标签
PostgreSQL , 数组 , 相似度 , 文本分析 , 图像分析 , 字符串分析 , 婚姻介绍 , 精确配对
背景
相似度分析是一个非常普遍的需求，例如根据用户提供的线索，从一堆文本数据、图片数据、视频数据中筛选一段与用户的描述相近的。
我之前写过一系列的文章来介绍，文本、图片相似度搜索的技术和使用场景。
本文提到的技术实际上是很早以前的相似度计算的技术，现在已经改进了很多，但是旧的东西比较简单，也容易理解，了解一下初心未尝不可，还是挺有意思的。
从最简单的说起 - 如何计算两个数组的相似度
假设有两个数组，里面分别有一些元素，这些元素是用来表示用户的画像的。
那么通过计算不同用户之间的数组的相似度，就可以知道他们是否有共同的癖好，有没有话题可聊。
好像又扯到一些婚介网站啦，没错，确实可以用来配对呢。
那么怎么计算这两个数组的相似度呢？
算法介绍
首先了解几个数组相关的术语。
Na, Nb – the number of unique elements in the arrays
Nu – the number of unique elements in the union of sets
Ni – the number of unique elements in the intersection of arrays
1. 最简单的相似度算法如下
好处
- 容易理解
- 速度=N*log(N)
- 当Nb, Na很大时，也可以很好的支持
2. 另一种相似度算法
好处
- 速度=N*log(N)
- 当Nb, Na很大时，也可以很好的支持
注意以上两种方法都存在一定的问题
- Few elements -> large scatter of similarity (当元素很少时，相似度可能会很分散)
- Frequent elements -> weight below (当元素频繁出现时，没有词频的权重，无法得到合理的相似度)
3. TF/IDF系数，解决以上问题
http://en.wikipedia.org/wiki/Tf*idf
其中
有了理论基础，就可以来实现相似度了的运算了，PostgreSQL很容易扩展，所以不需要担心大改PG内核，加个插件就行了。
下面提到的smlar插件是一个古老的插件，但是它支持相似度公式，也就是说，你可以自定义相似度的算法公式，进行运算，同时还支持GiST和GIN的索引哦。
smlar相似度插件
部署
git clone git://sigaev.ru/smlar
cd smlar
USE_PGXS=1 make
USE_PGXS=1 make install设置参数，相似度阈值（大于阈值返回TRUE，小于阈值返回FALSE）
smlar.threshold = 0.8 # or any other value >0 and <1使用方法
psql
test=# CREATE EXTENSION smlar;
CREATE EXTENSION计算相似度
test=# SELECT smlar('{1,4,6}'::int[], '{5,4,6}' );
smlar
----------
0.666667
(1 row)
test=# SELECT smlar('{1,4,6}'::int[], '{5,4,6}', 'N.i / sqrt(N.a * N.b)' );
smlar
----------
0.666667
(1 row)根据相似度阈值，判断两者是否相似
test=# SELECT '{1,4,6,5,7,9}'::int[] % '{1,5,4,6,7,8,9}'::int[] as similar;
similar
---------
t
(1 row)索引支持，% 操作符支持索引检索，可以快速的得到你要查询的数据
GiST/GIN support for % operation.
The parameter "similar.type" allows you to specify what kind of formula used to calculate the similarity: cosine (default), overlap or tfidf.
For "tfidf" need to make additional configuration, but I will not consider this in the article (all can be found in the README file).
Now let's consider an example of using this extension.
前面讲了，相似度的计算算法，有3个公式可以使用，所以这里也一样，用户可以自定义公式来计算相似度
计算相似度时，用户可以提供计算公式。
test=# SELECT smlar('{1,4,6}'::int[], '{5,4,6}', 'N.i / sqrt(N.a * N.b)' );
smlar
----------
0.666667
(1 row)由数组的相似度运算到字符串、图片、..... 的相似度运算
前面分析了一同数组的相似度运算，马上会问了，字符串 怎么搞，图片，或者其他的特殊类型 怎么算相似度呢？
字符串相似度
字符串与字符串的相似度运算，其实也有思路的，比如PostgreSQL pg_trgm插件，将字符串打成很多的token，对tokens进行运算。(其实又回到了数组与数组的相似度计算)
https://www.postgresql.org/docs/9.6/static/pgtrgm.html
postgres=# select similarity('hello digoal','hell digoal');
similarity
------------
0.785714
(1 row)pg_trgm很好用，有很多的索引检索，排序的支持。
包括对正则表达式的索引支持，有更详细的文本请参考。
《聊一聊双十一背后的技术 - 毫秒分词算啥, 试试正则和相似度》
图片相似度
说完文本，该说说图片了，其实图片也可以数字化，比如有一张大图，
首先压缩为1515 pixel的小图，1515一共225个小格子，每个小格子里面由RGB三原色组成。
可以将每个格子的三原色计算成一个值，这样就组成了一个15*15的矩阵数组。
例如某个格子的值为 0.299 * red + 0,587 * green + 0,114 * blue
那么又回到了数组与数组的相似度计算上面了。
以下是使用以上方法完成的，对两张图片的近似度运算
是不是很神奇呢？
例子
CREATE TABLE images (
id serial PRIMARY KEY,
name varchar(50),
image_array integer[]
);
INSERT into images(image_array) VALUES ('{1010257,...,2424257}');
test=# SELECT count(*) from images;
count
--------
200000
(1 row)
test=# EXPLAIN ANALYZE SELECT id FROM images WHERE images.image_array % '{1010259,...,2424252}'::int[];
Aggregate (cost=14.58..14.59 rows=1 width=0) (actual time=1.785..1.785 rows=1 loops=1)
-> Seq Scan on images (cost=0.00..14.50 rows=33 width=0) (actual time=0.115..1.772 rows=20 loops=1)
Filter: (image_array % '{1010259,1011253,...,2423253,2424252}'::integer[])
Total runtime: 5152.819 ms
(4 rows)
CREATE INDEX image_array_gin ON images USING GIN(image_array _int4_sml_ops);
or
CREATE INDEX image_array_gist ON images USING GIST(image_array _int4_sml_ops);索引的使用测试
test=# EXPLAIN ANALYZE SELECT id FROM images WHERE images.image_array % '{1010259,1011253,...,2423253,2424252}'::int[];
Aggregate (cost=815.75..815.76 rows=1 width=0) (actual time=320.428..320.428 rows=1 loops=1)
-> Bitmap Heap Scan on images (cost=66.42..815.25 rows=200 width=0) (actual time=108.127..304.524 rows=40000 loops=1)
Recheck Cond: (image_array % '{1010259,1011253,...,2424252}'::integer[])
-> Bitmap Index Scan on image_array_gist (cost=0.00..66.37 rows=200 width=0) (actual time=90.814..90.814 rows=40000 loops=1)
Index Cond: (image_array % '{1010259,1011253,...,2424252}'::integer[])
Total runtime: 320.487 ms
(6 rows)
test=# SELECT count(*) from images;
count
---------
1000000
(1 row)
test=# EXPLAIN ANALYZE SELECT count(*) FROM images WHERE images.image_array % '{1010259,1011253,...,2423253,2424252}'::int[];
Bitmap Heap Scan on images (cost=286.64..3969.45 rows=986 width=4) (actual time=504.312..2047.533 rows=200000 loops=1)
Recheck Cond: (image_array % '{1010259,1011253,...,2423253,2424252}'::integer[])
-> Bitmap Index Scan on image_array_gist (cost=0.00..286.39 rows=986 width=0) (actual time=446.109..446.109 rows=200000 loops=1)
Index Cond: (image_array % '{1010259,1011253,...,2423253,2424252}'::integer[])
Total runtime: 2152.411 ms
(5 rows)
EXPLAIN ANALYZE SELECT smlar(images.image_array, '{1010259,...,2424252}'::int[]) as similarity FROM images WHERE images.image_array % '{1010259,1011253, ...,2423253,2424252}'::int[] ORDER BY similarity DESC;
Sort (cost=4020.94..4023.41 rows=986 width=924) (actual time=2888.472..2901.977 rows=200000 loops=1)
Sort Key: (smlar(image_array, '{...,2424252}'::integer[]))
Sort Method: quicksort Memory: 15520kB
-> Bitmap Heap Scan on images (cost=286.64..3971.91 rows=986 width=924) (actual time=474.436..2729.638 rows=200000 loops=1)
Recheck Cond: (image_array % '{...,2424252}'::integer[])
-> Bitmap Index Scan on image_array_gist (cost=0.00..286.39 rows=986 width=0) (actual time=421.140..421.140 rows=200000 loops=1)
Index Cond: (image_array % '{...,2424252}'::integer[])
Total runtime: 2912.207 ms
(8 rows)文本的相似度分析
文本的分析，是指将文本使用全文检索的方式，转换为ts_vector数据类型，然后对FTS进行相似度分析，详见我写的如下文章
《PostgreSQL 全文检索加速 快到没有朋友 - RUM索引接口(潘多拉魔盒)》
《PostgreSQL 文本数据分析实践之 - 相似度分析》
更优秀的图片相似度分析方法
其实图像搜索有更好的技术，相比前面简单粗暴的pixel 矩阵的运算更合理，Haar wavelet的算法，一样是嫁接到PostgreSQL里面，详见我写的如下文章
《PostgreSQL 在视频、图片去重，图像搜索业务中的应用》
《弱水三千,只取一瓢,当图像搜索遇见PostgreSQL(Haar wavelet)》
smlar readme
float4 smlar(anyarray, anyarray)
- computes similary of two arrays. Arrays should be the same type.
float4 smlar(anyarray, anyarray, bool useIntersect)
- computes similary of two arrays of composite types. Composite type looks like:
CREATE TYPE type_name AS (element_name anytype, weight_name FLOAT4);
useIntersect option points to use only intersected elements in denominator
see an exmaples in sql/composite_int4.sql or sql/composite_text.sql
float4 smlar( anyarray a, anyarray b, text formula );
- computes similary of two arrays by given formula, arrays should
be the same type.
Predefined variables in formula:
N.i - number of common elements in both array (intersection)
N.a - number of uniqueelements in first array
N.b - number of uniqueelements in second array
Example:
smlar('{1,4,6}'::int[], '{5,4,6}' )
smlar('{1,4,6}'::int[], '{5,4,6}', 'N.i / sqrt(N.a * N.b)' )
That calls are equivalent.
anyarray % anyarray
- returns true if similarity of that arrays is greater than limit
float4 show_smlar_limit() - deprecated
- shows the limit for % operation
float4 set_smlar_limit(float4) - deprecated
- sets the limit for % operation
Use instead of show_smlar_limit/set_smlar_limit GUC variable
smlar.threshold (see below)
text[] tsvector2textarray(tsvector)
- transforms tsvector type to text array
anyarray array_unique(anyarray)
- sort and unique array
float4 inarray(anyarray, anyelement)
- returns zero if second argument does not present in a first one
and 1.0 in opposite case
float4 inarray(anyarray, anyelement, float4, float4)
- returns fourth argument if second argument does not present in
a first one and third argument in opposite case
GUC configuration variables:
smlar.threshold FLOAT
Array's with similarity lower than threshold are not similar
by % operation
smlar.persistent_cache BOOL
Cache of global stat is stored in transaction-independent memory
smlar.type STRING
Type of similarity formula: cosine(default), tfidf, overlap
smlar.stattable STRING
Name of table stored set-wide statistic. Table should be
defined as
CREATE TABLE table_name (
value data_type UNIQUE,
ndoc int4 (or bigint) NOT NULL CHECK (ndoc>0)
);
And row with null value means total number of documents.
See an examples in sql/*g.sql files
Note: used on for smlar.type = 'tfidf'
smlar.tf_method STRING
Calculation method for term frequency. Values:
"n" - simple counting of entries (default)
"log" - 1 + log(n)
"const" - TF is equal to 1
Note: used on for smlar.type = 'tfidf'
smlar.idf_plus_one BOOL
If false (default), calculate idf as log(d/df),
if true - as log(1+d/df)
Note: used on for smlar.type = 'tfidf'
Module provides several GUC variables smlar.threshold, it's highly
recommended to add to postgesql.conf:
custom_variable_classes = 'smlar' # list of custom variable class names
smlar.threshold = 0.6 #or any other value > 0 and < 1
and other smlar.* variables
GiST/GIN support for % and && operations for:
Array Type | GIN operator class | GiST operator class
---------------+----------------------+----------------------
bit[] | _bit_sml_ops |
bytea[] | _bytea_sml_ops | _bytea_sml_ops
char[] | _char_sml_ops | _char_sml_ops
cidr[] | _cidr_sml_ops | _cidr_sml_ops
date[] | _date_sml_ops | _date_sml_ops
float4[] | _float4_sml_ops | _float4_sml_ops
float8[] | _float8_sml_ops | _float8_sml_ops
inet[] | _inet_sml_ops | _inet_sml_ops
int2[] | _int2_sml_ops | _int2_sml_ops
int4[] | _int4_sml_ops | _int4_sml_ops
int8[] | _int8_sml_ops | _int8_sml_ops
interval[] | _interval_sml_ops | _interval_sml_ops
macaddr[] | _macaddr_sml_ops | _macaddr_sml_ops
money[] | _money_sml_ops |
numeric[] | _numeric_sml_ops | _numeric_sml_ops
oid[] | _oid_sml_ops | _oid_sml_ops
text[] | _text_sml_ops | _text_sml_ops
time[] | _time_sml_ops | _time_sml_ops
timestamp[] | _timestamp_sml_ops | _timestamp_sml_ops
timestamptz[] | _timestamptz_sml_ops | _timestamptz_sml_ops
timetz[] | _timetz_sml_ops | _timetz_sml_ops
varbit[] | _varbit_sml_ops |
varchar[] | _varchar_sml_ops | _varchar_sml_ops参考
https://github.com/postgrespro/imgsmlr
http://railsware.com/blog/2012/05/10/effective-similarity-search-in-postgresql/
https://github.com/postgrespro/pg_trgm_pro
https://www.postgresql.org/docs/9.6/static/pgtrgm.html