llletriclearniugData X ERM'd

= Ex.

,#

.. .

Al x. a IRD

hrut-fa.ae . . .

ans× if ?÷÷¥:]

" linearmap

"

not . ably k=2ucai ) → IR

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⇒ Draw

D Cai,

a ;) = Hula : ) - Mcgill,

picture

No ltimensioual Dimensional Scaling Clubs)-

Input either C D nxn distance matrix

classical - D.

. Dis = dcai,

a ;)MDS@forcJwnfCai.a;) -_ dlacyaj)God '

. Embedding Ex, ,4 ,

.. . . oxen ) EIR

"

sit . txeyx ; idKai,a ;) = llxinxjll

.

assume dcai,

a ;) ← derived cream Euclidean

Hai - as 'll'

= Kain 't Ha,'ll

'- zhai

, as >

Lai , as > = tzfllai- ask 'tHaiti -1Haiti)

if I know A- f) elf" 'd

M - AAT EID" n

←answer

!

less ( M )= UUVUT ④gyznxk

Mi;

= Lai,

as' > = tfllai-

ajli-llaillkllg.tl)

Euclid an embedding YzT 9

shit invariant Dii Dii D;?↳ X ,

so ← the origin ⇒ 1k¥11-0

Hai - a.HI Kaa 'll

'

in

Diii

Lineaments LDA

Input Xelfznxdked

-

: assume dlxi.si/--llxi-xjllzclusters S

,,

Sz.

. .Se CX Sins ; = of

u - ¥141,5 ui-q.EI.siUS :-X

I :ci.es#&.s..cx.a.xx.nisiefEasxaNEbetween class &B=¥ ,

II. Killer . - a) ( di - EDTcovariance

within class

covariance&w= II. Isildur

Find vectors u which maximize

UT IBO Set do, . . .biz ) tell -1

FE

Answer top Iz eigenvectors if

adj'

dats

Distance Metric Learning

In theosis Dishonor

-dm Cp . g) = Cp - g) TIU C p-

g )

Pcg EIR

e Rd'd

µ=I ⇒ EuclideanM

Mft on.

.:Dgeneral

Ight and word

Input: God MEIR

'd 'd

XEIR" 'd

s . in dinclosepairs

C e Xxx C close

fer pairs Fcxxx F fer

JMLR 12 Yiustli

METTE're .ee

dmlxiix ;)'

sit. El dmlxi

,It

Hi,

EC

• H -

⇐ftp..cl/i-xi)G-x5elRd*d gsm.

"

Full Rank i en .H -

- Ht JI

a Restrict Trace Car )=d TRIM ) -

- II,

eight ,i )

Me LP TrCI)=d

n D= HER' "

I ?! ai = I end azo )

• T - I ; E F A = Xp

,

= C Xi - x ;) cxi.q.IT C- IRD'd

IF It- "

AH'

' '

'd ,uHt )µ*= arg Max

-

MHP III f÷ACxI ,m )

start M - I

A- d. lotsgradient

go C in ) = ¥eee×PtLEiu7lr)xIpd ,

IIeexpf-LXI.MS/o)F-wDML-o

.

Init

ME

I

I . for tf I,

2,

. . .T do

a.

Set G - go ( Me . , )b

.Let ve = Vogue ,

← max eigenvector ( G )C . Update Me = Me . ,

+ ¥ HUI

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