图形信号处理（GSP）中的基本前提是，将目标信号的成对（反）相关性作为边缘权重以用于图形过滤。但是，现有的快速图抽样方案仅针对描述正相关的正图设计和测试。在本文中，我们表明，对于具有强固有抗相关的数据集，合适的图既包含正边缘和负边缘。作为响应，我们提出了一种以平衡签名图的概念为中心的线性时间签名的图形采样方法。具体而言，给定的经验协方差数据矩阵$ \ bar {\ bf {c}} $，我们首先学习一个稀疏的逆矩阵（Graph laplacian）$ \ MATHCAL {l} $对应于签名图$ \ Mathcal $ \ Mathcal {G} $ 。我们为平衡签名的图形$ \ Mathcal {g} _b $ - 近似$ \ Mathcal {g} $通过Edge Exge Exgement Exgmentation -As Graph频率组件定义Laplacian $ \ Mathcal {L} _b $的特征向量。接下来，我们选择样品以将低通滤波器重建误差分为两个步骤最小化。我们首先将Laplacian $ \ Mathcal {L} _b $的所有Gershgorin圆盘左端对齐，最小的EigenValue $ \ lambda _ {\ min}（\ Mathcal {l} _b）$通过相似性转换$ \ MATHCAL $ \ MATHCAL} s \ Mathcal {l} _b \ s^{ - 1} $，利用最新的线性代数定理，称为gershgorin disc perfect perfect对齐（GDPA）。然后，我们使用以前的快速gershgorin盘式对齐采样（GDAS）方案对$ \ Mathcal {L} _p $进行采样。实验结果表明，我们签名的图形采样方法在各种数据集上明显优于现有的快速采样方案。

在县粒度上预测每年农作物的产量对于国家粮食生产和价格稳定至关重要。在本文中，为了实现更好的作物产量预测，利用最新的图形信号处理（GSP）工具来利用相邻县之间的空间相关性，我们通过图形光谱滤波来证明相关的特征，这些特征是深度学习预测模型的输入。具体而言，我们首先构建一个具有边缘权重的组合图，该图可以通过公制学习编码土壤和位置特征的县对县的相似性。然后，我们通过最大的后验（MAP）配方使用图形laplacian正常化程序（GLR）来定性特征。我们关注的挑战是估算关键的权重参数$ \ mu $，交易忠诚度和GLR，这是噪声差异的函数，以无监督的方式。我们首先使用发现局部恒定区域的图集集合检测（GCD）过程直接从噪声浪费的图形信号估算噪声方差。然后，我们通过通过偏置变化分析来计算最佳$ \ mu $最大程度地减少近似平方误差函数。收集到的USDA数据的实验结果表明，使用DeNo的特征作为输入，可以明显改善作物产量预测模型的性能。

我们的目标是有效地计算输入图中的节点的低维潜在坐标 - 称为图形嵌入 - 用于后续数据处理，例如群集。专注于在连续歧管上解释为均匀样品的有限图（称为歧管图），我们利用现有的快速极端特征向量计算算法来快速执行。我们首先为稀疏矩阵配对构成普遍的特征值问题，其中$ \ a = \ l - \ mu \ q + \ epsilon \ i $是图表拉普拉斯$ \ l \ l的总和断开双跳差异矩阵$ \ q $。特征向量$ \ v $最小化瑞利商$ \ frac {\ v ^ {\ top} \ top} \ a \ a \ v} $，从而最大限度地降低$ 1 $ -hop邻居距离，同时最大化断开连接2美元之间的距离$ -hop邻居，保留图形结构。矩阵$ \ b = \ text {diag}（\ {\ b_i \}），然后选择定义特征向量正交性，以便采样域中的边界/内部节点具有相同的广义度。 $ k $ -dimensional潜在的$ n $ graph节点是$（\ a，\ b）$的$ k $概括的特征向量，在$ \ co（n）$中使用lobpcg，其中$ k \ ll n $。实验表明，我们的嵌入是文献中最快的，同时为歧管图产生了最佳聚类性能。

3D点云通常由一个或多个观点处由传感器获取的深度测量构成。测量值遭受量化和噪声损坏。为了提高质量，以前的作品在将不完美深度数据投射到3D空间之后，将点云\ Textit {a postiriori}代名。相反，在合成3D点云之前，我们在感测图像\ Texit {a先验}上直接增强深度测量。通过增强物理传感过程附近，在后续处理步骤模糊测量误差之前，我们将我们的优化定制到我们的深度形成模型。具体而言，我们将深度形成为信号相关噪声添加和非均匀日志量化的组合过程。使用来自实际深度传感器的收集的经验数据验证设计的模型（配有参数）。为了在深度图像中增强每个像素行，我们首先通过特征图学习将可用行像素之间的视图帧内相似性编码为边缘权重。接下来我们通过观点映射和稀疏线性插值建立与另一个整流的深度图像的视图间相似性。这导致最大的后验（MAP）图滤波物镜，其凸显和可微分。我们使用加速梯度下降（AGD）有效地优化目标，其中最佳步长通过Gershgorin圆定理（GCT）近似。实验表明，我们的方法在两个既定点云质量指标中显着优于最近的近期云去噪方案和最先进的图像去噪方案。

在半监督的基于图的二进制分类器学习中，假设标签信号$ \ mathbf {x} $相对于相似性，则使用已知标签的子集$ \ hat {x} _i $来推断未知标签图形由拉普拉斯矩阵指定。当将标签$ x_i $限制为二进制值时，问题是NP-HARD。虽然可以在多项式时间内使用乘数的交替方向方法（ADMM）在多项式时间内解决常规半准编程放松（SDR），但投射候选矩阵$ \ mathbf {m mathbf {m mathbf {m} $的复杂性-definite（PSD）锥（$ \ Mathbf {M} \ succeq 0 $）每个迭代仍然很高。在本文中，我们利用一种称为Gershgorin Disc Perfect Alignment（GDPA）的最新线性代数理论，我们通过求解一系列线性程序（LP）提出了一种快速投影方法。具体而言，我们首先将SDR重新铸造为二元，其中可行的解决方案$ \ mathbf {h} \ succeq 0 $解释为与平衡签名的图相对应的laplacian矩阵减去最后一个节点。为了达到图表平衡，我们将最后一个节点分为两个，每个节点保留了原始的正 /负边缘，从而导致新的laplacian $ \ bar {\ mathbf {h}} $。我们在解决方案$ \ bar {\ mathbf {h}} $上放置sdr dual，然后替换PSD锥约束$ \ bar {\ Mathbf {h} \ succeq 0 $，具有从GDPA衍生的线性约束 - 可确保足够的条件 - 确保足够的条件$ \ bar {\ mathbf {h}} $是psd-因此，优化成为LP，每次迭代。最后，我们从融合解决方案$ \ bar {\ mathbf {h}} $中提取预测标签。实验表明，我们的算法在下一个最快的方案中享受了$ 28 \ times $速度，同时达到了可比的标签预测性能。

Biological systems and processes are networks of complex nonlinear regulatory interactions between nucleic acids, proteins, and metabolites. A natural way in which to represent these interaction networks is through the use of a graph. In this formulation, each node represents a nucleic acid, protein, or metabolite and edges represent intermolecular interactions (inhibition, regulation, promotion, coexpression, etc.). In this work, a novel algorithm for the discovery of latent graph structures given experimental data is presented.

Aligning users across networks using graph representation learning has been found effective where the alignment is accomplished in a low-dimensional embedding space. Yet, achieving highly precise alignment is still challenging, especially when nodes with long-range connectivity to the labeled anchors are encountered. To alleviate this limitation, we purposefully designed WL-Align which adopts a regularized representation learning framework to learn distinctive node representations. It extends the Weisfeiler-Lehman Isormorphism Test and learns the alignment in alternating phases of "across-network Weisfeiler-Lehman relabeling" and "proximity-preserving representation learning". The across-network Weisfeiler-Lehman relabeling is achieved through iterating the anchor-based label propagation and a similarity-based hashing to exploit the known anchors' connectivity to different nodes in an efficient and robust manner. The representation learning module preserves the second-order proximity within individual networks and is regularized by the across-network Weisfeiler-Lehman hash labels. Extensive experiments on real-world and synthetic datasets have demonstrated that our proposed WL-Align outperforms the state-of-the-art methods, achieving significant performance improvements in the "exact matching" scenario. Data and code of WL-Align are available at https://github.com/ChenPengGang/WLAlignCode.

Three main points: 1. Data Science (DS) will be increasingly important to heliophysics; 2. Methods of heliophysics science discovery will continually evolve, requiring the use of learning technologies [e.g., machine learning (ML)] that are applied rigorously and that are capable of supporting discovery; and 3. To grow with the pace of data, technology, and workforce changes, heliophysics requires a new approach to the representation of knowledge.

We propose an extrinsic Bayesian optimization (eBO) framework for general optimization problems on manifolds. Bayesian optimization algorithms build a surrogate of the objective function by employing Gaussian processes and quantify the uncertainty in that surrogate by deriving an acquisition function. This acquisition function represents the probability of improvement based on the kernel of the Gaussian process, which guides the search in the optimization process. The critical challenge for designing Bayesian optimization algorithms on manifolds lies in the difficulty of constructing valid covariance kernels for Gaussian processes on general manifolds. Our approach is to employ extrinsic Gaussian processes by first embedding the manifold onto some higher dimensional Euclidean space via equivariant embeddings and then constructing a valid covariance kernel on the image manifold after the embedding. This leads to efficient and scalable algorithms for optimization over complex manifolds. Simulation study and real data analysis are carried out to demonstrate the utilities of our eBO framework by applying the eBO to various optimization problems over manifolds such as the sphere, the Grassmannian, and the manifold of positive definite matrices.

With the development of gene sequencing technology, an explosive growth of gene data has been witnessed. And the storage of gene data has become an important issue. Traditional gene data compression methods rely on general software like G-zip, which fails to utilize the interrelation of nucleotide sequence. Recently, many researchers begin to investigate deep learning based gene data compression method. In this paper, we propose a transformer-based gene compression method named GeneFormer. Specifically, we first introduce a modified transformer structure to fully explore the nucleotide sequence dependency. Then, we propose fixed-length parallel grouping to accelerate the decoding speed of our autoregressive model. Experimental results on real-world datasets show that our method saves 29.7% bit rate compared with the state-of-the-art method, and the decoding speed is significantly faster than all existing learning-based gene compression methods.