Sparse Structure Research Articles

ModelNet-O: A large-scale synthetic dataset for occlusion-aware point cloud classification

Recently, 3D point cloud classification has made significant progress with the help of many datasets. However, these datasets do not reflect the incomplete nature of real-world point clouds caused by occlusion, which limits the practical application of current methods. To bridge this gap, we propose ModelNet-O, a large-scale synthetic dataset of 123,041 samples that emulates real-world point clouds with self-occlusion caused by scanning from monocular cameras. ModelNet-O is 10 times larger than existing datasets and offers more challenging cases to evaluate the robustness of existing methods. Our observation on ModelNet-O reveals that well-designed sparse structures can preserve structural information of point clouds under occlusion, motivating us to propose a robust point cloud processing method that leverages a critical point sampling (CPS) strategy in a multi-level manner. We term our method PointMLS. Through extensive experiments, we demonstrate that our PointMLS achieves state-of-the-art results on ModelNet-O and competitive results on regular datasets such as ModelNet40 and ScanObjectNN, and we also demonstrate its robustness and effectiveness. Code available: https://github.com/fanglaosi/ModelNet-O_PointMLS.

High dimensional discriminant rules with shrinkage estimators of the covariance matrix and mean vector

Linear discriminant analysis (LDA) is a typical method for classification problems with large dimensions and small samples. There are various types of LDA methods that are based on the different types of estimators for the covariance matrices and mean vectors. In this paper, we consider shrinkage methods based on a non-parametric approach. For the precision matrix, methods based on the sparsity structure or data splitting are examined. Regarding the estimation of mean vectors, Non-parametric Empirical Bayes (NPEB) methods and Non-parametric Maximum Likelihood Estimation (NPMLE) methods, also known as f-modeling and g-modeling, respectively, are adopted. The performance of linear discriminant rules based on combined estimation strategies of the covariance matrix and mean vectors are analyzed in this study. Particularly, the study presents a theoretical result on the performance of the NPEB method and compares it with previous studies. Simulation studies with various covariance matrices and mean vector structures are conducted to evaluate the methods discussed in this paper. Furthermore, real data examples such as gene expressions and EEG data are also presented.

Sparse Generalized Canonical Correlation Analysis: Distributed Alternating Iteration-Based Approach.

Sparse canonical correlation analysis (CCA) is a useful statistical tool to detect latent information with sparse structures. However, sparse CCA, where the sparsity could be considered as a Laplace prior on the canonical variates, works only for two data sets, that is, there are only two views or two distinct objects. To overcome this limitation, we propose a sparse generalized canonical correlation analysis (GCCA), which could detect the latent relations of multiview data with sparse structures. Specifically, we convert the GCCA into a linear system of equationsand impose $\ell _1$ minimization penalty to pursue sparsity. This results in a nonconvex problem on the Stiefel manifold. Based on consensus optimization, a distributed alternating iteration approach is developed, and consistency is investigated elaborately under mild conditions. Experiments on several synthetic and real-world data sets demonstrate the effectiveness of the proposed algorithm.

Exploring Clique Transversal Problems for d-degenerate Graphs with Fixed d: From Polynomial-Time Solvability to Parameterized Complexity

This paper explores the computational challenges of clique transversal problems in d-degenerate graphs, which are commonly encountered across theoretical computer science and various network applications. We examine d-degenerate graphs to highlight their utility in representing sparse structures and assess several variations of clique transversal problems, including the b-fold and {b}-clique transversal problems, focusing on their computational complexities for different graph categories. Our analysis identifies that certain instances of these problems are polynomial-time solvable in specific graph classes, such as 1-degenerate or 2-degenerate graphs. However, for d-degenerate graphs where d≥2, these problems generally escalate to NP-completeness. We also explore the parameterized complexity, pinpointing specific conditions that render these problems fixed-parameter tractable.

Spatio-Temporal Hierarchical Data Structure Based on Sparse Voxel Octrees for Representation of the Geometry of Time-Variable Three-Dimensional Scenes

Abstract The paper deals with the problematics of representation of the geometry of three-dimensional scenes in computer graphics using domain-specific hierarchical data structures based on octant trees or directed acyclic graphs as the means of space saving binary representation of this information. Several hierarchical data structures were introduced in this field in past decades. In this paper we are moving this problematic to the field of the representation of three-dimensional scenes which are rather dynamic in time, so their geometry is changing on the regular basis. We are investigating the influence of this time-variability on the size of the related hierarchical data structure on binary level. We are comparing the approach in which each time step is considered as the stand-alone static three-dimensional scene and therefore is represented by its own hierarchical data structure with the approach when this time-variable scene is considered as the four dimensional space and spatio-temporal sparse voxel octree hierarchical data structure is used for the representation of the geometry of this scene. We tested both approaches on three different scenes which were obtained by voxelization into two different resolutions of polygonal surface models represented originally as the mesh of triangles in Wavefront Object file format. Results of the tests show that spatio-temporal sparse voxel octree is better solution, when we obtained from 1.73 to 2.08 more compact binary representation, in comparison to the solution when time frames were encoded separately as the set of sparse voxel octrees.

3D Vascular Segmentation Supervised by 2D Annotation of Maximum Intensity Projection.

Vascular structure segmentation plays a crucial role in medical analysis and clinical applications. The practical adoption of fully supervised segmentation models is impeded by the intricacy and time-consuming nature of annotating vessels in the 3D space. This has spurred the exploration of weakly-supervised approaches that reduce reliance on expensive segmentation annotations. Despite this, existing weakly supervised methods employed in organ segmentation, which encompass points, bounding boxes, or graffiti, have exhibited suboptimal performance when handling sparse vascular structure. To alleviate this issue, we employ maximum intensity projection (MIP) to decrease the dimensionality of 3D volume to 2D image for efficient annotation, and the 2D labels are utilized to provide guidance and oversight for training 3D vessel segmentation model. Initially, we generate pseudo-labels for 3D blood vessels using the annotations of 2D projections. Subsequently, taking into account the acquisition method of the 2D labels, we introduce a weakly-supervised network that fuses 2D-3D deep features via MIP to further improve segmentation performance. Furthermore, we integrate confidence learning and uncertainty estimation to refine the generated pseudo-labels, followed by fine-tuning the segmentation network. Our method is validated on five datasets (including cerebral vessel, aorta and coronary artery), demonstrating highly competitive performance in segmenting vessels and the potential to significantly reduce the time and effort required for vessel annotation. Our code is available at: https://github.com/gzq17/Weakly-Supervised-by-MIP.

Comparison of autoencoder architectures for fault detection in industrial processes

Fault detection constitutes a fundamental task for predictive maintenance, requiring mathematical models that can be conveniently provided by data-driven techniques. Autoencoders are a particular type of unsupervised Artificial Neural Networks that can be suitable for fault detection applications. Diverse architectures might be used for autoencoders, resulting in different fault detection performances, which are usually compared by means of Fault Detection Rates for a fixed threshold of the False Alarm Rate, limiting the conclusions to particular cases. To improve the comparability, the present work uses the area under the receiver operating characteristic curve to compare autoencoder architectures for a range of false alarm rates using the Tennessee Eastman Process benchmark. Performances obtained for shallow and deep autoencoders were compared with those of the denoising and variational autoencoders for undercomplete and sparse structures. Overall, the results indicate better performances for sparse structures, especially for the variational autoencoder and the deep denoising autoencoder, with area under the curve of 98.35%.

A Generalized Formulation for Group Selection via ADMM

This paper studies a statistical learning model where the model coefficients have a pre-determined non-overlapping group sparsity structure. We consider a combination of a loss function and a regularizer to recover the desired group sparsity patterns, which can embrace many existing works. We analyze directional stationary solutions of the proposed formulation, obtaining a sufficient condition for a directional stationary solution to achieve optimality and establishing a bound of the distance from the solution to a reference point. We develop an efficient algorithm that adopts an alternating direction method of multiplier (ADMM), showing that the iterates converge to a directional stationary solution under certain conditions. In the numerical experiment, we implement the algorithm for generalized linear models with convex and nonconvex group regularizers to evaluate the model performance on various data types, noise levels, and sparsity settings.

Optimizing sparse general matrix–matrix multiplication for DCUs

Sparse general matrix–matrix multiplication (SpGEMM) is a crucial and complex computational task in many practical applications. Improving the performance of SpGEMM on SIMT processors like modern GPUs is challenging due to the unpredictable sparsity of sparse matrices. Although existing GPU solutions have made progress in improving performance through advanced algorithm design, they ignore some optimizations related to specific processor architectures. This can result in a partially inefficient implementation of their algorithms. This paper focuses on optimizing four inefficient parts of the NSparse algorithm on DCU (a GPU-like accelerator). The optimizations include: 1) setting parameters to improve the load balance of the second matrix by extracting maximum row information at runtime; 2) reducing overhead of binning operations by making full use of registers and shared memory effectively; 3) improving numerical SpGEMM performance by adjusting its calculation mode; and 4) enhancing global load balance through finer-grained grouping and kernel configurations. Experiment results demonstrate that when compared to five state-of-the-art SpGEMM algorithms (bhSparse, KokkosKernels, NSparse, rocSparse, and spECK), our optimized method achieves an average of 7.99x (up to 18.2x), 8.01x (up to 20.83x), 2.37x (up to 6.16x), 1.82x (up to 4.20x), and 1.63x (up to 5.01x) speedups on 29 sparse matrices with different sparse structures, respectively.

A structured iterative division approach for non-sparse regression models and applications in biological data analysis.

In this paper, we focus on the modeling problem of estimating data with non-sparse structures, specifically focusing on biological data that exhibit a high degree of relevant features. Various fields, such as biology and finance, face the challenge of non-sparse estimation. We address the problems using the proposed method, called structured iterative division. Structured iterative division effectively divides data into non-sparse and sparse structures and eliminates numerous irrelevant variables, significantly reducing the error while maintaining computational efficiency. Numerical and theoretical results demonstrate the competitive advantage of the proposed method on a wide range of problems, and the proposed method exhibits excellent statistical performance in numerical comparisons with several existing methods. We apply the proposed algorithm to two biology problems, gene microarray datasets, and chimeric protein datasets, to the prognostic risk of distant metastasis in breast cancer and Alzheimer's disease, respectively. Structured iterative division provides insights into gene identification and selection, and we also provide meaningful results in anticipating cancer risk and identifying key factors.

Tuning-free sparse clustering via alternating hard-thresholding

Model-based clustering is a commonly-used technique to partition heterogeneous data into homogeneous groups. When the analysis is to be conducted with a large number of features, analysts face simultaneous challenges in model interpretability, clustering accuracy, and computational efficiency. Several Bayesian and penalization methods have been proposed to select important features for model-based clustering. However, the performance of those methods relies on a careful algorithmic tuning, which can be time-consuming for high-dimensional cases. In this paper, we propose a new sparse clustering method based on alternating hard-thresholding. The new method is conceptually simple and tuning-free. With a user-specified sparsity level, it efficiently detects a set of key features by eliminating a large number of features that are less useful for clustering. Based on the selected key features, one can readily obtain an effective clustering of the original high-dimensional data under a general sparse covariance structure. Under mild conditions, we show that the new method leads to clusters with a misclassification rate consistent to the optimal rate as if the underlying true model were used. The promising performance of the new method is supported by both simulated and real data examples.

Efficient subspace clustering and feature extraction via [formula omitted]-norm and [formula omitted]-norm minimization

The nuclear norm-based Latent Low-Rank Representation (LatLRR) has gained much attention due to its success in subspace clustering and feature extraction. However, it suffers from high computational costs due to the calculation of singular value decomposition for large matrices. To this end, we develop an efficient subspace clustering and feature extraction method (ESCFE) which substitutes the nuclear norm with the ℓ2,1-norm and ℓ1,2-norm respectively. Theoretically proof shows both the ℓ2,1-norm and ℓ1,2-norm can serve as the convex surrogates of the nuclear norm while can derive closed-form solutions. Furthermore, the ℓ2,1-norm (or ℓ1,2-norm) regularization promotes column (or row) structure sparsity due to the discriminative nature inherited from the ℓ1-norm. Thus the proposed ESCFE is robust to outliers in data and can extract features with joint sparsity. Extensive experiments on multiple benchmark datasets demonstrate the superiority of our method in both efficiency and effectiveness.

Filtering After Shading With Stochastic Texture Filtering

2D texture maps and 3D voxel arrays are widely used to add rich detail to the surfaces and volumes of rendered scenes, and filtered texture lookups are integral to producing high-quality imagery. We show that applying the texture filter after evaluating shading generally gives more accurate imagery than filtering textures before BSDF evaluation, as is current practice. These benefits are not merely theoretical, but are apparent in common cases. We demonstrate that practical and efficient filtering after shading is possible through the use of stochastic sampling of texture filters. Stochastic texture filtering offers additional benefits, including efficient implementation of high-quality texture filters and efficient filtering of textures stored in compressed and sparse data structures, including neural representations. We demonstrate applications in both real-time and offline rendering and show that the additional error from stochastic filtering is minimal. We find that this error is handled well by either spatiotemporal denoising or moderate pixel sampling rates.

Efficient Structure from Motion for Large-Size Videos from an Open Outdoor UAV Dataset.

Modern UAVs (unmanned aerial vehicles) equipped with video cameras can provide large-scale high-resolution video data. This poses significant challenges for structure from motion (SfM) and simultaneous localization and mapping (SLAM) algorithms, as most of them are developed for relatively small-scale and low-resolution scenes. In this paper, we present a video-based SfM method specifically designed for high-resolution large-size UAV videos. Despite the wide range of applications for SfM, performing mainstream SfM methods on such videos poses challenges due to their high computational cost. Our method consists of three main steps. Firstly, we employ a visual SLAM (VSLAM) system to efficiently extract keyframes, keypoints, initial camera poses, and sparse structures from downsampled videos. Next, we propose a novel two-step keypoint adjustment method. Instead of matching new points in the original videos, our method effectively and efficiently adjusts the existing keypoints at the original scale. Finally, we refine the poses and structures using a rotation-averaging constrained global bundle adjustment (BA) technique, incorporating the adjusted keypoints. To enrich the resources available for SLAM or SfM studies, we provide a large-size (3840 × 2160) outdoor video dataset with millimeter-level-accuracy ground control points, which supplements the current relatively low-resolution video datasets. Experiments demonstrate that, compared with other SLAM or SfM methods, our method achieves an average efficiency improvement of 100% on our collected dataset and 45% on the EuRoc dataset. Our method also demonstrates superior localization accuracy when compared with state-of-the-art SLAM or SfM methods.

Sparsify dynamically expandable network via variational dropout

This paper develops a new method for lifelong learning referred to as Sparsify Dynamically Expandable Network (SDEN) via Variational Dropout, which explores a sparse model while preserving the performance. Dynamically Expandable Network (DEN) can learn a sequence of tasks via performing network retraining, network expansion by adding only the necessary neurons, and network split to effectively prevent semantic drift in an online manner. To overcome point estimation of parameters in DEN, Bayesian Compression for DEN is developed under the Bayesian framework. However, this method demands more time for model training and testing. To improve the model efficiency, we propose SDEN under the efficient sparse learning framework. We validate our SDEN in the lifelong learning scenarios with multiple frequently used benchmarks, on which it can obtain comparable classification accuracy, and less training and testing time compared with the comparison methods. Furthermore, our method can also learn a more sparse network structure which means fewer network parameters.

Multiagent trajectory prediction with global‐local scene‐enhanced social interaction graph network

AbstractTrajectory prediction is essential for intelligent autonomous systems like autonomous driving, behavior analysis, and service robotics. Deep learning has emerged as the predominant technique due to its superior modeling capability for trajectory data. However, deep learning‐based models face challenges in effectively utilizing scene information and accurately modeling agent interactions, largely due to the complexity and uncertainty of real‐world scenarios. To mitigate these challenges, this study presents a novel multiagent trajectory prediction model, termed the global‐local scene‐enhanced social interaction graph network (GLSESIGN), which incorporates two pivotal strategies: global‐local scene information utilization and a social adaptive attention graph network. The model hierarchically learns scene information relevant to multiple intelligent agents, thereby enhancing the understanding of complex scenes. Additionally, it adaptively captures social interactions, improving adaptability to diverse interaction patterns through sparse graph structures. This model not only improves the understanding of complex scenes but also accurately predicts future trajectories of multiple intelligent agents by flexibly modeling intricate interactions. Experimental validation on public datasets substantiates the efficacy of the proposed model. This research offers a novel model to address the complexity and uncertainty in multiagent trajectory prediction, providing more accurate predictive support in practical application scenarios.

Exploiting Structured Sparsity With Low Complexity Sparse Bayesian Learning for RIS-Assisted MIMO mmWave Channel Estimation

Exploiting Structured Sparsity With Low Complexity Sparse Bayesian Learning for RIS-Assisted MIMO mmWave Channel Estimation

Compiling Recurrences over Dense and Sparse Arrays

We present a framework for compiling recurrence equations into native code. In our framework, users specify a system of recurrences, the types of data structures that store inputs and outputs, and scheduling commands for optimization. Our compiler then lowers these specifications into native code that respects the dependencies in the recurrence equations. Our compiler can generate code over both sparse and dense data structures, and determines if the recurrence system is solvable with the provided scheduling primitives. We evaluate the performance and correctness of the generated code on several recurrences, from domains as diverse as dense and sparse matrix solvers, dynamic programming, graph problems, and sparse tensor algebra. We demonstrate that the generated code has competitive performance to hand-optimized implementations in libraries. However, these handwritten libraries target specific recurrences, specific data structures, and specific optimizations. Our system, on the other hand, automatically generates implementations from recurrences, data formats, and schedules, giving our system more generality than library approaches.

UniSparse: An Intermediate Language for General Sparse Format Customization

The ongoing trend of hardware specialization has led to a growing use of custom data formats when processing sparse workloads, which are typically memory-bound. These formats facilitate optimized software/hardware implementations by utilizing sparsity pattern- or target-aware data structures and layouts to enhance memory access latency and bandwidth utilization. However, existing sparse tensor programming models and compilers offer little or no support for productively customizing the sparse formats. Additionally, because these frameworks represent formats using a limited set of per-dimension attributes, they lack the flexibility to accommodate numerous new variations of custom sparse data structures and layouts. To overcome this deficiency, we propose UniSparse, an intermediate language that provides a unified abstraction for representing and customizing sparse formats. Unlike the existing attribute-based frameworks, UniSparse decouples the logical representation of the sparse tensor (i.e., the data structure) from its low-level memory layout, enabling the customization of both. As a result, a rich set of format customizations can be succinctly expressed in a small set of well-defined query, mutation, and layout primitives. We also develop a compiler leveraging the MLIR infrastructure, which supports adaptive customization of formats, and automatic code generation of format conversion and compute operations for heterogeneous architectures. We demonstrate the efficacy of our approach through experiments running commonly-used sparse linear algebra operations with specialized formats on multiple different hardware targets, including an Intel CPU, an NVIDIA GPU, an AMD Xilinx FPGA, and a simulated processing-in-memory (PIM) device.

Structured residual sparsity for video compressive sensing reconstruction

Recent advancements in the residual sparsity strategy have garnered widespread attention in video compressive sensing (CS) reconstruction. However, most of the existing residual sparsity-based video CS reconstruction methods usually suffer from some limitations that lead to undesired visual artifacts. Firstly, these methods only rely on a patch sparsity scheme that is limited by their focus on the local structures of each video frame, neglecting the nonlocal self-similarity (NSS) property inherent to each video frame. Secondly, these methods concentrate on utilizing the NSS property of external reference frames for multi-hypothesis (MH) prediction while disregarding the internal NSS property of the current frame. In this paper, we propose a new structured residual sparsity (SRS) approach for video CS reconstruction, which jointly exploits the NSS properties of the current frame and its reference frames. Specifically, due to the unavailability of the original video frames, we first devise an effective intraframe CS (EICS) reconstruction method that leverages the internal NSS property of each frame. This approach enables us to obtain initial recovery frames, which then facilitate the execution of MH prediction. Following this, we generate a residual frame for the current frame by employing the MH prediction. Then, we propose a novel SRS model jointly using the NSS properties of the current frame and its reference frames to explore both the correlations of intraframe and interframe for reconstructing the current frame. Furthermore, for the sake of optimization feasibility, we develop an effective alternating direction method of multipliers (ADMM) algorithm to address the objective. Our experimental findings reveal that the proposed SRS not only yields superior quantitative results, but also uncovers finer details and causes fewer visual artifacts compared to many popular or state-of-the-art video CS reconstruction approaches.