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)