超平面树:度量空间中相似性搜索的索引结构

相似性搜索是从数据库中检索出同给定数据对象相似的数据对象，已有的基于R-tree的相似性搜索，当搜索空间的维的个数较小时效率较高，但当搜索空间的维的个数较大时则效率很低．针对此问题，提出了新的度量空间分割方法和索引结构pgh-tree，利用数据对象与很少几个固定参考对象的距离之差进行数据分割和索引，产生一个平衡的索引树．在此基础上，提出了新的算法，利用查询数据对象与固定参考对象的距离之差过滤掉大部分的不相关数据，具有较小的I／O代价和距离计算复杂性，平均复杂性为θ(n^0.58)，是目前复杂性最小的相似性搜索算法．另外还讨论了基于pgh-tree的最近相邻点搜索策略．     

相似时间子序列快速搜索的改进算法

索引空间相似性度量标准的精确度较低,在现有的相似时间子序列搜索算法中,后期处理过程中内外存之间数据的I／O时间较长。针对该问题,引用一种非线性维数约简技术,提出改进的相似时间子序列快速搜索算法,提高索引空间相似性度量标准的精确度,降低错误匹配的发生率。实验结果表明,该算法可有效降低重复估算的数据量,提高相似性搜索的效率。     

基于不相似性度量优化的密度峰值聚类算法

密度峰值聚类（clustering by fast search and find of density peaks,简称DPC）是一种基于局部密度和相对距离属性快速寻找聚类中心的有效算法.DPC通过决策图寻找密度峰值作为聚类中心,不需要提前指定类簇数,并可以得到任意形状的簇聚类.但局部密度和相对距离的计算都只是简单依赖基于距离度量的相似度矩阵,所以在复杂数据上DPC聚类结果不尽如人意,特别是当数据分布不均匀、数据维度较高时.另外,DPC算法中局部密度的计算没有统一的度量,根据不同的数据集需要选择不同的度量方式.第三,截断距离d_c的度量只考虑数据的全局分布,忽略了数据的局部信息,所以d_c的改变会影响聚类的结果,尤其是在小样本数据集上.针对这些弊端,提出一种基于不相似性度量优化的密度峰值聚类算法（optimized density peaks clustering algorithm based on dissimilarity measure,简称DDPC）,引入基于块的不相似性度量方法计算相似度矩阵,并基于新的相似度矩阵计算样本的K近邻信息,然后基于样本的K近邻信息重新定义局部密度的度量方法.经典数据集的实验结果表明,基于不相似性度量优化的密度峰值聚类算法优于DPC的优化算法FKNN-DPC和DPC-KNN,可以在密度不均匀以及维度较高的数据集上得到满意的结果;同时统一了局部密度的度量方式,避免了传统DPC算法中截断距离d_c对聚类结果的影响.     

背包类问题的并行O(25n/6)时间-空间-处理机折衷

将串行动态二表算法应用于并行三表算法的设计中,提出一种求解背包、精确的可满足性和集覆盖等背包类NP完全问题的并行三表六子表算法.基于EREW-PRAM模型,该算法可使用O(2^n/8)的处理机在O(2^7n/16)的时间和O(2^13n/48)的空间求解n维背包类问题,其时间-空间-处理机折衷为O(2^5n/6).与现有文献的性能对比分析表明,该算法极大地提高了并行求解背包类问题的时间-空间-处理机折衷性能.由于该算法能够破解更高维数的背包类公钥和数字水印系统,其结论在密钥分析领域具有一定的理论和实际意义.     

k-Median近似计算复杂度与局部搜索近似算法分析

k-Median问题的近似算法研究一直是计算机科学工作者关注的焦点,现有研究结果大多是关于欧式空间和Metric空间的,一般距离空间k-Median的结果多年来一直未见.考虑一般距离空间k-Median问题,设d_max/d_min表示k-Median实例中与客户点邻接的最长边长比最短边长的最大者.首先证明d_max/d_min≤ω+ε的k-Median问题不存在近似度小于1+ω-1/e的多项式时间近似算法,除非,由此推出Metric k-Median问题不可近似到1+2/e,除非NP(∈)DTME(N^{O(log logn)}).然后给出k-Median问题的一个局部搜索算法,分析表明,若有d_max/d_min≤ω,则算法的近似度为1+ω-1/2.该结果亦适用于Metric k-Median,ω≤5时,局部搜索算法求解Metric k-Median的近似度为3,好于现有结果3+2/P.通过计算机实验,进一步研究了k-Median局部搜索求解算法的实际计算效果和该算法的改进方法.     

求解大规模谱聚类的近似加权核k-means算法

谱聚类将聚类问题转化成图划分问题,是一种基于代数图论的聚类方法.在求解图划分目标函数时,一般利用Rayleigh熵的性质,通过计算Laplacian矩阵的特征向量将原始数据点映射到一个低维的特征空间中,再进行聚类.然而在谱聚类过程中,存储相似矩阵的空间复杂度是O(n²),对Laplacian矩阵特征分解的时间复杂度一般为O(n³),这样的复杂度在处理大规模数据时是无法接受的.理论证明,Normalized Cut图聚类与加权核k-means都等价于矩阵迹的最大化问题.因此,可以用加权核k-means算法来优化Normalized Cut的目标函数,这就避免了对Laplacian矩阵特征分解.不过,加权核k-means算法需要计算核矩阵,其空间复杂度依然是O(n²).为了应对这一挑战,提出近似加权核k-means算法,仅使用核矩阵的一部分来求解大数据的谱聚类问题.理论分析和实验对比表明,近似加权核k-means的聚类表现与加权核k-means算法是相似的,但是极大地减小了时间和空间复杂性.     

目标识别的相似性测量方法

相似性测量是图像后期特征匹配的关键步骤,本文深入研究了特征向量顺序比对和交叉比对方法的差异,并以形状上下文提取的图像二维直方图特征为基础,分别结合x²距离、推土机距离和扩散距离三种不同的相似性测量方法对多种图像标准库进行了识别验证.     

网格多处理机的一种改进的子网分配算法

子网分配问题是指识别并分配一个空闲的、满足指定大小要求的节点机.首先,提出了网格结构中一种新的具有O(N²_a·1og₂N_a)时间复杂度的空闲子网搜索算法,它优于现有的O(N³_a)时间复杂度的搜索算法.然后,用该算法对基于保留因子的最佳匹配类子网分配算法——RF(reservation factor)算法进行了改进,得到了     

半动态矩形交查询算法

本文讨论了动态矩形交查询算法.文中介绍了两个半动态矩形查询的新算法，它们分别基于一维数据结构和二维数据结构.一维查询算法的查询时间复杂度是O（logM＋k′），更新时间复杂度是O（logMlogn），空间复杂度是O（nlogM/）.二维查询算法的查询时间复杂度是O（log²M＋k），更新时间复杂度是O（log²Mlogn），空间复杂度是O（nlog²M）.本文分别实现了这两个算法，通过对它们的性能进行比较，发现一维查询算法是一种高效、实用的算法.     

一种半监督K均值多关系数据聚类算法

提出了一种半监督K均值多关系数据聚类算法.该算法在K均值聚类算法的基础上扩展了其初始类簇的选择方法和对象相似性度量方法,以用于多关系数据的半监督学习.为了获取高性能,该算法在聚类过程中充分利用了标记数据、对象属性及各种关系信息.多关系数据库Movie上的实验结果验证了该算法的有效性.     

Adapting metric indexes for searching in multi-metric spaces

An important research issue in multimedia databases is the retrieval of similar objects. For most applications in multimedia databases, an exact search is not meaningful. Thus, much effort has been devoted to develop efficient and effective similarity search techniques. A recent approach that has been shown to improve the effectiveness of similarity search in multimedia databases resorts to the usage of combinations of metrics (i.e., a search on a multi-metric space). In this approach, the desirable contribution (weight) of each metric is chosen at query time. It follows that standard metric indexes cannot be directly used to improve the efficiency of dynamically weighted queries, because they assume that there is only one fixed distance function at indexing and query time. This paper presents a methodology for adapting metric indexes to multi-metric indexes, that is, to support similarity queries with dynamic combinations of metric functions. The adapted indexes are built with a single distance function and store partial distances to estimate the dynamically weighed distances. We present two novel indexes for multimetric space indexing, which are the result of the application of the proposed methodology.     

Bulk construction of dynamic clustered metric trees

Repositories of complex data types, such as images, audio, video and free text, are becoming increasingly frequent in various fields. A general searching approach for such data types is that of similarity search, where the search is for similar objects and similarity is modeled by a metric distance function. An important class of access methods for similarity search in metric data is that of dynamic clustered metric trees, where the index is structured as a paged and balanced tree and the space is partitioned hierarchically into compact regions. While access methods of this class allow dynamic insertions typically of single objects, the problem of efficiently inserting a given data set into the index in bulk is largely open. In this article we address this problem and propose novel algorithms corresponding to its two cases, where the index is initially empty (i.e. bulk loading), and where the index is initially non empty (i.e. bulk insertion). The proposed bulk loading algorithm builds the index bottom-up layer by layer, using a new sampling based clustering method, which improves clustering results by improving the quality of the selected sample sets. The proposed bulk insertion algorithm employs the bulk loading algorithm to load the given data into a new index structure, and then merges the new and the existing structures into a unified high quality index, using a novel decomposition method to reduce overlaps between the structures. Both algorithms yield significantly improved construction and search performance, and are applicable to all dynamic clustered metric trees. Results from an extensive experimental study show that the proposed algorithms outperform alternative methods, reducing construction costs by up to 47% for CPU costs and 99% for I/O costs, and search costs by up to 48% for CPU costs and 30% for I/O costs.     

一种支持快速相似检索的多维索引结构

基于内容的图像检索是一种典型的相似检索问题,对于尺度空间上的图像相似匹配问题,一般认为距离计算费用很高.因此,需要建立有效的索引结构,以减少每个查询中的距离计算次数.为此,基于数据空间的"优化划分",并且使用"代表点",以层次结构方式划分数据,提出了一种新的基于距离的相似索引结构opt-树及其变种(-树.为了更有效地支持基于内容的图像检索,在(-树索引结构中采用了"(-最优化划分"和"(-对称冗余存储"策略,以提高相似检索的效率.详细讨论了这种索引结构的建立与检索等问题,并给出了相应的算法.实验结果显示了这种索引技术的有效性.     

A graph-based cache for large-scale similarity search engines

Large-scale similarity search engines are complex systems devised to process unstructured data like images and videos. These systems are deployed on clusters of distributed processors communicated through high-speed networks. To process a new query, a distance function is evaluated between the query and the objects stored in the database. This process relays on a metric space index distributed among the processors. In this paper, we propose a cache-based strategy devised to reduce the number of computations required to retrieve the top-k object results for user queries by using pre-computed information. Our proposal executes an approximate similarity search algorithm, which takes advantage of the links between objects stored in the cache memory. Those links form a graph of similarity among pre-computed queries. Compared to the previous methods in the literature, the proposed approach reduces the number of distance evaluations up to 60%.     

Improving the space cost of <Emphasis Type="Italic">k</Emphasis>-NN search in metric spaces by using distance estimators

Similarity searching in metric spaces has a vast number of applications in several fields like multimedia databases, text retrieval, computational biology, and pattern recognition. In this context, one of the most important similarity queries is the k nearest neighbor (k-NN) search. The standard best-first k-NN algorithm uses a lower bound on the distance to prune objects during the search. Although optimal in several aspects, the disadvantage of this method is that its space requirements for the priority queue that stores unprocessed clusters can be linear in the database size. Most of the optimizations used in spatial access methods (for example, pruning using MinMaxDist) cannot be applied in metric spaces, due to the lack of geometric properties. We propose a new k-NN algorithm that uses distance estimators, aiming to reduce the storage requirements of the search algorithm. The method stays optimal, yet it can significantly prune the priority queue without altering the output of the query. Experimental results with synthetic and real datasets confirm the reduction in storage space of our proposed algorithm, showing savings of up to 80% of the original space requirement.

Searching in metric spaces by spatial approximation

We propose a new data structure to search in metric spaces. A metric space is formed by a collection of objects and a distance function defined among them which satisfies the triangle inequality. The goal is, given a set of objects and a query, retrieve those objects close enough to the query. The complexity measure is the number of distances computed to achieve this goal. Our data structure, called sa-tree (“spatial approximation tree”), is based on approaching the searched objects spatially, that is, getting closer and closer to them, rather than the classic divide-and-conquer approach of other data structures. We analyze our method and show that the number of distance evaluations to search among n objects is sublinear. We show experimentally that the sa-tree is the best existing technique when the metric space is hard to search or the query has low selectivity. These are the most important unsolved cases in real applications. As a practical advantage, our data structure is one of the few that does not need to tune parameters, which makes it appealing for use by non-experts. Edited by R. Sacks-Davis Received: 17 April 2001 / Accepted: 24 January 2002 / Published online: 14 May 2002     

CM-tree: A dynamic clustered index for similarity search in metric databases

Repositories of unstructured data types, such as free text, images, audio and video, have been recently emerging in various fields. A general searching approach for such data types is that of similarity search, where the search is for similar objects and similarity is modeled by a metric distance function. In this article we propose a new dynamic paged and balanced access method for similarity search in metric data sets, named CM-tree (Clustered Metric tree). It fully supports dynamic capabilities of insertions and deletions both of single objects and in bulk. Distinctive from other methods, it is especially designed to achieve a structure of tight and low overlapping clusters via its primary construction algorithms (instead of post-processing), yielding significantly improved performance. Several new methods are introduced to achieve this: a strategy for selecting representative objects of nodes, clustering based node split algorithm and criteria for triggering a node split, and an improved sub-tree pruning method used during search. To facilitate these methods the pairwise distances between the objects of a node are maintained within each node. Results from an extensive experimental study show that the CM-tree outperforms the M-tree and the Slim-tree, improving search performance by up to 312% for I/O costs and 303% for CPU costs.     

CM-tree: A dynamic clustered index for similarity search in metric databases

Repositories of unstructured data types, such as free text, images, audio and video, have been recently emerging in various fields. A general searching approach for such data types is that of similarity search, where the search is for similar objects and similarity is modeled by a metric distance function. In this article we propose a new dynamic paged and balanced access method for similarity search in metric data sets, named CM-tree (Clustered Metric tree). It fully supports dynamic capabilities of insertions and deletions both of single objects and in bulk. Distinctive from other methods, it is especially designed to achieve a structure of tight and low overlapping clusters via its primary construction algorithms (instead of post-processing), yielding significantly improved performance. Several new methods are introduced to achieve this: a strategy for selecting representative objects of nodes, clustering based node split algorithm and criteria for triggering a node split, and an improved sub-tree pruning method used during search. To facilitate these methods the pairwise distances between the objects of a node are maintained within each node. Results from an extensive experimental study show that the CM-tree outperforms the M-tree and the Slim-tree, improving search performance by up to 312% for I/O costs and 303% for CPU costs.     

Using extended feature objects for partial similarity retrieval

In this paper, we introduce the concept of extended feature objects for similarity retrieval. Conventional approaches for similarity search in databases map each object in the database to a point in some high-dimensional feature space and define similarity as some distance measure in this space. For many similarity search problems, this feature-based approach is not sufficient. When retrieving partially similar polygons, for example, the search cannot be restricted to edge sequences, since similar polygon sections may start and end anywhere on the edges of the polygons. In general, inherently continuous problems such as the partial similarity search cannot be solved by using point objects in feature space. In our solution, we therefore introduce extended feature objects consisting of an infinite set of feature points. For an efficient storage and retrieval of the extended feature objects, we determine the minimal bounding boxes of the feature objects in multidimensional space and store these boxes using a spatial access structure. In our concrete polygon problem, sets of polygon sections are mapped to 2D feature objects in high-dimensional space which are then approximated by minimal bounding boxes and stored in an R-tree. The selectivity of the index is improved by using an adaptive decomposition of very large feature objects and a dynamic joining of small feature objects. For the polygon problem, translation, rotation, and scaling invariance is achieved by using the Fourier-transformed curvature of the normalized polygon sections. In contrast to vertex-based algorithms, our algorithm guarantees that no false dismissals may occur and additionally provides fast search times for realistic database sizes. We evaluate our method using real polygon data of a supplier for the car manufacturing industry. Edited by R. Güting. Received October 7, 1996 / Accepted March 28, 1997     

基于马氏距离度量的局部线性嵌入算法

局部线性嵌入算法(LLE)中常用欧氏距离度量样本间相似度。而对于图像等高维数据,欧氏距离不能准确体现样本间的相似程度。文中提出基于马氏距离度量的局部线性嵌入算法(MLLE)。算法首先从现有样本中学习到一个马氏度量,然后在LLE算法的近邻选择、现有样本及新样本降维过程中用马氏度量作为相似性度量。将MLLE算法及其它典型的流形学习算法在ORL和USPS数据库上进行对比实验,结果表明MLLE算法具有良好的识别性能。