주성분 분석[adp,python]

주성분 분석

import pandas as pd
from sklearn.preprocessing import StandardScaler
from sklearn.decomposition import PCA

df = pd.read_csv("C:/adp/ISLR-python/Notebooks/Data/USArrests.csv",index_col='Unnamed: 0' )

display(df.describe())
display(df.info())
display(df.head())

	Murder	Assault	UrbanPop	Rape
count	50.00000	50.000000	50.000000	50.000000
mean	7.78800	170.760000	65.540000	21.232000
std	4.35551	83.337661	14.474763	9.366385
min	0.80000	45.000000	32.000000	7.300000
25%	4.07500	109.000000	54.500000	15.075000
50%	7.25000	159.000000	66.000000	20.100000
75%	11.25000	249.000000	77.750000	26.175000
max	17.40000	337.000000	91.000000	46.000000

<class 'pandas.core.frame.DataFrame'>
Index: 50 entries, Alabama to Wyoming
Data columns (total 4 columns):
 #   Column    Non-Null Count  Dtype  
---  ------    --------------  -----  
 0   Murder    50 non-null     float64
 1   Assault   50 non-null     int64  
 2   UrbanPop  50 non-null     int64  
 3   Rape      50 non-null     float64
dtypes: float64(2), int64(2)
memory usage: 2.0+ KB



None

	Murder	Assault	UrbanPop	Rape
Alabama	13.2	236	58	21.2
Alaska	10.0	263	48	44.5
Arizona	8.1	294	80	31.0
Arkansas	8.8	190	50	19.5
California	9.0	276	91	40.6

df.columns

Index(['Murder', 'Assault', 'UrbanPop', 'Rape'], dtype='object')

• 데이터 표준화

X = df
scaler = StandardScaler()
X_scaled = StandardScaler().fit_transform(X)
X = pd.DataFrame(data=X_scaled, index=X.index, columns=X.columns)

X.head()

	Murder	Assault	UrbanPop	Rape
Alabama	1.255179	0.790787	-0.526195	-0.003451
Alaska	0.513019	1.118060	-1.224067	2.509424
Arizona	0.072361	1.493817	1.009122	1.053466
Arkansas	0.234708	0.233212	-1.084492	-0.186794
California	0.281093	1.275635	1.776781	2.088814

• 주성분 분석

pca = PCA(n_components=4) # 주성분의 갯수
pca.fit(X)
pc_score = pca.transform(X)
pc_score = pd.DataFrame(data=pc_score, columns = ['PC1', 'PC2','PC3','PC4'])# 주성분으로 이루어진 데이터 프레임 구성
loadings = pd.DataFrame(pca.components_.T, columns=['PC1', 'PC2','PC3','PC4'], index=df.columns) # 주성분 계수 

pc_score.head() #주성분 score

	PC1	PC2	PC3	PC4
0	0.985566	1.133392	-0.444269	0.156267
1	1.950138	1.073213	2.040003	-0.438583
2	1.763164	-0.745957	0.054781	-0.834653
3	-0.141420	1.119797	0.114574	-0.182811
4	2.523980	-1.542934	0.598557	-0.341996

• 주성분 계수

loadings 

	PC1	PC2	PC3	PC4
Murder	0.535899	0.418181	-0.341233	0.649228
Assault	0.583184	0.187986	-0.268148	-0.743407
UrbanPop	0.278191	-0.872806	-0.378016	0.133878
Rape	0.543432	-0.167319	0.817778	0.089024

• PC1 = 0.53Murder + 0.583Assault + 0.278UrbanPop + 0.543432Rape

---

pca.explained_variance_ratio_  

array([0.62006039, 0.24744129, 0.0891408 , 0.04335752])

• 주성분 2개만 사용해도 85%의 설명력을 가진다.

pc_score.corr()

	PC1	PC2	PC3	PC4
PC1	1.000000e+00	2.444648e-17	7.732791e-17	1.071531e-15
PC2	2.444648e-17	1.000000e+00	-2.878039e-16	2.180585e-16
PC3	7.732791e-17	-2.878039e-16	1.000000e+00	3.147523e-16
PC4	1.071531e-15	2.180585e-16	3.147523e-16	1.000000e+00

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