PCA_python_BiPlot_sample_Code.md

PCA With Python

Habib Ezatabadi

import require libraries

import numpy as np
import pandas as pd
import matplotlib.pyplot as plt

create a pca model

from sklearn.preprocessing import StandardScaler
from sklearn.decomposition import PCA
import plyer

## get path
pathh = plyer.filechooser.open_file()[0]

implement Model

dat = pd.read_excel(pathh)
dat.shape
index = dat['RTO_Name'].values
ind = [2, 3, 8, 9, 10, 11, 12, 13, 14, 15, 16]
dat2 = pd.DataFrame(dat.iloc[:, ind])
dat2.index = index
dat2

## To define a standardizer for the data
scaler = StandardScaler() 

C:\Users\habib\AppData\Local\Programs\Python\Python311\Lib\site-packages\openpyxl\worksheet\header_footer.py:48: UserWarning:

Cannot parse header or footer so it will be ignored

colNames = dat2.columns
Index = dat2.index
dat_scaled = pd.DataFrame(scaler.fit_transform(dat2), columns = colNames, 
index = Index)
dat_scaled

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	Distance to city	Coast view	Distance to airport	Water	Mountain	Access to recreation	Indigenous forest	Exotic forest	Wetland	Protected areas	Grassland
Northland	-0.686103	1.586737	-0.742950	-0.612804	-0.782828	1.610523	0.097830	1.921760	1.681944	-0.288129	0.703268
Auckland	1.642576	1.042838	1.453905	-0.791149	-0.782828	1.248176	-0.521973	-0.193935	-0.117435	-0.599138	-0.413467
Waikato	1.460370	-0.253715	0.325011	-0.198949	-0.722732	0.756420	0.123552	1.439688	0.221058	-0.292149	1.910050
Coromandel	1.122623	0.435060	0.937476	-0.744737	-0.746784	0.161136	-0.314260	-0.410327	-0.437439	-0.402754	-1.011192
Coastal Bay of Plenty	0.082717	-0.483791	-1.021791	-0.721735	-0.628414	0.083490	0.208546	1.627785	-0.443297	-0.469362	-0.857253
Rotorua	0.513789	-0.790882	-0.784969	0.124169	-0.762075	-0.874141	-0.556055	0.067029	-0.605130	-0.626512	-1.057294
Taupo	-0.006164	-0.790882	-1.367395	2.131880	-0.527693	1.921105	-0.134862	2.537547	-0.132630	-0.285582	-0.872732
Gisborne	-1.712677	0.342334	-2.494167	-0.502331	0.174644	-0.744731	0.536604	1.992106	-0.523847	-0.129995	0.016901
Hawke's Bay	-1.339378	0.068866	-1.830211	-0.136521	-0.124518	0.782302	0.081913	1.284276	-0.267369	-0.331107	1.009243
Ruapehu	-0.241699	-0.790882	-1.195866	-0.719512	-0.683906	0.394073	0.046514	-0.194476	0.054649	-0.195076	-0.397781
Taranaki	-0.761652	-0.315437	-1.170520	-0.700275	-0.719424	0.005844	0.211963	-0.625114	-0.622521	-0.230316	-0.069157
Whanganui	-0.694991	-0.711205	-0.638488	-0.712298	-0.782822	-1.417661	-0.480049	-0.542324	-0.718449	-0.577364	-1.069369
Manawatu	-0.241699	-0.759218	-0.149954	-0.700139	-0.659114	-1.262369	-0.640070	-0.855736	-0.693552	-0.603903	-0.646857
Wairarapa	0.989302	-0.179253	1.000356	-0.336734	-0.621974	-1.029432	-0.426790	-0.171011	-0.565587	-0.427922	-0.276159
Wellington	1.731457	-0.287360	1.609405	-0.794280	-0.663815	0.083490	-0.415951	-0.719367	-0.613551	-0.568114	-1.236987
Marlborough	0.340471	1.985651	0.415818	-0.357105	1.251240	0.109372	0.040651	0.234919	-0.403388	0.531133	0.242280
Nelson Tasman	-0.659439	0.066182	-0.492312	-0.433914	0.680182	0.937593	1.180509	0.966852	-0.085032	0.901347	-0.754703
West Coast	-0.917193	0.911825	-0.200559	1.767386	3.543260	2.619917	4.281577	-0.280869	3.798765	4.225748	0.506587
Kaikoura	0.024944	-0.441983	0.139734	-0.736888	-0.295203	-1.236487	-0.655901	-0.953673	-0.717534	-0.428481	-1.150367
Hurunui	0.655998	-0.461589	0.735354	-0.242412	0.348016	-0.925904	-0.275464	-0.393478	-0.621240	0.002759	0.406527
Canterbury	1.007078	0.290866	1.096842	2.188636	1.043728	0.937593	-0.225364	-0.319415	0.352501	0.364135	2.484867
Timaru	-0.090601	-0.722779	0.102320	-0.531367	-0.529597	-1.391779	-0.689324	-0.829078	-0.645405	-0.569832	-0.701560
Mackenzie	-0.779428	-0.790882	-0.273799	1.329440	0.442936	-1.081196	-0.671121	-0.862024	-0.463984	-0.106960	0.403960
Waitaki	0.224926	-0.572226	0.112008	-0.055447	0.112961	-0.925904	-0.653659	-0.737150	-0.180777	-0.300214	0.530434
Central Otago	0.402688	-0.790882	1.009902	-0.481597	0.331983	0.187018	-0.690384	-0.889893	1.063173	-0.373206	1.503276
Wanaka	-1.019407	-0.790882	1.032463	1.059540	0.317922	-0.460030	-0.464954	-0.968508	-0.647968	-0.064301	-0.517491
Queenstown	-0.948302	-0.790882	1.684426	0.824257	0.451035	-0.408266	-0.528939	-0.941932	-0.565038	-0.265253	-0.402185
Dunedin	1.740345	-0.291409	0.025501	-0.770189	-0.730655	0.497601	-0.681868	-0.684735	-0.228192	-0.596843	-0.566696
Clutha	0.927085	-0.381890	0.082201	-0.570520	-0.714932	-0.097683	-0.489586	0.276789	0.009614	-0.503719	0.039331
Southland	-0.690547	0.943797	0.287143	-0.291138	0.199830	-0.123565	0.374117	0.179032	2.516736	0.482781	2.479312
Fiordland	-2.077089	3.723873	0.313117	2.716731	2.581575	-0.356502	2.332801	-0.954737	0.600925	2.728328	-0.234787

Obtaining all the main components

from sklearn.preprocessing import MinMaxScaler
scaler2 = MinMaxScaler(feature_range=(0, 1))
pca = PCA(0.8) 
pca.fit(dat_scaled)
pca.n_components_  ## The number of components that cover 90% of the variance

Loading = pca.components_

temp1 = np.repeat("PC", 4); temp2 = [1, 2, 3, 4]
temp3 = list(map(lambda x, y: x + str(y), temp1, temp2))
df_loading = pd.DataFrame(Loading.T, index = colNames, columns = temp3)
df_loading

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	PC1	PC2	PC3	PC4
Distance to city	-0.219206	-0.181906	0.574417	-0.310554
Coast view	0.306437	-0.048555	0.043187	-0.242322
Distance to airport	-0.038953	-0.620115	0.317013	-0.104865
Water	0.297139	-0.158074	-0.142196	0.204141
Mountain	0.405449	-0.235702	-0.152537	0.041566
Access to recreation	0.260759	0.253984	0.457195	-0.292648
Indigenous forest	0.420337	0.070839	-0.095976	-0.263878
Exotic forest	0.062256	0.642903	0.176965	-0.028062
Wetland	0.363113	0.034148	0.304077	0.114888
Protected areas	0.435472	-0.124187	-0.108149	-0.160795
Grassland	0.183865	-0.005248	0.412894	0.771571

create biplot

from adjustText import adjust_text
#| fig-width: 9
#| fig-height: 9
Scores = pca.transform(dat_scaled)

df_score = pd.DataFrame(scaler2.fit_transform(Scores[:, 0:2]), 
index = index, columns = ["PC1", "PC2"])



def abbreviate(strings, length = 4):
    if len(strings) > length:
        ri = round(length/2)
        le = length - ri
        res = strings[:le] + strings[(len(strings) - le):len(strings)]
    else:
        res = strings
    return res

fig, ax = plt.subplots(figsize=(14, 9))
for i, feature in enumerate(df_loading.index):
    ax.arrow(0, 0, df_loading.iloc[i, 0], 
    df_loading.iloc[i, 1])



Texts = [ax.text(df_loading.iloc[i, 0] * 1.01, 
        df_loading.iloc[i, 1] * 1.01, 
        abbreviate(feature), fontsize=18, color = "purple", 
        style = "italic") for i, feature in enumerate(df_loading.index)]
adjust_text(Texts)

ax.scatter(df_score.PC1, df_score.PC2)
ax.set_xlabel('PC1', fontsize=20)
ax.set_ylabel('PC2', fontsize=20)
ax.set_title('Figure 1', fontsize=20)
plt.show()