머신러닝을 위한 기초 수학 살펴보기

ݠन۞׬ਸਤೠӝୡࣻ೟࢓ಝࠁӝ
(FUUJOHTUBSUFEUPMFBSOUIFMJOFBSBMHFCSBXJUIQZUIPO

ӂ޹੤

View Slide

ݠन۞׬ਸ ਤೠ ӝୡ ࣻ೟ ࢓ಝࠁӝ
MinJae Kwon (@mingrammer)
2017.08.12
(Getting started to learn the linear algebra with python)

View Slide

Name
ӂ޹੤ (MinJae Kwon)
Nickname
@mingrammer
Email
[email protected]
Who
Game Server Engineer @ SundayToz
Blog
https://mingrammer.com
Facebook
https://facebook.com/mingrammer
Github
https://github.com/mingrammer
Eng Blog
https://medium.com/@mingrammer

View Slide

2. ࢶഋ؀ࣻ೟੉ۆ?
4. ୶о ӝୡ ࣻ೟ ࢓ಝࠁӝ
Contents
5. ࢶഋ ഥӈ ҳഅ೧ࠁӝ
1. ࣻ೟੄ ೙ਃࢿ
3. NumPy۽ ࢶഋ؀ࣻ೟ ׮ܞࠁӝ
6. Next (more LA and Mathematics)

View Slide

ࣻ೟੄ ೙ਃࢿ
੉ߣࣁ࣌਷઱۽ӝୡ ࢶഋ؀
ࣻ೟ਸ׮ܖ޲۽
׮਺ࣻधٜ੉੊ࣼೞ૑ঋ਷ٜ࠙ਸ؀࢚ਵ۽೤פ׮
W ←W −α
∂L
∂W
E = − 1
N
t
nk
log(y
nk
)
k
∑
n
∑
d(u
!
u
!
T
) = 2u
!

View Slide

ࣻ೟੄ ೙ਃࢿ
ਢ ѐߊ
জ ѐߊ
API ѐߊ
ࣻ೟

T(x)
∂
∂θ f (x,θ)dx
∫
−log(t)y(t)
∑
x∇f (x)
1
σ 2π
e
−(x−µ)2
2σ 2
−∞
∞
∫

View Slide

ࣻ೟੄ ೙ਃࢿ
ਢ ѐߊ
জ ѐߊ
API ѐߊ
ࣻ೟

*UEFQFOETPOjCVU
T(x)
∂
∂θ f (x,θ)dx
∫
−log(t)y(t)
∑
x∇f (x)
1
σ 2π
e
−(x−µ)2
2σ 2
−∞
∞
∫

View Slide

ࣻ೟੄ ೙ਃࢿ
ߑޙ੗ࣻ҅ஏ
୶ୌঌҊ્ܻ
ঐഐࢸ҅
঑୷ঌҊ્ܻ
%ݽ؛݂
ѱ੐ূ૓
୭ࣗ࠺ਊঌҊ્ܻ
೐۽ࣁझझாે݂
Ӓې೗୊ܻ
ഛܫݽ؛
ҊബਯҊࢿמ҅࢑ࢸ҅
ݠन۞׬
ؘ੉ఠ߬੉झ
नഐ୊ܻ

View Slide

ࣻ೟੄ ೙ਃࢿ
ݠन۞׬
ߑޙ੗ࣻ҅ஏ
୶ୌঌҊ્ܻ
ঐഐࢸ҅
঑୷ঌҊ્ܻ
%ݽ؛݂
ѱ੐ূ૓
୭ࣗ࠺ਊঌҊ્ܻ
೐۽ࣁझझாે݂
Ӓې೗୊ܻ
ഛܫݽ؛
ҊബਯҊࢿמ҅࢑ࢸ҅
ؘ੉ఠ߬੉झ
नഐ୊ܻ

View Slide

ࣻ೟੄ ೙ਃࢿ
.BDIJOF-FBSOJOH
"MHPSJUINT
5SBJO%BUB .PEFMT
7BMJEBUJPO%BUB
0VUQVUT
/FX%BUB

View Slide

ࣻ೟੄ ೙ਃࢿ
6 7 8 ... 5
7 5 6 ... 3
8 4 1 ... 4
... ... ... ... 2
0 1 5 4 3
⎡
⎣
⎢
⎢
⎢
⎢
⎢
⎢
⎤
⎦
⎥
⎥
⎥
⎥
⎥
⎥
W = W −α
∂L
∂W
0 0 1 ... 0
1 0 0 ... 0
0 1 0 ... 0
... ... ... ... 0
0 0 0 0 1
⎡
⎣
⎢
⎢
⎢
⎢
⎢
⎢
⎤
⎦
⎥
⎥
⎥
⎥
⎥
⎥
0 1 0 ... 0
1 0 0 ... 0
0 1 0 ... 0
... ... ... ... 0
0 0 1 0 0
⎡
⎣
⎢
⎢
⎢
⎢
⎢
⎢
⎤
⎦
⎥
⎥
⎥
⎥
⎥
⎥
4 1 5 ... 8
⎡
⎣
⎤
⎦
1
2
(y
k
− t
k
)2
∑
y
k
= eak
eai
∑ 0.5 0.4 ... ... 0.8
0.1 −0.3 ... ... 0.2
... ... ... ... 0.1
... ... ... ... 0.43
0.03 0.23 0.1 0.3 0.13
⎡
⎣
⎢
⎢
⎢
⎢
⎢
⎢
⎤
⎦
⎥
⎥
⎥
⎥
⎥
⎥
0 1 0 ... 0
⎡
⎣
⎤
⎦
Y = X ⋅W + B

View Slide

ࣻ೟੄ ೙ਃࢿ
6 7 8 ... 5
7 5 6 ... 3
8 4 1 ... 4
... ... ... ... 2
0 1 5 4 3
⎡
⎣
⎢
⎢
⎢
⎢
⎢
⎢
⎤
⎦
⎥
⎥
⎥
⎥
⎥
⎥
W = W −α
∂L
∂W
0 0 1 ... 0
1 0 0 ... 0
0 1 0 ... 0
... ... ... ... 0
0 0 0 0 1
⎡
⎣
⎢
⎢
⎢
⎢
⎢
⎢
⎤
⎦
⎥
⎥
⎥
⎥
⎥
⎥
0 1 0 ... 0
1 0 0 ... 0
0 1 0 ... 0
... ... ... ... 0
0 0 1 0 0
⎡
⎣
⎢
⎢
⎢
⎢
⎢
⎢
⎤
⎦
⎥
⎥
⎥
⎥
⎥
⎥
4 1 5 ... 8
⎡
⎣
⎤
⎦
1
2
(y
k
− t
k
)2
∑
y
k
= eak
eai
∑ 0.5 0.4 ... ... 0.8
0.1 −0.3 ... ... 0.2
... ... ... ... 0.1
... ... ... ... 0.43
0.03 0.23 0.1 0.3 0.13
⎡
⎣
⎢
⎢
⎢
⎢
⎢
⎢
⎤
⎦
⎥
⎥
⎥
⎥
⎥
⎥
Y = X ⋅W + B
ࢶഋ؀ࣻ೟ ࢶഋ؀ࣻ೟ ࢶഋ؀ࣻ೟
ഛܫҗా҅ ഛܫҗా҅
޷੸࠙೟
0 1 0 ... 0
⎡
⎣
⎤
⎦

View Slide

ࣻ೟੄ ೙ਃࢿ
6 7 8 ... 5
7 5 6 ... 3
8 4 1 ... 4
... ... ... ... 2
0 1 5 4 3
⎡
⎣
⎢
⎢
⎢
⎢
⎢
⎢
⎤
⎦
⎥
⎥
⎥
⎥
⎥
⎥
W = W −α
∂L
∂W
0 0 1 ... 0
1 0 0 ... 0
0 1 0 ... 0
... ... ... ... 0
0 0 0 0 1
⎡
⎣
⎢
⎢
⎢
⎢
⎢
⎢
⎤
⎦
⎥
⎥
⎥
⎥
⎥
⎥
0 1 0 ... 0
1 0 0 ... 0
0 1 0 ... 0
... ... ... ... 0
0 0 1 0 0
⎡
⎣
⎢
⎢
⎢
⎢
⎢
⎢
⎤
⎦
⎥
⎥
⎥
⎥
⎥
⎥
4 1 5 ... 8
⎡
⎣
⎤
⎦
1
2
(y
k
− t
k
)2
∑
y
k
= eak
eai
∑ 0.5 0.4 ... ... 0.8
0.1 −0.3 ... ... 0.2
... ... ... ... 0.1
... ... ... ... 0.43
0.03 0.23 0.1 0.3 0.13
⎡
⎣
⎢
⎢
⎢
⎢
⎢
⎢
⎤
⎦
⎥
⎥
⎥
⎥
⎥
⎥
Y = X ⋅W + B
ഛܫҗా҅ ޷੸࠙೟
ࢶഋ؀ࣻ೟
ؘ੉ఠ಴അ
҅࢑੄ബਯࢿ
୭੸ച
ౠࢿ୶୹
ഛܫ࠙ನ
୶ۿ߂৘ஏ
оࢸѨૐ
೧ࢳ೟੸੽Ӕ
ӝ਎ӝ҅࢑
ಞ޷࠙
੿ӏച
0 1 0 ... 0
⎡
⎣
⎤
⎦

View Slide

ࢶഋ؀ࣻ೟੉ۆ?
߭ఠҕр
x
11
x
12
x
13
x
14
x
15
x
21
x
22
x
23
x
24
x
25
x
31
x
32
x
33
x
34
x
35
x
41
x
42
x
43
x
44
x
45
x
51
x
52
x
53
x
54
x
55
⎡
⎣
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎤
⎦
⎥
⎥
⎥
⎥
⎥
⎥
⎥
T
y
1
y
2
y
3
y
4
y
5
⎡
⎣
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎤
⎦
⎥
⎥
⎥
⎥
⎥
⎥
⎥
−3 −2 6
⎡
⎣
⎤
⎦
2 2 8
⎡
⎣
⎤
⎦
߭ఠো࢑
೯۳ো࢑
ରਗ
ࢶഋߑ੿ध
ݠन۞׬
ঐഐച
੿ࠁѨ࢝
੉޷૑೐۽ࣁय
؀ӏݽ୊ܻ

View Slide

਋ܻח ࢶഋ؀ࣻܳ ׮ܖӝ ਤ೧ Numpyܳ ࢎਊ೤פ׮
ৈӝח౵੉௑੉૑݅
ࣽࣻ1ZUIPO਷ખוܿ
/VNQZח௏যо$'PSUSBOӝ߈੉ۄࡅܴ
ࡅܳࡺ݅ইפۄߓৌਸബਯ੸ਵ۽୊ܻ೧ݫݽܻب؏ࢎਊೣ
пઙಞܻೠҊࣻળੋఠಕ੉झ৬بҳٜਸઁҕ
NumPy۽ ࢶഋ؀ࣻ೟ ׮ܞࠁӝ

View Slide

߭ఠ (vector)
↟ ߭ఠ
ҕрীࢲ੄ਗࣗܳ಴അ
↟߭ఠחпਗࣗ੄ؘ੉ఠఋੑ੉زੌ
↟ࠁాBSSBZ۽಴അ OVNQZBSSBZ

View Slide

߭ఠ (vector)
x = x
1
x
2
... x
n
⎡
⎣
⎤
⎦ x =
x
1
x
2
...
x
n
⎡
⎣
⎢
⎢
⎢
⎢
⎢
⎤
⎦
⎥
⎥
⎥
⎥
⎥
೯߭ఠ SPXWFDUPS
ৌ߭ఠ DPMVNOWFDUPS

View Slide

߭ఠ (vector)

View Slide

߭ఠ ো࢑
↟ؔࣅ BEEJUJPO

↟ࡓࣅ TVCUSBDUJPO

↟झணۄғ 4DBMBS1SPEVDU

↟ࢿ࠙ғ &MFNFOUXJTF.VMUJQMJDBUJPO

↟ղ੸ *OOFS1SPEVDU

߭ఠח׮਺੄ো࢑ٜਸࣻ೯ೡࣻ੓਺

View Slide

߭ఠ ো࢑ 1
↟ؔࣅ BEEJUJPO


v + u = (v
1
+ u
1
,...,v
n
+ u
n
)
v − u = (v
1
− u
1
,...,v
n
− u
n
)

View Slide

߭ఠ ো࢑ 1

View Slide

߭ఠ ো࢑ 2


↟ղ੸ *OOFS1SPEVDU

v⊗u = (v
1
u
1
,...,v
n
u
n
)
av = (av
1
,...,av
n
)
v⋅u = v
i
u
i
i=1
n
∑

View Slide

߭ఠ ো࢑ 2

View Slide

೯۳ (Matrix)
↟NYO੄ഋకܳо૗
↟п೯ৌਸ߭ఠ۽಴അоמ
↟ࠁాରਗBSSBZ۽಴അ

View Slide

೯۳ ো࢑
↟ؔࣅ BEEJUJPO




↟೯۳ғ .BUSJY.VMUJQMJDBUJPO

೯۳਷׮਺੄ো࢑ٜਸࣻ೯ೡࣻ੓਺

View Slide

೯۳ ো࢑ 1
↟ؔࣅ BEEJUJPO


X +Y =
x
11
+ y
11
... x
1n
+ y
1n
... ... ...
x
m1
+ y
m1
... x
mn
+ y
mn
⎡
⎣
⎢
⎢
⎢
⎤
⎦
⎥
⎥
⎥
X −Y =
x
11
− y
11
... x
1n
− y
1n
... ... ...
x
m1
− y
m1
... x
mn
− y
mn
⎡
⎣
⎢
⎢
⎢
⎤
⎦
⎥
⎥
⎥

View Slide

೯۳ ো࢑ 1

View Slide

೯۳ ো࢑ 2


aX =
ax
11
... ax
1n
... ... ...
ax
m1
... ax
mn
⎡
⎣
⎢
⎢
⎢
⎤
⎦
⎥
⎥
⎥
X ⊗Y =
x
11
y
11
... x
1n
y
1n
... ... ...
x
m1
y
m1
... x
mn
y
mn
⎡
⎣
⎢
⎢
⎢
⎤
⎦
⎥
⎥
⎥

View Slide

೯۳ ো࢑ 2

View Slide

೯۳ ো࢑ 3
x
11
x
12
x
13
x
14
x
21
x
22
x
23
x
24
x
31
x
32
x
33
x
34
⎡
⎣
⎢
⎢
⎢
⎢
⎤
⎦
⎥
⎥
⎥
⎥
೯۳ғ .BUSJY.VMUJQMJDBUJPO

=
y
11
y
12
y
13
y
21
y
22
y
23
y
31
y
32
y
33
y
41
y
42
y
43
⎡
⎣
⎢
⎢
⎢
⎢
⎢
⎤
⎦
⎥
⎥
⎥
⎥
⎥
x
11
y
11
+ x
12
y
21
+ x
13
y
31
+ x
14
y
41
... ...
... ... ...
... ... ...
⎡
⎣
⎢
⎢
⎢
⎤
⎦
⎥
⎥
⎥
Y Y Y
=
Y

View Slide

೯۳ ো࢑ 3

View Slide

੹஖ (Transpose)
XT =
x
11
x
12
x
13
x
14
x
21
x
22
x
23
x
24
x
31
x
32
x
33
x
34
⎡
⎣
⎢
⎢
⎢
⎢
⎤
⎦
⎥
⎥
⎥
⎥
T
=
x
11
x
12
x
13
x
21
x
22
x
23
x
31
x
32
x
33
x
41
x
42
x
43
⎡
⎣
⎢
⎢
⎢
⎢
⎢
⎤
⎦
⎥
⎥
⎥
⎥
⎥
xT = x
1
x
2
... x
n
⎡
⎣
⎤
⎦
T
=
x
1
x
2
...
x
n
⎡
⎣
⎢
⎢
⎢
⎢
⎢
⎤
⎦
⎥
⎥
⎥
⎥
⎥

View Slide

੹஖ (Transpose)

View Slide

ױਤ ೯۳ (Identity Matrix)
I
n
=
1 0 0 ... 0
0 1 0 ... 0
0 0 1 ... 0
... ... ... ... 0
0 0 0 0 1
⎡
⎣
⎢
⎢
⎢
⎢
⎢
⎢
⎤
⎦
⎥
⎥
⎥
⎥
⎥
⎥

View Slide

ױਤ ೯۳ (Identity Matrix)

View Slide

৉೯۳ (Inverse Matrix)
XX−1 = I
n
= X−1X
৉೯۳਷ ೦࢚ ઓ੤ೞ૑ח ঋ਺

View Slide

৉೯۳ (Inverse Matrix)

View Slide

୶о ӝୡ ࣻ೟ ࢓ಝࠁӝ
੿ӏച 1
y
i
= x
i
x
i
∑ ੹୓ sumਵ۽ ա׃ਵ۽ॄ [0, 1] ҳрਵ۽ ੿ӏച

View Slide

୶о ӝୡ ࣻ೟ ࢓ಝࠁӝ
੿ӏച 1

View Slide

ӝఋ ӝୡ ࣻ೟ ࢓ಝࠁӝ
੿ӏച 2
Xi
= X
i
− E(X)
σ
E(X) = 1
N
X
i
i=1
N
∑
σ = 1
N
(X
i
− E(X))2
i=1
N
∑
಴ળ ੿ӏ ࠙ನܳ ഝਊ೧ ಣӐ = 0, ࠙࢑ = 1۽ ੿ӏച

View Slide

੿ӏച 2

View Slide

޷࠙ ߂ Ӓۄ٣঱౟
1
2
3
0 0 1 ... 0
1 0 0 ... 0
0 1 0 ... 0
... ... ... ... 0
0 0 0 0 1
⎡
⎣
⎢
⎢
⎢
⎢
⎢
⎢
⎤
⎦
⎥
⎥
⎥
⎥
⎥
⎥
0 1 0 ... 0
1 0 0 ... 0
0 1 0 ... 0
... ... ... ... 0
0 0 1 0 0
⎡
⎣
⎢
⎢
⎢
⎢
⎢
⎢
⎤
⎦
⎥
⎥
⎥
⎥
⎥
⎥
৘ஏ ݽ؛ীࢲ੄ Ѿҗчҗ पઁ Ѿҗчҗ੄

рӓ੄ ૑಴ੋ ର੉ “ࣚप"ਸ ઴੉ӝ ਤೣ
ࣚप ೣࣻ Ӓې೐

View Slide

ಞ޷࠙
f (x) = g(x
1
)+...+ g(x
n
)
∂ f (x)
∂x
1
=
∂g(x
1
)
∂x
1 ׮߸ࣻ ҕр ഑਷ ೣࣻীࢲ ౠ੿ ߸ࣻܳ ؀࢚ਵ۽ ޷࠙

ݠन ۞׬ীࢶ ࠁా ೯۳ਸ ؀࢚ਵ۽ೠ ೯۳ ಞ޷࠙ ࢎਊ
∂L
∂X
=
∂L
∂x
11
...
∂L
∂x
1n
... ... ...
∂L
∂x
m1
...
∂L
∂x
mn
⎡
⎣
⎢
⎢
⎢
⎢
⎢
⎢
⎤
⎦
⎥
⎥
⎥
⎥
⎥
⎥

View Slide

ࢶഋ ഥӈ ҳഅ೧ࠁӝ
ਤ੄ѐ֛ٜਸഝਊ೧рױೠ
ࢶഋഥӈݽ؛ਸٜ݅যࠁѷणפ׮

View Slide

୭੸੄ ࢶഋ ࢚ҙ ҙ҅ܳ ಴അೞח ૒ࢶਸ ଺ਵ۰Ҋ ೣ → ୭੸੄ ߬ఋܳ ೟ण
y = β
0
x
0
+ β
1
x
1
y
i
= x
i
T β

View Slide

y = β
0
x
0
+ β
1
x
1
ױੌؘ੉ఠ

View Slide

y = β
0
x
0
+ β
1
x
1
y
i
= x
i0
β
0
+ x
i1
β
1
ױੌؘ੉Tఠ ׮઺ؘ੉ఠ઺Jߣ૩ؘ੉ఠ

View Slide

y = β
0
x
0
+ β
1
x
1
y
i
= x
i
T β
y
i
= x
i0
β
0
+ x
i1
β
1
ױੌؘ੉ఠ ׮઺ؘ੉ఠ઺Jߣ૩ؘ੉ఠ Jߣ૩ؘ੉ఠ߭ఠ಴അ

View Slide

Y = Xβ Y =
y
1
y
2
...
y
n
⎡
⎣
⎢
⎢
⎢
⎢
⎢
⎤
⎦
⎥
⎥
⎥
⎥
⎥
X =
x
1
T
x
2
T
...
x
n
T
⎡
⎣
⎢
⎢
⎢
⎢
⎢
⎤
⎦
⎥
⎥
⎥
⎥
⎥
β =
β
0
β
1
⎡
⎣
⎢
⎢
⎤
⎦
⎥
⎥
ੌ߈ചػ׮઺ؘ੉ఠ੄೯۳಴അ

View Slide

1.0
1.1
1.2
...
10.0
⎡
⎣
⎢
⎢
⎢
⎢
⎢
⎢
⎤
⎦
⎥
⎥
⎥
⎥
⎥
⎥

View Slide

1.0
1.1
1.2
...
10.0
⎡
⎣
⎢
⎢
⎢
⎢
⎢
⎢
⎤
⎦
⎥
⎥
⎥
⎥
⎥
⎥
0.1
0.11
0.12
...
1.0
⎡
⎣
⎢
⎢
⎢
⎢
⎢
⎢
⎤
⎦
⎥
⎥
⎥
⎥
⎥
⎥

View Slide

y = ax + b = b + ax
y
1
= b + ax
1
y
2
= b + ax
2

View Slide

1 0.1
1 0.11
1 0.12
1 ...
1 1.0
⎡
⎣
⎢
⎢
⎢
⎢
⎢
⎢
⎤
⎦
⎥
⎥
⎥
⎥
⎥
⎥

View Slide

r
1
r
2
r
3
...
r
100
⎡
⎣
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎤
⎦
⎥
⎥
⎥
⎥
⎥
⎥
⎥
1 0.1
1 0.11
1 0.12
1 ...
1 1.0
⎡
⎣
⎢
⎢
⎢
⎢
⎢
⎢
⎤
⎦
⎥
⎥
⎥
⎥
⎥
⎥

View Slide

r
1
r
2
r
3
...
r
100
⎡
⎣
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎤
⎦
⎥
⎥
⎥
⎥
⎥
⎥
⎥
1 x
i1
1 x
i2
1 x
i3
... ...
1 x
i20
⎡
⎣
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎤
⎦
⎥
⎥
⎥
⎥
⎥
⎥
⎥
1 0.1
1 0.11
1 0.12
1 ...
1 1.0
⎡
⎣
⎢
⎢
⎢
⎢
⎢
⎢
⎤
⎦
⎥
⎥
⎥
⎥
⎥
⎥

View Slide

Ӓۄ٣঱౟ ࢸ҅
1 0.1
1 0.11
1 0.12
... ...
1 1.0
⎡
⎣
⎢
⎢
⎢
⎢
⎢
⎢
⎤
⎦
⎥
⎥
⎥
⎥
⎥
⎥
w
0
w
1
⎡
⎣
⎢
⎢
⎤
⎦
⎥
⎥

View Slide

Ӓۄ٣঱౟ ࢸ҅
1 0.1
1 0.11
1 0.12
... ...
1 1.0
⎡
⎣
⎢
⎢
⎢
⎢
⎢
⎢
⎤
⎦
⎥
⎥
⎥
⎥
⎥
⎥
w
0
w
1
⎡
⎣
⎢
⎢
⎤
⎦
⎥
⎥
y
1
y
2
y
3
...
y
20
⎡
⎣
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎤
⎦
⎥
⎥
⎥
⎥
⎥
⎥
⎥
−
w
0
+ 0.1w
1
w
0
+ 0.11w
1
w
0
+ 0.12w
1
...
w
0
+1.0w
1
⎡
⎣
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎤
⎦
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎛
⎝
⎜
⎜
⎜
⎜
⎜
⎜
⎞
⎠
⎟
⎟
⎟
⎟
⎟
⎟
T

View Slide

Ӓۄ٣঱౟ ࢸ҅
1 0.1
1 0.11
1 0.12
... ...
1 1.0
⎡
⎣
⎢
⎢
⎢
⎢
⎢
⎢
⎤
⎦
⎥
⎥
⎥
⎥
⎥
⎥
w
0
w
1
⎡
⎣
⎢
⎢
⎤
⎦
⎥
⎥
y
1
y
2
y
3
...
y
20
⎡
⎣
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎤
⎦
⎥
⎥
⎥
⎥
⎥
⎥
⎥
−
w
0
+ 0.1w
1
w
0
+ 0.11w
1
w
0
+ 0.12w
1
...
w
0
+1.0w
1
⎡
⎣
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎤
⎦
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎛
⎝
⎜
⎜
⎜
⎜
⎜
⎜
⎞
⎠
⎟
⎟
⎟
⎟
⎟
⎟
T
1
20
error
i
2
i=1
20
∑ = 1
20
(y
i
− e
i
)2
i=1
20
∑

View Slide

Ӓۄ٣঱౟ ࢸ҅
1 0.1
1 0.11
1 0.12
... ...
1 1.0
⎡
⎣
⎢
⎢
⎢
⎢
⎢
⎢
⎤
⎦
⎥
⎥
⎥
⎥
⎥
⎥
w
0
w
1
⎡
⎣
⎢
⎢
⎤
⎦
⎥
⎥
y
1
y
2
y
3
...
y
20
⎡
⎣
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎤
⎦
⎥
⎥
⎥
⎥
⎥
⎥
⎥
−
w
0
+ 0.1w
1
w
0
+ 0.11w
1
w
0
+ 0.12w
1
...
w
0
+1.0w
1
⎡
⎣
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎤
⎦
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎛
⎝
⎜
⎜
⎜
⎜
⎜
⎜
⎞
⎠
⎟
⎟
⎟
⎟
⎟
⎟
T
1
20
error
i
2
i=1
20
∑ = 1
20
(y
i
− e
i
)2
i=1
20
∑
∂(mse)
∂W
= [error][x]

View Slide

Ӓۄ٣঱౟ ࢸ҅
∂(mse)
∂W
೯۳ಞ޷࠙→ ೯۳੄ п ਗࣗী ؀೧ ಞ޷࠙

View Slide

Ӓۄ٣঱౟ ࢸ҅
∂(mse)
∂w
0
=
∂( (y
i
− (w
0
+ x
i
w
1
))2 )
∑
∂w
0
= (y
i
− (w
0
+ x
i
w
1
))⋅1
∑
∂(mse)
∂w
1
=
∂( (y
i
− (w
0
+ x
i
w
1
))2 )
∑
∂w
1
= (y
i
− (w
0
+ x
i
w
1
))⋅ x
i
∑

View Slide

Ӓۄ٣঱౟ ࢸ҅
∂(mse)
∂W
= [ y
i
− (w
0
+ x
i
w
1
)
∑ ]
1 0.1
1 0.11
1 0.12
... ...
1 1.0
⎡
⎣
⎢
⎢
⎢
⎢
⎢
⎢
⎤
⎦
⎥
⎥
⎥
⎥
⎥
⎥
= [error][x]

View Slide

पઁ ೟ण ױ҅
W ←W −α
∂(mse)
∂W

View Slide

೟ण Ӓې೐
<ഥ>&SSPS <ഥ>&SSPS
<ഥ>&SSPS <ഥ>&SSPS

View Slide

୭ઙ ೟ण Ѿҗ
&SSPS
β =
−2.152736
11.075026
⎡
⎣
⎢
⎤
⎦
⎥
y
k
= x
k
T β
→

View Slide

Next (more LA and Mathematics)
↟઱ࢿ࠙࠙ࢳ 1$"

↟ױੌч࠙೧ 47%

↟-6࠙೧
↟ҊਬчҊਬ߭ఠ
↟಴ળച
↟j
↟߬੉૑উా҅
↟ഛܫӏ஗
↟ࢠ೒݂ߑध
↟୭؀਋بஏ੿
↟j
↟೯۳޷੸࠙೟
↟Ӓۄ٣঱౟
↟j

View Slide

хࢎ೤פ׮
MinJae Kwon (@mingrammer)
Getting started to learn the linear algebra with python
2017.08.12

View Slide

머신러닝을 위한 기초 수학 살펴보기

머신러닝을 위한 기초 수학 살펴보기

mingrammer

More Decks by mingrammer

Other Decks in Technology

Featured

Transcript