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TM HIU GOM CM D LIU

V H GII THUT K-MEAN

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GOM CM D LIU

Gom cm d liu l mt tc v trong khaiph d liu.

Gom cm d liu gip ta c th h thng lid liu lm cho chng khng b ri rc.

Vi mt c s d liu ln v ri rc th vicgom cm rt cn thit v hu nh l khngth thiu.

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MC CH CA GOM CM

Mc ch ca gom cm d liu l nhmkhm ph ra cu trc d liu thnh lpcc tp d liu t cc nhm d liu ln

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YU CU CA GOM CM D LIU Gom cm d liu l lm cho cc d liu

trong cm th tng t nhau. Cn ccphn t khc cm th khng tng tnhau.

tng t gia cc cm d liu do ngidng nh ngha. c xc nh da trncc i tng thuc tnh m t i tng.Thng ta o khon cch gia cc itng.

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YU CU CA GOM CM D LIU

Kh nng gom cm tng dn c lp vi dliu nhp

Kh nng x l d liu a chiu

Kh nng gom cm da trn rng buc Kh din v kh dng

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PHN LOI CC PHNG PHP GOM CM Phn hoch (partitioning): cc phn hochcto

ra v nh gi theo mt tiu ch no .

Phn cp (hierarchical): phn r tpdliu/itng c thtphn cp theo mt tiu ch no .

Da trn mt (density-based): da trn

connectivity and density functions.

Da trn li (grid-based): da trn a multiple-levelgranularity structure.

Da trn m hnh (model-based): mt m hnh githuytca ra cho micm; sau hiuchnhcc thng s m hnh ph hpvicmdliu/itngnht.

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PHNG PHP NH GI GOM CM D LIU nh gi ngoi (external validation)

nh gi ktqu gom cmda vo cu trc cchnhtrccho tpdliu

o : Rand statistic, Jaccard coefficient, Folkes and Mallowsindex

nh gi ni (internal validation)

nh gi ktqu gom cm theo slng cc vector ca chnh tpdliu (ma trngnproximity matrix)

o : :Huberts statistic, Silhouette index, Dunns index,

nh gi tngi (relative validation)

nh gi ktqu gom cmbngvic so snh cc ktqu gomcm khc ngvi cc btr thng s khc nhau

Tiu ch cho vicnh gi v chnktqu gom cmtiu- nn (compactness): cc itng trong cm nn gn nhau.

- phn tch (separation): cc cm nn xa nhau.

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PHNG PHP NH GI GOM CM D LIU nh gi theo Entropy (trnh khi chtlng

gom cmtt)

ii

ij

ji

iji

ii

ij

ji

ij

in

n

n

n

n

n

p

p

p

ppIEntropy )log()log()(

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CC VN CN GII QUYT BiuDinKiuDLiu

+ Ta ch quan tm nnhngkiu mcnthit cho vic gom cm m thi

+ Ta nhngha d(i,j) l khon cch

gia 2 itng i v j. d(i,j) 0 d(i,i) = 0

d(i,j) =d(j,i)

d(i,j)d(i,k) +d(k,j)vi k l mtimbt k khc i,j.

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CC VN CN GII QUYT itng i,j cbiudinbi vector

x,y tngt(similarity) gia i v j dc

tnh theo cng thc

x = (x1, , xp)

y = (y1, , yp)

s(x, y) = (x1*y1 + + xp*yp)/((x12+ + xp2)1/2*(y12+ + yp2)1/2)

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CC VN CN GII QUYT Interval-scaled variables/attributes

+ khonlch

+ khon cch

+ Z-score measurement

|)|...|||(|121 fnffffff

mxmxmxns

.)...21

1nffffxx(xnm

f

fif

if s

mx

z

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CC VN CN GII QUYT Cc cng thc tnh okhon cch

+ okhong cch Minkowski

+ okhon cch Manhattan

+ okhon cch Euclidean

||...||||),(2211 pp j

xi

xj

xi

xj

xi

xjid

)||...|||(|),( 2222

2

11 pp jx

ix

jx

ix

jx

ixjid

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CC VN CN GII QUYT Binary variables/attributes

Obj j

Obj ipdbcasum

dcdc

baba

sum

0

1

01

Hs so trng ngin (nuixng):

Hs so trng Jaccard (nubtixng):

dcbacbjid

),(

cbacbjid

),(

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CC VN CN GII QUYT Variables/attributes of mixed types

)(1

)()(1),(

fij

pf

fij

fij

pf djid

Nu xifhoc xjfbthiu (missing) th

f (variable/attribute): binary (nominal)

dij(f) = 0 if xif= xjf , or dij

(f) = 1 otherwise

f: interval-scaled (Minkowski, Manhattan,

Euclidean)

f: ordinal or ratio-scaled

tnh ranks rifv

ziftrthnh interval-scaled1

1

f

if

Mr

zif

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CC VN CN GII QUYT

1

1

f

if

Mr

zif

1

1

f

if

Mr

zif

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NGHA CA VIC PHN CM

Phn cm ta c th i su vo phn tchnghin cu tng cm d liu nhm khmph v tm kim cc thng tin n nhm h

tr cho vic ra quyt nh

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CC GII THUT GOM CM D LIU

Trong gom cm d liu c nhiu gii thut ,tiu biu l gii thut k-mean v gii thutgom cm phn cp nhm.

Chng ta s tm hiu gii thut K-Meantrong gom cm d liu

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GII THUT K-MEANS INPUT: Mt CSDL gm n i tng v s cc cm k.

OUTPUT: Cc cm Ci (i=1,..,k) sao cho hm tiu chun E t gi tr ti

thiu. Bc 1: Khi to

Chn k i tng mj (j=1...k) l trng tm ban u ca k cm t tp dliu

(vic la chn ny c th l ngu nhin hoc theo kinh nghim).

Bc 2: Tnh ton khong cchi vi mi i tng Xi (1

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GII THUT K-MEANS phc tp d liu c tnh l

O(n.k.d.t.T)Trong : n l s i tng d liu

k l s cm d liu

d l s chiut l s vng lp

T l thi gian tnh ton mt

php tnh c s nh : cng , tr, nhn hocchia.....

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GII THUT K-MEANS u im :K-Means phn tch phn cm n

gin nn c th p dng vi tp d liu ln Nhc im: K-Means ch p dng vi d

liu c thuc tnh s v khm ph ra cc

cm c dng hnh cu, k-means cn rtnhy cm vi nhiu v cc phn t ngoi laitrong d liu. Ngoi ra cn ph thuc nhiuvo cc thng s u vo

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GII THUT K-MEANS

Trong trng hp, cc trng tm khi to ban um qu lch so vi cc trng tm cm t nhin thkt qu phn cm ca k-means l rt thp, ngha lcc cm d liu c khm ph rt lch so vi cc

cm trong thc t. Trn thc t ngi ta cha cmt gii php ti u no chn cc tham s uvo, gii php thngc s dng nht l thnghim vi cc gi tr u vo k khc nhau ri sau

chn gii php tt nht.

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GII THUT K-MEANS n nay, c rt nhiu thut ton k

tha t tng ca thut ton k-meansp dng trong khai ph d liu giiquyt tp d liu c kch thc rt lnang c p dng rt hiu qu v phbin nh thut ton k-medoid, PAM,CLARA, CLARANS, k- prototypes,