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Jayden1116

Jayden`s LifeTrip ๐Ÿ”†

๐Ÿ’ฟ Data/์ด๋ชจ์ €๋ชจ

๋ฒกํ„ฐ ๋‚ด์  ๋ฐ projection

2021. 12. 7. 13:41

์ฃผ์–ด์ง„ ๋ฐ์ดํ„ฐ (x, y)์— ๋Œ€ํ•ด์„œ y = x ๋ผ๋Š” ๋ฒกํ„ฐ์— ๋Œ€ํ•ด projection์„ ๊ณ„์‚ฐํ•˜๋Š” ํ•จ์ˆ˜๋ฅผ ์ž‘์„ฑํ•˜์„ธ์š”.

(x, y) ๋Š” (0, 0) ์—์„œ (x, y)๋กœ ๊ฐ€๋Š” ๋ฒกํ„ฐ๋ผ ๊ฐ€์ •ํ•ฉ๋‹ˆ๋‹ค.
์ดํ›„

์ž…๋ ฅ๋œ ๋ฐ์ดํ„ฐ๋ฅผ ํŒŒ๋ž€์ƒ‰ ์„ ์œผ๋กœ,
y = x ๋ผ๋Š” ๋ฒกํ„ฐ๋ฅผ ๋นจ๊ฐ„์ƒ‰ ์„ ์œผ๋กœ, ๋งˆ์ง€๋ง‰์œผ๋กœ
projection ๋œ ์„ ์„ ๋…น์ƒ‰ ์ ์„ (dashed)์œผ๋กœ ๊ทธ๋ž˜ํ”„์— ๊ทธ๋ฆฌ์„ธ์š”.


  1. y=x์— ํ•ด๋‹นํ•˜๋Š” ์ž„์˜์˜ ๋ฒกํ„ฐ([10, 10])๋ฅผ ์„ค์ •ํ•˜์—ฌ ๋‚ด์  ๋ฐ projection์„ ์ง„ํ–‰ํ•˜์˜€์Šต๋‹ˆ๋‹ค.
import numpy as np

v = [7, 4]
a = [10, 10] # y = x ์ƒ์˜ ์ž„์˜์˜ ๋ฒกํ„ฐ ์„ ์ •
# u๋Š” v๋ฅผ y = x ์ƒ์— projectionํ•œ ๋ฒกํ„ฐ

def myProjection(v, a):
    v = np.array(v)
    a = np.array(a)

    u_value = np.dot(v,a) / np.linalg.norm(a) # ํฌ๊ธฐ ๊ตฌํ•˜๊ธฐ
    u_hat = np.array(a) / np.linalg.norm(a)
    return u_value * u_hat

vprime = myProjection(v, a)
vprime

array([5.5, 5.5])

  1. ์‹œ๊ฐํ™”
import matplotlib.pyplot as plt
%matplotlib inline
plt.arrow(0, 0, v[0], v[1], head_width = .5, head_length = .5, color='b')
plt.arrow(0, 0, a[0], a[1], head_width = .5, head_length = .5, color='r')
plt.arrow(0, 0, vprime[0], vprime[1], head_width = .5, head_length = .5, color='g', ls=(0, (3, 10, 1, 10)))
plt.xlim(0, 15)
plt.ylim(0, 15)
plt.title('projection')
plt.show()

์ด์ƒ์ž…๋‹ˆ๋‹ค. ๊ฐ์‚ฌํ•ฉ๋‹ˆ๋‹ค. :)

'๐Ÿ’ฟ Data > ์ด๋ชจ์ €๋ชจ' ์นดํ…Œ๊ณ ๋ฆฌ์˜ ๋‹ค๋ฅธ ๊ธ€

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    '๐Ÿ’ฟ Data/์ด๋ชจ์ €๋ชจ' ์นดํ…Œ๊ณ ๋ฆฌ์˜ ๋‹ค๋ฅธ ๊ธ€
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    • Scree Plot ํ™œ์šฉ๋ฒ•
    • Dendrogram์„ ํ†ตํ•œ Clustering ์‹œ๊ฐํ™” ๋ฐ Elbow Method
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