaging genetic association of triple negative breast cancer (TNBC). Multilevel experimental results demonstrate that the proposed algorithm better estimates potential associations between pathological image features and miRNA-gene and identifies consistent multimodal imaging genetic biomarkers to guide the interpretation of TNBC. ConclusionThe propose method provides a novel idea of data association analysis oriented to complex diseases.

DELWAVE 1.0: deep learning surrogate model of surface wave climate in the Adriatic Basin

Abstract. We propose a new point-prediction model, the DEep Learning WAVe Emulating model (DELWAVE), which successfully emulates the behaviour of a numerical surface ocean wave model (Simulating WAves Nearshore, SWAN) at a sparse set of locations, thus enabling numerically cheap large-ensemble prediction over synoptic to climate timescales. DELWAVE was trained on COSMO-CLM (Climate Limited-area Model) and SWAN input data during the period of 1971–1998, tested during 1998–2000, and cross-evaluated over the far-future climate time window of 2071–2100. It is constructed from a convolutional atmospheric encoder block, followed by a temporal collapse block and, finally, a regression block. DELWAVE reproduces SWAN model significant wave heights with a mean absolute error (MAE) of between 5 and 10 cm, mean wave directions with a MAE of 10–25°, and a mean wave period with a MAE of 0.2 s. DELWAVE is able to accurately emulate multi-modal mean wave direction distributions related to dominant wind regimes in the basin. We use wave power analysis from linearised wave theory to explain prediction errors in the long-period limit during southeasterly conditions. We present a storm analysis of DELWAVE, employing threshold-based metrics of precision and recall to show that DELWAVE reaches a very high score (both metrics over 95 %) of storm detection. SWAN and DELWAVE time series are compared to each other in the end-of-century scenario (2071–2100) and compared to the control conditions in the 1971–2000 period. Good agreement between DELWAVE and SWAN is found when considering climatological statistics, with a small (≤ 5 %), though systematic, underestimate of 99th-percentile values. Compared to control climatology over all wind directions, the mismatch between DELWAVE and SWAN is generally small compared to the difference between scenario and control conditions, suggesting that the noise introduced by surrogate modelling is substantially weaker than the climate change signal.

Exceptional characters and prime numbers in sparse sets

Exceptional characters and prime numbers in sparse sets

Advancing machine learning with OCR2SEQ: an innovative approach to multi-modal data augmentation

OCR2SEQ represents an innovative advancement in Optical Character Recognition (OCR) technology, leveraging a multi-modal generative augmentation strategy to overcome traditional limitations in OCR systems. This paper introduces OCR2SEQ’s unique approach, tailored to enhance data quality for sequence-to-sequence models, especially in scenarios characterized by sparse character sets and specialized vocabularies. At the heart of OCR2SEQ lies a set of novel augmentation techniques designed to simulate realistic text extraction errors. These techniques are adept at generating diverse and challenging data scenarios, thereby substantially improving the training efficacy and accuracy of text-to-text transformers. The application of OCR2SEQ has shown notable improvements in data processing accuracy, particularly in sectors heavily dependent on OCR technologies such as healthcare and library sciences. This paper demonstrates the capability of OCR2SEQ to transform OCR systems by enriching them with augmented, domain-specific data, paving the way for more sophisticated and reliable machine learning interpretations. This advancement in OCR technology, as presented in the study, not only enhances the accuracy and reliability of data processing but also sets a new benchmark in the integration of augmented data for refining OCR capabilities.

Augmented degree correction for bipartite networks with applications to recommender systems

In recommender systems, users rate items, and are subsequently served other product recommendations based on these ratings. Even though users usually rate a tiny percentage of the available items, the system tries to estimate unobserved preferences by finding similarities across users and across items. In this work, we treat the observed ratings data as partially observed, dense, weighted, bipartite networks. For a class of systems without outside information, we adapt an approach developed for dense, weighted networks to account for unobserved edges and the bipartite nature of the problem. The approach begins with clustering both users and items into communities, and locally estimates the patterns of ratings within each subnetwork induced by restricting attention to one community of users and one community of items community. The local fitting procedure relies on estimating local sociability parameters for every user and item, and selecting the function that determines the degree correction contours which best models the underlying data. We compare the performance of our proposed approach to existing methods on a simulated data set, as well as on a data set of joke ratings, examining model performance in both cases at differing levels of sparsity. On the joke ratings data set, our proposed model performs better than existing alternatives in relatively sparse settings, though other approaches achieve better results when more data is available. Collectively, the results indicate that despite struggling to pick up subtler signals, the proposed approach’s recovery of large scale, coarse patterns may still be useful in practical settings where high sparsity is typical.

Sex inequalities in cardiovascular risk prediction.

Evaluate sex differences in cardiovascular disease (CVD) risk prediction, including use of i) optimal sex-specific risk predictors and ii) sex-specific risk thresholds. Prospective cohort study using UK Biobank, including 121,724 and 182,632 healthy men and women, respectively, aged 38-73 years at baseline. There were 11,899 (men) and 9,110 (women) incident CVD cases (hospitalization or mortality) with median 12.1 years follow-up. We used recalibrated Pooled Cohort Equations (PCE, 7.5% 10-year risk threshold as per US guidelines), QRISK3 (10% 10-year risk threshold as per UK guidelines) and Cox survival models using sparse sex-specific variable sets (via LASSO stability selection) to predict CVD risk separately in men and women. LASSO stability selection included 12 variables in common between men and women, with three additional variables selected for men and one for women. C-statistics were slightly lower for PCE than QRISK3 and models using stably-selected variables, but were similar between men and women: 0.67 [0.66-0.68], 0.70 [0.69-0.71], and 0.71 [0.70-0.72] in men and 0.69 [0.68-0.70], 0.72 [0.71-0.73], and 0.72 [0.71-0.73] in women for PCE, QRISK3 and models using stably-selected variables, respectively. At current clinically implemented risk thresholds, test sensitivity was markedly lower in women than men for all models: at 7.5% 10-year risk, sensitivity was 65.1% and 68.2% in men and 24.0% and 33.4% in women for PCE and models using stably-selected variables, respectively; at 10% 10-year risk, sensitivity was 53.7% and 52.3% in men and 16.8% and 20.2% in women for QRISK3 and models using stably-selected variables, respectively. Specificity was correspondingly higher in women than men. However, the sensitivity in women at 5% 10-year risk threshold increased to 50.1%, 58.5% and 55.7% for PCE, QRISK3 and models using stably-selected variables, respectively. Use of sparse sex-specific variables improved CVD risk prediction compared with PCE but not QRISK3. At current risk thresholds, PCE and QRISK3 work less well for women than men but sensitivity was improved in women using a 5% 10-year risk threshold. Use of sex-specific risk thresholds should be considered in any re-evaluation of CVD risk calculators. Cardiovascular disease (CVD) risk prediction is an important component of clinical risk management and disease prevention. We find that at risk prediction thresholds used by currently applied risk prediction algorithms (PCE 7.5% 10-year risk threshold in the US and QRISK3 10% risk threshold in the UK), sensitivity of these risk prediction tools is markedly lower in women than in men. This sex inequality implies that women are proportionately less likely to receive appropriate clinical management including lipid-lowering therapy. If the risk prediction threshold is lowered to 5% 10-year risk in women, then sensitivity in women is substantially increased.

Oscillations of Fourier coefficients over the sparse set of integers

Oscillations of Fourier coefficients over the sparse set of integers

Doubly Sparse estimator for high-dimensional covariance matrices

The classical sample covariance estimator lacks desirable properties such as consistency and suffers from eigenvalue spreading in high-dimensional settings. Improved estimators have been proposed that shrink sample eigenvalues but retain the eigenvectors of the sample covariance estimator. In high dimensions, however, sample eigenvectors are generally strongly inconsistent, rendering eigenvalue shrinkage estimators suboptimal. A Doubly Sparse Covariance Estimator (DSCE) is developed that goes beyond mere eigenvalue shrinkage: a covariance matrix is decomposed into a signal part, where sparse eigenvectors are estimated via truncation, and an idiosyncratic part, estimated via thresholding. It is shown that accurate estimation is possible if the leading eigenvectors are sufficiently sparse affecting proportionately less than p of the variables. DSCE fills the gap for empirical applications that fall in-between fully sparse settings and conditionally sparse settings: DSCE takes advantage of conditional sparsity implied by factor models while allowing only a subset of variables to load on factors, which relaxes pervasiveness assumption of traditional factor models. An empirical application to the constituents of the S&P 1500 illustrates that DSCE-based portfolios outperform competing methods in terms of Sharpe ratio, maximum drawdown, and cumulative return for monthly and daily data.

Local and extensive fluctuations in sparsely interacting ecological communities.

Ecological communities with many species can be classified into dynamical phases. In systems with all-to-all interactions, a phase where species abundances always reach a fixed point and a phase where they continuously fluctuate have been found. The dynamics when interactions are sparse, with each species interacting with only a few others, has remained largely unexplored. Here we study a system of sparse interactions, first when interactions are of constant strength and completely unidirectional, and then when adding variability and bidirectionality. We show that in this case a phase unique to the sparse setting appears in the phase diagram, where for the same control parameters different communities may reach either a fixed point or a state where the abundances of only a finite subset of species fluctuate, and we calculate the probability for each outcome. These fluctuating species are organized around short cycles in the interaction graph, and their abundances undergo large nonlinear fluctuations. We characterize the approach from this phase to a phase with extensively many fluctuating species, and show that the probability of fluctuations grows continuously to one as the transition is approached, and that the number of fluctuating species diverges. This is qualitatively distinct from the transition to extensive fluctuations coming from a fixed point phase, which is marked by a loss of linear stability. The differences are traced back to the emergent binary character of the dynamics when far from short cycles.

Dense-sparse quantum Monte Carlo algebraic diagrammatic construction and importance ranking.

Quantum Monte Carlo Algebraic Diagrammatic Construction (QMCADC) has been proposed as a reformulation of the second-order ADC scheme for the polarization propagator within the projection quantum Monte Carlo formalism. Dense-sparse partitioning and importance ranking filtering strategies are now exploited to accelerate its convergence and to alleviate the signproblem inherent in such calculations. By splitting the configuration space into dense and sparse subsets, the corresponding projection operator is decomposed into four distinct blocks. Deterministic calculations handle the dense-to-dense and sparse-to-dense blocks, while the remaining blocks, dense-to-sparse and sparse-to-sparse, are stochastically evaluated. The dense set is efficiently stored in a fixed-size array, and the sparse set is represented through conventional floating random Monte Carlo walks. The stochastic projection is further refined through importance ranking criteria, enabling a reduction in the required number of walkers with a controllable bias. Our results demonstrate the integration of dense-sparse partitioning with importance ranking filtering to significantly enhance the efficiency of QMCADC, enabling large-scale molecular excited-state calculations. Furthermore, this novel approach maximizes the utilization of the sparsity of ADC(2), transforming QMCADC into a tailored framework for ADC calculations.

Dissipative imitation learning for discrete dynamic output feedback control with sparse data sets

AbstractImitation learning enables synthesis of controllers for systems with complex objectives and uncertain plant models. However, ensuring an imitation learned controller is stable requires copious amounts of data and/or a known plant model. In this paper, we explore an input–output (IO) stability approach to imitation learning, which achieves stability with sparse data sets while only requiring coarse knowledge of the energy characteristics of the plant. A constrained optimization problem is developed, in which the controller learns to mimic expert data while maintaining stabilizing energy characteristics induced by the plant. While the learning objective is nonconvex, iterative convex overbounding (ICO) and projected gradient descent (PGD) are explored as methods to learn the controller. In numerical examples, it is shown that with little knowledge of the plant model and a small data set, the dissipativity constrained learned controller achieves closed loop stability and successfully mimics the behavior of the expert controller, while other methods often fail to maintain stability and achieve good performance.

An evaluation of computational methods for aggregate data meta-analyses of diagnostic test accuracy studies

BackgroundA Generalized Linear Mixed Model (GLMM) is recommended to meta-analyze diagnostic test accuracy studies (DTAs) based on aggregate or individual participant data. Since a GLMM does not have a closed-form likelihood function or parameter solutions, computational methods are conventionally used to approximate the likelihoods and obtain parameter estimates. The most commonly used computational methods are the Iteratively Reweighted Least Squares (IRLS), the Laplace approximation (LA), and the Adaptive Gauss-Hermite quadrature (AGHQ). Despite being widely used, it has not been clear how these computational methods compare and perform in the context of an aggregate data meta-analysis (ADMA) of DTAs.MethodsWe compared and evaluated the performance of three commonly used computational methods for GLMM - the IRLS, the LA, and the AGHQ, via a comprehensive simulation study and real-life data examples, in the context of an ADMA of DTAs. By varying several parameters in our simulations, we assessed the performance of the three methods in terms of bias, root mean squared error, confidence interval (CI) width, coverage of the 95% CI, convergence rate, and computational speed.ResultsFor most of the scenarios, especially when the meta-analytic data were not sparse (i.e., there were no or negligible studies with perfect diagnosis), the three computational methods were comparable for the estimation of sensitivity and specificity. However, the LA had the largest bias and root mean squared error for pooled sensitivity and specificity when the meta-analytic data were sparse. Moreover, the AGHQ took a longer computational time to converge relative to the other two methods, although it had the best convergence rate.ConclusionsWe recommend practitioners and researchers carefully choose an appropriate computational algorithm when fitting a GLMM to an ADMA of DTAs. We do not recommend the LA for sparse meta-analytic data sets. However, either the AGHQ or the IRLS can be used regardless of the characteristics of the meta-analytic data.

Tracking and co-location of global point clouds for large-area indoor environments

Extended reality (XR) experiences are on the verge of becoming widely adopted in diverse application domains. An essential part of the technology is accurate tracking and localization of the headset to create an immersive experience. A subset of the applications require perfect co-location between the real and the virtual world, where virtual objects are aligned with real-world counterparts. Current headsets support co-location for small areas, but suffer from drift when scaling up to larger ones such as buildings or factories. This paper proposes tools and solutions for this challenge by splitting up the simultaneous localization and mapping (SLAM) into separate mapping and localization stages. In the pre-processing stage, a feature map is built for the entire tracking area. A global optimizer is applied to correct the deformations caused by drift, guided by a sparse set of ground truth markers in the point cloud of a laser scan. Optionally, further refinement is applied by matching features between the ground truth keyframe images and their rendered-out SLAM estimates of the point cloud. In the second, real-time stage, the rectified feature map is used to perform localization and sensor fusion between the global tracking and the headset. The results show that the approach achieves robust co-location between the virtual and the real 3D environment for large and complex tracking environments.