聚類、富集分析原理與實踐2013年12月1數據2OUTLINE1.Cluster聚類1.距離計算2.聚類方法3.

R語言實現2.Enrient富集1.正態分布2.超幾何分布3.富集工具3聚類分析-1.1距離算法A.PEARSON

CORRELATIONIf

you

were

to

make

a

scatterplot

of

the

values

of

x

against

y

(pairing

x1

with

y1,x2

withy2,etc),then

r

reportshow

well

you

can

fit

a

line

to

thevalues.反應了變量間的線性相關程度的大小（趨勢）identicalcomple y

uncorrelated10-1

perfect

oppositeD=1-rD=1-

|r|45聚類分析-1.1距離算法B.NON-PARAMETRIC

DISTANCEMEASURESSpearman

rank

correlationKendall’s

τ為了使用Pearson線性相關系數，必須假設數據是成對地從正態分布中取得的（服從二維正太分布）These

methods

are

more

robust

against

outliers聚類分析-1.1距離算法B.NON-PARAMETRIC

DISTANCEMEASURES-Spearman

rank

correlation6聚類分析-1.1距離算法B.NON-PARAMETRIC

DISTANCEMEASURES-Kendall

tau

correlation7聚類分析-1.1距離算法B.NON-PARAMETRIC

DISTANCEMEASURES-Kendall

tau

correlation8聚類分析-1.1距離算法B.NON-PARAMETRIC

DISTANCEMEASURES-Kendall

tau

correlation9聚類分析-1.1距離算法B.Euclidean

distanceUnlike

thecorrelation-based

distancemeasures,

the

Euclidean

distance

takes

themagnitude

of

changes

in

t

eexpression

levels

into

account,It

shouldtherefore

only

be

used

for

expression

datathat

are

suitably

normalized.1011聚類分析-1.2聚類方法A.HIERARCHICAL

CLUSTERINGHierarchical

clustering

methods

organizes

genesor/and

samples

in

a

tree

structure,

based

on

theirsimilarity.The

basic

idea

is

to

assemble

a

set

of

items

(genesor

arrays)

into

a

tree,

where

items

are

joined

byvery

short

branches

if

they

are

very

similar

to

each

other,

and

by

increasingly

longer

branches

astheir

similarity

decreases.聚類分析-1.2聚類方法A.HIERARCHICAL

CLUSTERING1213聚類分析-1.2聚類方法B.K-MEANS

CLUSTERINGChoose

k

initial

center

points

randomlyCluster

data

using

Euclidean

distance

(or

other

distancemetric)Calculate

new

center

points

for

each

cluster

using

only

pointswithin

the

clusterRe-Cluster

all

data

using

the

new

center

pointsRepeat

steps

3

&

4

for

defined

times聚類分析-1.3

R語言實現union_for_cluster.txtclustering.r14聚類分析-1.3其它方法15OUTLINE1.Cluster聚類1.距離計算2.聚類方法3.

R語言實現2.Enrient富集1.正態分布2.超幾何分布3.富集工具16富集分析17富集分析-2.1正態分布一（mu），尺度參數為σ（sigma）若隨

量X服從的概率分布，且其量，正態隨量服從的分布就稱則這個隨

量就稱為正態隨為正態分布。記作X~N(μ,σ2)18富集分析-2.1正態分布量的疊加結果，那么這量都可以用正態分布表示或一個變量如果是由大量微小的、獨立的隨個變量就服從正態分布。因此許多隨近似描述。表達量例子：microarray考試成績身高19富集分析-2.1正態分布在一個假設檢驗問題中原假設H0所需的最小顯著性水平稱為檢驗的p值20富集分析-2.2超幾何分布在一個口袋中裝有60個球，其中有10個白球，其余為黑球。

者一次從中摸出8個球。摸到5個白球的概率是多少？摸到x個白球的概率呢？a.排列組合的解法>choose()>factorial()>(choose(10,5)*choose(50,3))/choose(60,8)[1]

0.001930415b.超幾何分布分布律與分布函數dhyper(5,10,50,8)[1]

0.0019304151-phyper(4,10,50,8)[1]

0.00203332phyper(4,10,50,8,

lower.tail=FALSE)[1]

0.0020333221富集分析-2.2超幾何分布在一個口袋中裝有60個球，其中有10個白球，其余為黑球。

者一次從中摸出8個球。摸到5個白球的概率是多少？摸到x個白球的概率呢？列聯表(contingency

table)抽中未抽中合計白色5510黑色34750合計85260counts<-matrix(c(5,3,5,47),

nrow=2,ncol=2)counts[,1]

[,2][1,]

5

5[2,] 3

47fisher.test(counts)Fisher's

Exact

Test

for

Count

Datadata:

countsp-value

=

0.002033alternative

hypothesis:

true

odds

ratio

is

not

equalto

195

percent

confidence

interval:2.124677

123.487719sample

estimates:odds

ratio14.4213822富集分析-2.2超幾何分布GO

accession:

GO:0008283Desription:

cell

proliferationTerm

type:

biological_process差異差異背景背景中與該term相關的總數:2545中與該term相關的總數:18374數:113數:528Is

“cell

proliferation”

overrepresented

in

the

diffe