Q: Apply k$-$means and hierarchical clustering to the ORL face dataset. Set k $=2$ in k$-$means and select $2$ clusters in hierarchical clustering. Do the clustering results match the two genders? Following is the code that is need to be corrected:

import numpy as np

import pandas as pd

import matplotlib.pyplot as plt

import warnings

from PIL import Image

from sklearn.preprocessing import StandardScaler

from sklearn.cluster import KMeans

#hierarchical clustering

from sklearn.cluster import AgglomerativeClustering

# load data

df $=$ pd$.$DataFrame$($np$.$zeros$((400,2576)))$

count $=0$

for i in range$(40)$:

for j in range$(10)$:

image $=$ Image.open$("/$Users$/$ORL$\_$Faces$/"+$ str$($i$+1)+"\_"+$ str$($j$+1)+".$png$")$

image$\_$array $=$ np$.$array$($image$)$

image$\_$array $=$ image$\_$array.reshape$(1,-1)$

df$.$iloc$[$count$]=$ image$\_$array

count $+=1$

df$["$Gender$"]=$ np$.$ones$((400,1))$

df$.$iloc$[0$:$10,2576]=0\mathrm{.}0$

df$.$iloc$[70$:$80,2576]=0\mathrm{.}0$

df$.$iloc$[90$:$100,2576]=0\mathrm{.}0$

df$.$iloc$[310$:$320,2576]=0\mathrm{.}0$

print$($df$)$

# k$-$means

X $=$ df$.$iloc$[$:$,0$:$2576]$

scaler $=$ StandardScaler$()$

X $=$ scaler.fit$\_$transform$($X$)$

X $=$ pd$.$DataFrame$($X$)$

warnings.filterwarnings$("$ignore$")$

kmeans$\_$model $=$ KMeans$($n$\_$clusters $=2)$

kmeans$\_$model.fit$($X$)$

X$["$clusters$"]=$ kmeans$\_$model.labels$\_$

true$\_$label $=$ sum$($X$["$clusters$"]==$ df$["$Gender$"])$

false$\_$label $=$ sum$($X$["$clusters$"]!=$ df$["$Gender$"])$

print$("$True Labels: $\{\}$

False Labels: $\{\}".$format$($true$\_$label, false$\_$label$))$

true$\_$lab $=[]$

false$\_$lab $=[]$

for i in range$(100)$:

kmeans$\_$model $=$ KMeans$($n$\_$clusters $=2)$

kmeans$\_$model.fit$($X$)$

true$\_$label $=$ sum$($kmeans$\_$model.labels$\_==$ df$["$Gender$"])$

false$\_$label $=$ sum$($kmeans$\_$model.labels$\_!=$ df$["$Gender$"])$

true$\_$lab.append$($true$\_$label$)$

false$\_$lab.append$($false$\_$label$)$

plt$.$scatter$($true$\_$lab, false$\_$lab$)$

plt$.$xlabel$("$True Labels"$)$

plt$.$ylabel$("$False Labels"$)$

#hierarchical clustering

X $=$ df$.$iloc$[$:$,0$:$2576]$

scaler $=$ StandardScaler$()$

X $=$ scaler.fit$\_$transform$($X$)$

X $=$ pd$.$DataFrame$($X$)$

hierarchical$\_$cluster $=$ AgglomerativeClustering$($n$\_$clusters$=2,$ affinity$=$'euclidean', linkage$=$'ward'$)$

hierarchical$\_$cluster.fit$($X$)$

X$["$clusters$"]=$ hierarchical$\_$cluster.labels$\_$

true$\_$label $=$ sum$($X$["$clusters$"]==$ df$["$Gender$"])$

false$\_$label $=$ sum$($X$["$clusters$"]!=$ df$["$Gender$"])$

print$("$# of True Labeling: $\{\}$

# of False Labeling: $\{\}".$format$($true$\_$label, false$\_$label$))$

true$\_$lab $=[]$

false$\_$lab $=[]$

for i in range$(100)$:

kmeans$\_$model $=$ KMeans$($n$\_$clusters $=2)$

kmeans$\_$model.fit$($X$)$

true$\_$label $=$ sum$($kmeans$\_$model.labels$\_==$ df$["$Gender$"])$

false$\_$label $=$ sum$($kmeans$\_$model.labels$\_!=$ df$["$Gender$"])$

true$\_$lab.append$($true$\_$label$)$

false$\_$lab.append$($false$\_$label$)$

plt$.$scatter$($true$\_$lab, false$\_$lab$)$

plt$.$xlabel$("$True Labels"$)$

plt$.$ylabel$("$False Labels"$)$

Could you please give me the complete Python code to solve the problem$($not just the steps, but the code can get the result directly$).$ Thank you!:$)$