例如，近似K-Nearest的邻居搜索（AKNNS）现在已经在现代应用程序中变得无处不在，例如，作为一个快速搜索程序，具有两个塔式深度学习模型。特别是基于图的AKNN方法，由于其出色的性能，因此受到了极大的关注。这些方法依靠贪婪的图形搜索来遍历数据库中的载体。在这种贪婪的搜索方案下，我们进行了一个关键的观察：许多距离计算不会影响搜索更新，因此可以在不损害性能的情况下近似这些计算。结果，我们提出了手指，这是一种快速的推理方法，以实现有效的图形搜索。手指通过估计较低碱基和分布匹配的相邻残留向量之间的角度来近似距离函数。近似距离可用于绕过不必要的计算，从而导致更快的搜索。从经验上讲，在不同的基准数据集中加速了一种名为HNSW的流行基于图形的方法，其名称为HNSW的HNSW方法可超过现有的基于图的方法20％-60％。

K-Nearest邻居搜索是各种应用程序中的基本任务之一，层次可导航的小世界（HNSW）最近在大规模云服务中引起了人们的注意，因为它在提供快速搜索的同时很容易扩展数据库。另一方面，将可编程逻辑和单个板上的可编程逻辑模块结合在一起的计算存储设备（CSD）变得流行，以解决现代计算系统的数据带宽瓶颈。在本文中，我们提出了一个计算存储平台，该平台可以加速基于SMARTSSSD CSD的基于图形的最近的邻居搜索算法。为此，我们更修改算法在硬件上更适合，并使用基于HLS和RTL的方法实现两种类型的加速器，并采用各种优化方法。此外，我们扩展了提议的平台，以拥有4个SMARTSSS，并应用图形并行性以进一步提高系统性能。结果，拟议的计算存储平台在258.66W的功率耗散时，SIFT1B数据集的每秒吞吐量达到75.59个查询，该数据集的功率耗散为12.83倍，比常规CPU和GPU和GPU更快，更快的10.43 x和10.43 x和24.33 x - 基于基于的服务器平台。借助多稳定的存储和自定义加速能力，我们相信所提出的计算存储平台是针对成本敏感的云数据中心的有前途的解决方案。

State-of-the-art algorithms for Approximate Nearest Neighbor Search (ANNS) such as DiskANN, FAISS-IVF, and HNSW build data dependent indices that offer substantially better accuracy and search efficiency over data-agnostic indices by overfitting to the index data distribution. When the query data is drawn from a different distribution - e.g., when index represents image embeddings and query represents textual embeddings - such algorithms lose much of this performance advantage. On a variety of datasets, for a fixed recall target, latency is worse by an order of magnitude or more for Out-Of-Distribution (OOD) queries as compared to In-Distribution (ID) queries. The question we address in this work is whether ANNS algorithms can be made efficient for OOD queries if the index construction is given access to a small sample set of these queries. We answer positively by presenting OOD-DiskANN, which uses a sparing sample (1% of index set size) of OOD queries, and provides up to 40% improvement in mean query latency over SoTA algorithms of a similar memory footprint. OOD-DiskANN is scalable and has the efficiency of graph-based ANNS indices. Some of our contributions can improve query efficiency for ID queries as well.

Low-rank matrix approximations, such as the truncated singular value decomposition and the rank-revealing QR decomposition, play a central role in data analysis and scientific computing. This work surveys and extends recent research which demonstrates that randomization offers a powerful tool for performing low-rank matrix approximation. These techniques exploit modern computational architectures more fully than classical methods and open the possibility of dealing with truly massive data sets.This paper presents a modular framework for constructing randomized algorithms that compute partial matrix decompositions. These methods use random sampling to identify a subspace that captures most of the action of a matrix. The input matrix is then compressed-either explicitly or implicitly-to this subspace, and the reduced matrix is manipulated deterministically to obtain the desired low-rank factorization. In many cases, this approach beats its classical competitors in terms of accuracy, speed, and robustness. These claims are supported by extensive numerical experiments and a detailed error analysis.The specific benefits of randomized techniques depend on the computational environment. Consider the model problem of finding the k dominant components of the singular value decomposition of an m × n matrix. (i) For a dense input matrix, randomized algorithms require O(mn log(k)) floating-point operations (flops) in contrast with O(mnk) for classical algorithms. (ii) For a sparse input matrix, the flop count matches classical Krylov subspace methods, but the randomized approach is more robust and can easily be reorganized to exploit multi-processor architectures. (iii) For a matrix that is too large to fit in fast memory, the randomized techniques require only a constant number of passes over the data, as opposed to O(k) passes for classical algorithms. In fact, it is sometimes possible to perform matrix approximation with a single pass over the data.

索引是支持大型数据库中有效查询处理的有效方法。最近，已积极探索了替代或补充传统索引结构的学习指数的概念，以降低存储和搜索成本。但是，在高维度空间中准确有效的相似性查询处理仍然是一个开放的挑战。在本文中，我们提出了一种称为LIMS的新型索引方法，该方法使用数据群集，基于枢轴的数据转换技术和学习的索引来支持度量空间中的有效相似性查询处理。在LIM中，将基础数据分配到簇中，使每个群集都遵循相对均匀的数据分布。数据重新分布是通过利用每个集群的少量枢轴来实现的。类似的数据被映射到紧凑的区域，而映射的值是完全顺序的。开发机器学习模型是为了近似于磁盘上每个数据记录的位置。有效的算法设计用于基于LIMS的处理范围查询和最近的邻居查询，以及具有动态更新的索引维护。与传统索引和最先进的学习索引相比，对现实世界和合成数据集的广泛实验证明了LIM的优势。

高维空间中的大约最近的邻居搜索（ANN）对于许多现实生活应用程序（例如电子商务，Web，多媒体等）至关重要。在本文中，我们提出了一个端到端的学习框架，该框架将分区（ANN的一个关键步骤）和使用自定义损失函数进行学习进行搜索步骤。我们提出的解决方案的关键优势是，它不需要对数据集进行任何昂贵的预处理，这是最新方法的关键局限性之一。我们通过制定不需要地面真实标签来量化数据空间分区的质量的多目标自定义损失函数来实现上述边缘，从而完全不受监督。我们还通过在损失功能中添加不同的输入权重来训练模型集合以增强搜索质量来提出一种结合技术。在几个标准的ANN标准基准上，我们表明我们的方法击败了最新的空间分区方法和无处不在的K-均值聚类方法，同时使用较少的参数和较短的离线训练时间。在没有一般性的情况下，我们的无监督分区方法被证明是许多广泛使用的聚类方法（例如K-均值聚类和DBSCAN）的有希望的替代方法。

Similarity search finds application in specialized database systems handling complex data such as images or videos, which are typically represented by high-dimensional features and require specific indexing structures. This paper tackles the problem of better utilizing GPUs for this task. While GPUs excel at data-parallel tasks, prior approaches are bottlenecked by algorithms that expose less parallelism, such as k-min selection, or make poor use of the memory hierarchy.We propose a design for k-selection that operates at up to 55% of theoretical peak performance, enabling a nearest neighbor implementation that is 8.5× faster than prior GPU state of the art. We apply it in different similarity search scenarios, by proposing optimized design for brute-force, approximate and compressed-domain search based on product quantization. In all these setups, we outperform the state of the art by large margins. Our implementation enables the construction of a high accuracy k-NN graph on 95 million images from the Yfcc100M dataset in 35 minutes, and of a graph connecting 1 billion vectors in less than 12 hours on 4 Maxwell Titan X GPUs. We have open-sourced our approach 1 for the sake of comparison and reproducibility.

Data-driven neighborhood definitions and graph constructions are often used in machine learning and signal processing applications. k-nearest neighbor~(kNN) and $\epsilon$-neighborhood methods are among the most common methods used for neighborhood selection, due to their computational simplicity. However, the choice of parameters associated with these methods, such as k and $\epsilon$, is still ad hoc. We make two main contributions in this paper. First, we present an alternative view of neighborhood selection, where we show that neighborhood construction is equivalent to a sparse signal approximation problem. Second, we propose an algorithm, non-negative kernel regression~(NNK), for obtaining neighborhoods that lead to better sparse representation. NNK draws similarities to the orthogonal matching pursuit approach to signal representation and possesses desirable geometric and theoretical properties. Experiments demonstrate (i) the robustness of the NNK algorithm for neighborhood and graph construction, (ii) its ability to adapt the number of neighbors to the data properties, and (iii) its superior performance in local neighborhood and graph-based machine learning tasks.

图表学习方法为解决图形所代表的复杂的现实世界问题打开了新的可能性。但是，这些应用程序中使用的许多图包括数百万节点和数十亿个边缘，并且超出了当前方法和软件实现的功能。我们提供葡萄，这是一种用于图形处理和表示学习的软件资源，能够通过使用专业和智能数据结构，算法和快速并行实现来通过大图扩展。与最先进的软件资源相比，葡萄显示出经验空间和时间复杂性的数量级的改善，以及边缘预测和节点标签预测性能的实质和统计学上的显着改善。此外，葡萄提供了来自文献和其他来源的80,000多种图，标准化界面允许直接整合第三方库，61个节点嵌入方法，25个推理模型和3个模块化管道，以允许公平且可重复的方法比较以及用于图形处理和嵌入的库。

近年来，在平衡（超级）图分配算法的设计和评估中取得了重大进展。我们调查了过去十年的实用算法的趋势，用于平衡（超级）图形分区以及未来的研究方向。我们的工作是对先前有关该主题的调查的更新。特别是，该调查还通过涵盖了超图形分区和流算法来扩展先前的调查，并额外关注并行算法。

Kernel matrices, as well as weighted graphs represented by them, are ubiquitous objects in machine learning, statistics and other related fields. The main drawback of using kernel methods (learning and inference using kernel matrices) is efficiency -- given $n$ input points, most kernel-based algorithms need to materialize the full $n \times n$ kernel matrix before performing any subsequent computation, thus incurring $\Omega(n^2)$ runtime. Breaking this quadratic barrier for various problems has therefore, been a subject of extensive research efforts. We break the quadratic barrier and obtain $\textit{subquadratic}$ time algorithms for several fundamental linear-algebraic and graph processing primitives, including approximating the top eigenvalue and eigenvector, spectral sparsification, solving linear systems, local clustering, low-rank approximation, arboricity estimation and counting weighted triangles. We build on the recent Kernel Density Estimation framework, which (after preprocessing in time subquadratic in $n$) can return estimates of row/column sums of the kernel matrix. In particular, we develop efficient reductions from $\textit{weighted vertex}$ and $\textit{weighted edge sampling}$ on kernel graphs, $\textit{simulating random walks}$ on kernel graphs, and $\textit{importance sampling}$ on matrices to Kernel Density Estimation and show that we can generate samples from these distributions in $\textit{sublinear}$ (in the support of the distribution) time. Our reductions are the central ingredient in each of our applications and we believe they may be of independent interest. We empirically demonstrate the efficacy of our algorithms on low-rank approximation (LRA) and spectral sparsification, where we observe a $\textbf{9x}$ decrease in the number of kernel evaluations over baselines for LRA and a $\textbf{41x}$ reduction in the graph size for spectral sparsification.

数据处理的最新进展刺激了对非常大尺度的学习图的需求。众所周知，图形神经网络（GNN）是解决图形学习任务的一种新兴和有力的方法，很难扩大规模。大多数可扩展模型应用基于节点的技术来简化GNN的昂贵图形消息传播过程。但是，我们发现当应用于百万甚至数十亿尺度的图表时，这种加速度不足。在这项工作中，我们提出了Scara，这是一种可扩展的GNN，具有针对图形计算的特征优化。 Scara有效地计算出从节点功能中嵌入的图形，并进一步选择和重用功能计算结果以减少开销。理论分析表明，我们的模型在传播过程以及GNN培训和推理中具有确保精度，实现了子线性时间的复杂性。我们在各种数据集上进行了广泛的实验，以评估圣aca的功效和效率。与基线的性能比较表明，与快速收敛和可比精度相比，与当前的最新方法相比，圣aca最高可达到100倍的图形传播加速度。最值得注意的是，在100秒内处理最大的十亿个GNN数据集纸100m（1.11亿节点，1.6B边缘）上的预先计算是有效的。

我们提出了Falconn ++，这是一种新型的局部敏感滤波（LSF）方法，可在角距离上进行大约最近的邻居搜索。Falconn ++在查询之前可以在任何哈希桶中滤除潜在的远距离点，这与其他基于哈希的解决方案相比会导致更高质量的候选者。从理论上讲，Falconn ++渐近地达到比Falconn的查询时间复杂性较低，而Falconn是角度距离的最佳位置敏感散列方案。从经验上讲，Falconn ++在许多现实世界中的数据集中取得了比Falconn更高的召回速度权衡。Falconn ++也与HNSW具有竞争力，HNSW是高度搜索召回机制的有效代表。

多视图聚类（MVC）最佳地集成了来自不同视图的互补信息，以提高聚类性能。尽管在各种应用中证明了有希望的性能，但大多数现有方法都直接融合了多个预先指定的相似性，以学习聚类的最佳相似性矩阵，这可能会导致过度复杂的优化和密集的计算成本。在本文中，我们通过对齐方式最大化提出了晚期Fusion MVC，以解决这些问题。为此，我们首先揭示了现有K-均值聚类的理论联系以及基本分区和共识之一之间的对齐。基于此观察结果，我们提出了一种简单但有效的多视算法，称为LF-MVC-GAM。它可以从每个单独的视图中最佳地将多个源信息融合到分区级别，并最大程度地将共识分区与这些加权基础分区保持一致。这种对齐方式有助于整合分区级别信息，并通过充分简化优化过程来大大降低计算复杂性。然后，我们设计了另一个变体LF-MVC-LAM，以通过在多个分区空间之间保留局部内在结构来进一步提高聚类性能。之后，我们开发了两种三步迭代算法，以通过理论上保证的收敛来解决最终的优化问题。此外，我们提供了所提出算法的概括误差约束分析。对十八个多视图基准数据集进行了广泛的实验，证明了拟议的LF-MVC-GAM和LF-MVC-LAM的有效性和效率，范围从小到大型数据项不等。拟议算法的代码可在https://github.com/wangsiwei2010/latefusionalignment上公开获得。

本文提出了一种新颖的邻居搜索算法，可实现TPU（Google Tensor处理单元）的峰值性能，超过了最先进的GPU算法，其召回水平相似。所提出的算法的设计是由准确的加速器性能模型的动机，该模型同时考虑了内存和指令瓶颈。我们的算法具有预期召回的分析保证，并且不需要维护复杂的索引数据结构或调整，因此它适用于经常更新的应用程序。我们的工作可在TPU上的Jax和Tensorflow的开源软件包中获得。

本文研究了分层聚类问题，其中目标是生产一种在数据集的变化尺度上表示集群的树形图。我们提出了用于设计并行分层凝聚聚类（HAC）算法的Parchain框架，并使用该框架，我们获得了全面连锁，平均联系和病房的联动标准的新颖平行算法。与最先前的并行HAC算法相比，这需要二次存储器，我们的新算法仅需要线性存储器，并且可以扩展到大数据集。 PARCHAIN基于我们最近邻的链算法的并行化，并使多个群集能够在每一轮上合并。我们介绍了两个关键优化，这对于效率至关重要：范围查询优化，减少查找群集的最近邻居所需的距离计算数，以及存储可能重复使用的先前计算的距离子集的缓存优化。通过实验，我们表明，我们的高度优化实现，使用48个核心，通过双向超线程实现5.8--110.1倍的加速，通过最先进的并行HAC算法，实现了13.75--54.23倍的自相对加速。与最先进的算法相比，我们的算法较少的空间少于237.3倍。我们的算法能够扩展到具有数百万点的数据集大小，现有算法无法处理该算法。

我们研究了自然语言处理中出现的近似对相似矩阵的算法。通常，计算$ N $数据点的相似性矩阵需要$ \ omega（n ^ 2）$相似计算。这种二次缩放是一个重要的瓶颈，尤其是当通过昂贵的功能计算相似性时，例如，通过变压器模型计算。近似方法通过使用恰好计算的相似性的小子集来减少这种二次复杂性，以近似于完整成对相似性矩阵的其余部分。大量工作侧重于正半纤维（PSD）相似矩阵的有效近似，其在内核方法中。然而，关于无限期（非PSD）相似性矩阵的较少被理解得更少，这通常在NLP中产生。通过观察到，许多这些矩阵仍然有点接近PSD，我们将流行的NYSTR \“{o} M方法介绍到无限制地的概述。我们的算法可以应用于任何相似性矩阵并在Sublinear时间运行在矩阵的大小中，使用仅$ O（ns）$相似性计算产生秩的等级$近似。我们表明我们的方法以及CR Cur分解的简单变体，在近似各种相似度方面表现得非常好在NLP任务中产生的矩阵。我们在文档分类，句子相似度和跨文档COREREFED的下游任务中展示了近似相似性矩阵的高精度。

Cardinality estimation is one of the most fundamental and challenging problems in query optimization. Neither classical nor learning-based methods yield satisfactory performance when estimating the cardinality of the join queries. They either rely on simplified assumptions leading to ineffective cardinality estimates or build large models to understand the data distributions, leading to long planning times and a lack of generalizability across queries. In this paper, we propose a new framework FactorJoin for estimating join queries. FactorJoin combines the idea behind the classical join-histogram method to efficiently handle joins with the learning-based methods to accurately capture attribute correlation. Specifically, FactorJoin scans every table in a DB and builds single-table conditional distributions during an offline preparation phase. When a join query comes, FactorJoin translates it into a factor graph model over the learned distributions to effectively and efficiently estimate its cardinality. Unlike existing learning-based methods, FactorJoin does not need to de-normalize joins upfront or require executed query workloads to train the model. Since it only relies on single-table statistics, FactorJoin has small space overhead and is extremely easy to train and maintain. In our evaluation, FactorJoin can produce more effective estimates than the previous state-of-the-art learning-based methods, with 40x less estimation latency, 100x smaller model size, and 100x faster training speed at comparable or better accuracy. In addition, FactorJoin can estimate 10,000 sub-plan queries within one second to optimize the query plan, which is very close to the traditional cardinality estimators in commercial DBMS.

传染媒介符号架构将高维传染料空间与一组精心设计的操作员组合起来，以便使用大型数字向量进行符号计算。主要目标是利用他们的代表权力和处理模糊和歧义的能力。在过去几年中，已经提出了几个VSA实现。可用的实现在底层矢量空间和VSA运算符的特定实现中不同。本文概述了十一可用的VSA实现，并讨论了其潜在的矢量空间和运营商的共性和差异。我们创建了一种可用绑定操作的分类，并使用来自类比推理的示例来显示非自逆绑定操作的重要分支。主要贡献是可用实施的实验比较，以便评估（1）捆绑的容量，（2）非精确解除界操作的近似质量，（3）组合绑定和捆绑操作对查询的影响回答性能，（4）两个示例应用程序的性能：视觉地位和语言识别。我们预计此比较和系统化与VSA的开发相关，并支持选择特定任务的适当VSA。实现可用。

Graph embedding algorithms embed a graph into a vector space where the structure and the inherent properties of the graph are preserved. The existing graph embedding methods cannot preserve the asymmetric transitivity well, which is a critical property of directed graphs. Asymmetric transitivity depicts the correlation among directed edges, that is, if there is a directed path from u to v, then there is likely a directed edge from u to v. Asymmetric transitivity can help in capturing structures of graphs and recovering from partially observed graphs. To tackle this challenge, we propose the idea of preserving asymmetric transitivity by approximating high-order proximity which are based on asymmetric transitivity. In particular, we develop a novel graph embedding algorithm, High-Order Proximity preserved Embedding (HOPE for short), which is scalable to preserve high-order proximities of large scale graphs and capable of capturing the asymmetric transitivity. More specifically, we first derive a general formulation that cover multiple popular highorder proximity measurements, then propose a scalable embedding algorithm to approximate the high-order proximity measurements based on their general formulation. Moreover, we provide a theoretical upper bound on the RMSE (Root Mean Squared Error) of the approximation. Our empirical experiments on a synthetic dataset and three realworld datasets demonstrate that HOPE can approximate the high-order proximities significantly better than the state-ofart algorithms and outperform the state-of-art algorithms in tasks of reconstruction, link prediction and vertex recommendation.