高效开源Kd树指南：ANN编程详解

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《开源KD树手册 Ann》是一本详细介绍如何高效利用ANNSearch Library（Approximate Nearest Neighbors，近似最近邻搜索）的指南。ANNS是一种用于解决大数据集中的高效空间搜索问题的算法库，特别适用于高维空间中的相似度搜索，如在推荐系统、图像处理和自然语言处理等领域。该手册的第1章是入门介绍，主要涵盖以下几个关键知识点： 1.1 **什么是ANN?**：ANN库允许在无需精确匹配的情况下查找与查询对象最接近的数据点，通过牺牲一部分精确性来换取更快的搜索速度。它特别适合在大数据集上进行实时或近实时的搜索操作。 1.2 **下载和使用ANN**：介绍了如何从官方渠道下载最新版本的库，并提供了不同操作系统（如Unix/Linux和Microsoft Windows）的安装指导。对于初次使用者，这部分内容至关重要，因为它涉及了库的集成和配置步骤。 1.3 **编译ANN**：这部分详细阐述了编译库的具体方法，包括： - **Unix/Linux系统**：解释了如何在这些系统上配置编译环境并构建库。 - **Microsoft Windows系统**：提供了针对Windows用户的预编译文件以及自定义编译的步骤。 - **应用编译**：还提到了如何编写使用ANN库的应用程序，并确保它们正确链接到库。 2.1 **使用ANN**：这部分着重于实际操作，包括： - **坐标、点、距离和索引**：介绍了数据结构的基础概念，如如何表示和操作多维空间中的点。 - **最近邻搜索结构**：讲解了如何利用库中的数据结构进行高效搜索，以及搜索过程的原理。 - **点实用函数**：列举了一些辅助函数，用于处理数据准备和搜索结果分析。 - **示例程序**：给出了一个简短的程序示例，帮助读者理解如何在实际项目中使用库。 - **应用编译示例**：展示了如何将ANN整合到实际应用程序中，并确保正确运行。 2.2 **配置ANN**：这部分关注的是个性化设置和优化选项，如： - **范数和距离**：讨论了选择合适的距离度量（如欧几里得距离、曼哈顿距离等）对搜索性能的影响。 - **点、坐标和距离的进一步处理**：可能涉及数据预处理和特殊应用场景的需求。 - **自我匹配**：可能指的是处理自相似数据或避免搜索自身的情况。 2.3 **修改搜索结构**：如果需要根据特定需求调整库的行为，可以进行如下操作： - **ANN数据结构**：了解底层数据结构的可扩展性和定制性，可能涉及到代码级别的调整。 - **搜索结构的修改**：如何调整搜索算法的参数或者设计更高级的搜索策略。《开源KD树手册 Ann》不仅提供了一个全面的教程，还包括了从安装、配置到高级应用的方方面面，为想要在实际项目中使用ANNS的开发者提供了丰富的参考资源。

Figure 1: Sample output of ann2ﬁg for a kd-tree and a box-decomposition tree.

2.1 Using ANN

This section discusses how to use ANN for answering nearest neighbors in its default conﬁguration,

namely computing the nearest neighbor using Euclidean distance for points whose coordinates are

of type double. Later in Section 2.2 we discuss how to customize ANN for diﬀerent coordinate types

and diﬀerent norms.

2.1.1 Coordinates, Points, Distances, and Indices

Each point in d-dimensional space is assumed to be expressed as a d-vector of coordinates

p = (p

, p

, . . . , p

d−1

(Indices start from 0, as is C++’s convention.) A coordinate is of type ANNcoord. By default,

ANNcoord is deﬁned to be of type double, but it is possible to modify the ANN include ﬁles to

change this and other ANN types, as described in Section 2.2.2.

ANN deﬁnes the distance between two points to be their Euclidean distance, that is

dist(p, q) =





0≤i<d

− q

)





1/2

(Section 2.2.1 explains how to modify ANN for other Minkowski norms.) For the purposes of

comparing distances, it is not necessary to compute the ﬁnal square root in the above expression.

ANN actually computes squared distances rather than true Euclidean distances. A squared distance

is deﬁned to be of type ANNdist. It is deﬁned to be double by default (but can be changed). By

using squared distances rather than true Euclidean distances, ANN not only saves on the time of

computing square roots, but has the advantage that integer types can be used instead to accurately

represent distances when integer type coordinates are used. (It worth emphasizing that, even

though ANN represents distances internally as squared distances, when it computes -approximate

nearest neighbors, the approximation is relative to the true, not squared, distance.)

The most basic object manipulated by ANN is a point, which is deﬁned in C++ to be a dimen-

sionless array of coordinates, or more simply a pointer to a coordinate.

Thus we deﬁne ANNpoint

to be

It is natural to wonder why ANN does not deﬁne a special point class, which might store additional information

typedef ANNcoord* ANNpoint; // a point

It is the user’s responsibility to allocate and deallocate storage for points. Each point must

have at least as many components allocated as the dimension of the space. Any extra components

are ignored.

Since ANN operates on arrays of points and distances, we also deﬁne dimensionless arrays of

these two objects:

typedef ANNpoint* ANNpointArray; // an array of points

typedef ANNdist* ANNdistArray; // an array of squared distances

We will see later that a set of data points is presented to ANN as an ANNpointArray. ANN

returns the results of a nearest neighbor query as an integer index into this array. To make it clear

when we are doing so, ANN deﬁnes the type ANNidx to be a psuedonym for int. The result of a k-

nearest neighbor query is returned as a pointer to an array of indices, which is of type ANNidxArray,

deﬁned as follows.

typedef ANNidx* ANNidxArray; // an array of point indices

Finally, ANN provides a boolean type called ANNbool. (Although ANSI C++ provides a type

bool, this is not supported in some of the older compilers.) Its values are ANNfalse and ANNtrue.

2.1.2 Nearest Neighbor Search Structure

The principal structure that ANN uses for performing nearest neighbor searches is called an AN-

NpointSet. This is an abstract object which supports two search operations, annkSearch(), which

computes the approximate k nearest neighbors of a query point, and annKFRSearch(), which per-

forms a combination of a ﬁxed-radius approximate k nearest neighbor search and a range search

(see the description below).

ANN provides three concrete instantiations of an ANNpointSet: ANNbruteForce, ANNkd

tree,

and ANNbd tree. The ﬁrst of these stores the points as an array, and implements a simple brute-

force search for nearest neighbors. It is provided primarily for the use of the implementors to

validate the correctness of the more sophisticated search structures, and should not be used for

actual nearest neighbor queries. Among the other two, we will ﬁrst introduce only the more basic

one, the ANNkd tree, and leave the ANNbd tree to be discussed in Section 2.3. The ANNkd tree

supports the following operations.

Constructor: This builds a kd-tree from a set of n data points in dimension d, stored in a point

array pa. The procedure allocates the necessary storage for the data structure. It is assumed

that there is at least one data point (n ≥ 1) and that the dimension is strictly positive

(d ≥ 1). Warning: This procedure does virtually no error checking, and if these assumptions

are violated or if storage cannot be allocated, then the most likely result will be that the

program aborts.

A (simpliﬁed) prototype is given below. (See Section 2.3 for more complete information.) The

order in which the points appear in the points array is signiﬁcant, because nearest neighbors

about points. This would then necessitate that the library be templated about the point type. Since compiler support

for templating was rather weak in the mid-90’s when ANN was ﬁrst implemented designed, it was decided instead

to decouple the user’s point object from the ANN point type. In this way we allow the user to deﬁne a point object

in any way desired. The user then interfaces with ANN by simply providing a pointer to the point’s coordinates. In

many cases, this may just be a ﬁeld in the user’s own point class.

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