手撸golang 基本数据结构与算法 网页排名/PageRank,随机游走
缘起
最近阅读<<我的第一本算法书>>(【日】石田保辉；宫崎修一) 本系列笔记拟采用golang练习之
网页排名(PageRank/佩奇排名), 随机游走
网页排名（PageRank，也叫作佩奇排名）是一种在搜索网页时对搜索结果进行排序的算法。
网页排名就是利用网页之间的链接结构计算出网页价值的算法。
在网页排名中，链入页面越多的网页，它的重要性也就越高。
假设没有链入页面的网页权重为1。
有链入页面的网页权重是其链入页面的权重之和。
如果一个网页链向多个页面，那么其链向的所有页面将平分它的权重。
在网页排名中，链入的页面越多，该网页所发出的链接的价值就越高。
可以使用“随机游走模型”（random walk model）来解决网页互链的问题.
用户浏览网页的操作就可以这样来定义：
用户等概率跳转到当前网页所链向的一个网页的概率为1-α；
等概率远程跳转到其他网页中的一个网页的概率为α。
模拟用户随机访问页面的过程,
每访问一个页面, 其权重加1,
直到访问的总次数达到N次为止,
每个页面的权重值代表的是“某一刻正在浏览这个网页的概率”，
可直接将其作为网页的权重来使用。
摘自 <<我的第一本算法书>> 【日】石田保辉；宫崎修一
目标
- 实现基于随机游走模型的PageRank算法, 并验证其有效性和稳定性(网页权重在模拟若干次后, 保持稳定)
设计
- IPage: 网页模型接口
- IPageRanking: 网页排名算法接口
- tPage: 网页模型的实现
- tRandomWalkPageRanking: 基于随机游走模型的PageRank算法, 实现IPageRanking接口
单元测试
- page_rank_test.go, 验证网页排名算法的有效性和稳定性
- 首先通过简单case验证其有效性
- 然后随机生成大批量随机互链的网页, 验证在多轮随机游走后, 网页权重的稳定性
package others
import (
"fmt"
pr "learning/gooop/others/page_rank"
"math/rand"
"sort"
"testing"
"time"
)
func Test_PageRank(t *testing.T) {
fnAssertTrue := func(b bool, msg string) {
if !b {
t.Fatal(msg)
}
}
t.Log("testing simple case")
p11 := pr.NewPage("p11")
p12 := pr.NewPage("p12")
p13 := pr.NewPage("p13")
p21 := pr.NewPage("p21")
p22 := pr.NewPage("p22")
p31 := pr.NewPage("p31")
p32 := pr.NewPage("p32")
p11.AddLink(p21)
p11.AddLink(p22)
p12.AddLink(p21)
p12.AddLink(p22)
p13.AddLink(p21)
p13.AddLink(p22)
p21.AddLink(p31)
p22.AddLink(p31)
p31.AddLink(p32)
p32.AddLink(p31)
samples := []pr.IPage{
p11,p12,p13, p21, p22, p31, p32,
}
pr.RandomWalkPageRanking.RankAll(samples, 1000)
sort.Sort(sort.Reverse(pr.IPageSlice(samples)))
for _,p := range samples {
t.Log(p)
}
fnAssertTrue(samples[0].ID() == "p31", "expecting top.1 = p31")
fnAssertTrue(samples[1].ID() == "p32", "expecting top.2 = p32")
fnAssertTrue(samples[2].ID() == "p21" || samples[2].ID() == "p22", "expecting top.3 in (p21,p22)")
fnAssertTrue(samples[3].ID() == "p21" || samples[3].ID() == "p22", "expecting top.4 in (p21,p22)")
// generate 1000 random pages
iPageCount := 1000
pages := make([]pr.IPage, iPageCount)
for i,_ := range pages {
pages[i] = pr.NewPage(fmt.Sprintf("p%02d.com", i))
}
r := rand.New(rand.NewSource(time.Now().UnixNano()))
for i,p := range pages {
// add random page links
for j,iPageLinks := 0, r.Intn(10);j < iPageLinks; {
n := r.Intn(iPageCount)
if n != i {
j++
p.AddLink(pages[n])
}
}
}
// rank pages and get top 100
mapTop100 := make(map[string]bool, 0)
fnTestRanking := func(rounds int) {
t.Logf("testing page rank with %v rounds", rounds)
bFirstRound := len(mapTop100) == 0
// page ranking
pr.RandomWalkPageRanking.RankAll(pages, rounds)
// sort pages by ranking
sort.Sort(sort.Reverse(pr.IPageSlice(pages)))
hits := 0
for i,p := range pages {
if i < 10 {
t.Log(p)
}
if i < 100 {
if bFirstRound {
mapTop100[p.ID()] = true
} else if _,ok := mapTop100[p.ID()];ok {
hits++
}
} else {
break
}
}
if !bFirstRound {
t.Logf("hit rate: %s%v", "%", hits)
}
}
// test stability under different rounds
fnTestRanking(3000)
fnTestRanking(10000)
fnTestRanking(30000)
fnTestRanking(90000)
}
测试输出
- 测试表明, 当随机游走的总次数 >= 网页数量 * 每个网页的平均发出链接数时, 所得排名是比较稳定的
$ go test -v page_rank_test.go
=== RUN Test_PageRank
page_rank_test.go:19: testing simple case
page_rank_test.go:47: p(p31, 0.4206, [p32])
page_rank_test.go:47: p(p32, 0.3673, [p31])
page_rank_test.go:47: p(p21, 0.0639, [p31])
page_rank_test.go:47: p(p22, 0.0604, [p31])
page_rank_test.go:47: p(p11, 0.0300, [p21 p22])
page_rank_test.go:47: p(p12, 0.0291, [p21 p22])
page_rank_test.go:47: p(p13, 0.0287, [p21 p22])
page_rank_test.go:77: testing page rank with 3000 rounds
page_rank_test.go:89: p(p604.com, 0.0039, [])
page_rank_test.go:89: p(p807.com, 0.0035, [p709.com p328.com p303.com p110.com p858.com p394.com p231.com p731.com p83.com])
page_rank_test.go:89: p(p72.com, 0.0034, [p249.com p347.com p604.com p533.com p416.com p958.com p966.com p385.com])
page_rank_test.go:89: p(p712.com, 0.0033, [p485.com p451.com p236.com p141.com p168.com p693.com])
page_rank_test.go:89: p(p452.com, 0.0032, [p588.com p344.com p618.com p258.com p394.com p285.com p780.com p606.com p89.com])
page_rank_test.go:89: p(p709.com, 0.0031, [p666.com p554.com p103.com p202.com p230.com])
page_rank_test.go:89: p(p975.com, 0.0029, [])
page_rank_test.go:89: p(p840.com, 0.0029, [p974.com p698.com p49.com p851.com p73.com])
page_rank_test.go:89: p(p867.com, 0.0028, [p588.com p196.com p931.com p381.com p621.com p848.com])
page_rank_test.go:89: p(p633.com, 0.0028, [p840.com])
page_rank_test.go:77: testing page rank with 10000 rounds
page_rank_test.go:89: p(p604.com, 0.0039, [])
page_rank_test.go:89: p(p807.com, 0.0034, [p709.com p328.com p303.com p110.com p858.com p394.com p231.com p731.com p83.com])
page_rank_test.go:89: p(p72.com, 0.0034, [p249.com p347.com p604.com p533.com p416.com p958.com p966.com p385.com])
page_rank_test.go:89: p(p452.com, 0.0033, [p588.com p344.com p618.com p258.com p394.com p285.com p780.com p606.com p89.com])
page_rank_test.go:89: p(p712.com, 0.0033, [p485.com p451.com p236.com p141.com p168.com p693.com])
page_rank_test.go:89: p(p709.com, 0.0031, [p666.com p554.com p103.com p202.com p230.com])
page_rank_test.go:89: p(p975.com, 0.0029, [])
page_rank_test.go:89: p(p840.com, 0.0029, [p974.com p698.com p49.com p851.com p73.com])
page_rank_test.go:89: p(p612.com, 0.0028, [p116.com p562.com p179.com p37.com p761.com])
page_rank_test.go:89: p(p319.com, 0.0028, [p726.com p63.com p558.com p301.com p185.com p944.com])
page_rank_test.go:104: hit rate: %98
page_rank_test.go:77: testing page rank with 30000 rounds
page_rank_test.go:89: p(p604.com, 0.0039, [])
page_rank_test.go:89: p(p807.com, 0.0034, [p709.com p328.com p303.com p110.com p858.com p394.com p231.com p731.com p83.com])
page_rank_test.go:89: p(p72.com, 0.0034, [p249.com p347.com p604.com p533.com p416.com p958.com p966.com p385.com])
page_rank_test.go:89: p(p452.com, 0.0033, [p588.com p344.com p618.com p258.com p394.com p285.com p780.com p606.com p89.com])
page_rank_test.go:89: p(p712.com, 0.0032, [p485.com p451.com p236.com p141.com p168.com p693.com])
page_rank_test.go:89: p(p709.com, 0.0031, [p666.com p554.com p103.com p202.com p230.com])
page_rank_test.go:89: p(p975.com, 0.0029, [])
page_rank_test.go:89: p(p840.com, 0.0029, [p974.com p698.com p49.com p851.com p73.com])
page_rank_test.go:89: p(p319.com, 0.0028, [p726.com p63.com p558.com p301.com p185.com p944.com])
page_rank_test.go:89: p(p612.com, 0.0028, [p116.com p562.com p179.com p37.com p761.com])
page_rank_test.go:104: hit rate: %98
page_rank_test.go:77: testing page rank with 90000 rounds
page_rank_test.go:89: p(p604.com, 0.0039, [])
page_rank_test.go:89: p(p807.com, 0.0034, [p709.com p328.com p303.com p110.com p858.com p394.com p231.com p731.com p83.com])
page_rank_test.go:89: p(p72.com, 0.0034, [p249.com p347.com p604.com p533.com p416.com p958.com p966.com p385.com])
page_rank_test.go:89: p(p452.com, 0.0033, [p588.com p344.com p618.com p258.com p394.com p285.com p780.com p606.com p89.com])
page_rank_test.go:89: p(p712.com, 0.0032, [p485.com p451.com p236.com p141.com p168.com p693.com])
page_rank_test.go:89: p(p709.com, 0.0031, [p666.com p554.com p103.com p202.com p230.com])
page_rank_test.go:89: p(p975.com, 0.0029, [])
page_rank_test.go:89: p(p840.com, 0.0029, [p974.com p698.com p49.com p851.com p73.com])
page_rank_test.go:89: p(p612.com, 0.0028, [p116.com p562.com p179.com p37.com p761.com])
page_rank_test.go:89: p(p319.com, 0.0028, [p726.com p63.com p558.com p301.com p185.com p944.com])
page_rank_test.go:104: hit rate: %98
--- PASS: Test_PageRank (13.93s)
PASS
ok command-line-arguments 13.936s
IPage.go
网页模型接口
package page_rank
import "fmt"
type IPage interface {
fmt.Stringer
ID() string
GetWeight() float64
SetWeight(float64)
GetLinks() []IPage
AddLink(IPage)
}
type IPageSlice []IPage
func (me IPageSlice) Len() int {
return len(me)
}
func (me IPageSlice) Less(i,j int) bool {
return me[i].GetWeight() < me[j].GetWeight()
}
func (me IPageSlice) Swap(i,j int) {
me[i], me[j] = me[j], me[i]
}
IPageRanking.go
网页排名算法接口
package page_rank
type IPageRanking interface {
RankAll(pages []IPage, rounds int)
}
tPage.go
网页模型的实现
package page_rank
import (
"fmt"
"strings"
)
type tPage struct {
id string
weight float64
links []IPage
}
func NewPage(id string) IPage {
return &tPage{
id: id,
weight: 0,
links: []IPage{},
}
}
func (me *tPage) ID() string {
return me.id
}
func (me *tPage) GetWeight() float64 {
return me.weight
}
func (me *tPage) SetWeight(w float64) {
me.weight = w
}
func (me *tPage) GetLinks() []IPage {
return me.links
}
func (me *tPage) AddLink(p IPage) {
me.links = append(me.links, p)
}
func (me *tPage) String() string {
linkStrings := make([]string, len(me.links))
for i,p := range me.links {
linkStrings[i] = p.ID()
}
return fmt.Sprintf("p(%v, %8.4f, [%v])", me.id, me.weight, strings.Join(linkStrings, " "))
}
tRandomWalkPageRanking.go
基于随机游走模型的PageRank算法, 实现IPageRanking接口
package page_rank
import (
"math/rand"
"time"
)
type tRandomWalkPageRanking struct {
}
var gPossiblityToLinkedPage = 85
func newRandomWalkPageRanking() IPageRanking {
return &tRandomWalkPageRanking{}
}
func (me *tRandomWalkPageRanking) RankAll(pages []IPage, rounds int) {
iPageCount := len(pages)
if iPageCount <= 0 {
return
}
r := rand.New(rand.NewSource(time.Now().UnixNano()))
current := pages[0]
iVisitCount := iPageCount * rounds
for i := 0;i < iVisitCount;i++ {
// visit current page
current.SetWeight(current.GetWeight() + 1)
possibility := r.Intn(100)
if possibility < gPossiblityToLinkedPage && len(current.GetLinks())>0 {
// goto linked page
current = me.VisitLinkedPage(current, r)
} else {
// goto unlinked page
current = me.VisitUnlinkedPage(current, pages, r)
}
}
fVisitCount := float64(iVisitCount)
for _,p := range pages {
p.SetWeight(p.GetWeight() / fVisitCount)
}
}
func (me *tRandomWalkPageRanking) VisitLinkedPage(current IPage, r *rand.Rand) IPage {
links := current.GetLinks()
next := links[r.Intn(len(links))]
return next
}
func (me *tRandomWalkPageRanking) VisitUnlinkedPage(current IPage, pages []IPage, r *rand.Rand) IPage {
mapLinks := make(map[string]bool, 0)
mapLinks[current.ID()] = true
for _,p := range current.GetLinks() {
mapLinks[p.ID()] = true
}
n := len(pages)
for {
next := pages[r.Intn(n)]
if _,ok := mapLinks[next.ID()];!ok {
return next
}
}
}
var RandomWalkPageRanking = newRandomWalkPageRanking()
(end)
