Code$1$:

import numpy as np

import pandas as pd

from PIL import Image

from sklearn.preprocessing import StandardScaler

# Initialize dataframe

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 $+=1$

# Add gender labels to the dataframe

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

# Modify certain entries to represent actual gender labels

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

from sklearn.cluster import KMeans

# Standardize image data

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

scaler $=$ StandardScaler$()$

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

# Apply KMeans clustering

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

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

# Add cluster labels to the dataframe

df$["$KMeans$\_$Clusters"$]=$ kmeans$\_$model.labels$\_$

from sklearn.cluster import AgglomerativeClustering

from sklearn.preprocessing import StandardScaler

import pandas as pd

# Assuming df is your dataframe and it has been loaded correctly

X $=$ df$.$iloc$[$:$,0$:$2576]$ # Adjust the slice as necessary to include the right columns

# Standardize image data for hierarchical clustering

scaler $=$ StandardScaler$()$

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

# Apply Hierarchical clustering using Ward's method

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

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

# Add cluster labels to the dataframe

df$["$Hierarchical$\_$Clusters"$]=$ hierarchical$\_$cluster.labels$\_$

# Calculate true and false labelings for K$-$Means clustering

true$\_$label$\_$kmeans $=$ sum$($df$["$KMeans$\_$Clusters"$]==$ df$["$Gender$"])$

false$\_$label$\_$kmeans $=$ sum$($df$["$KMeans$\_$Clusters"$]!=$ df$["$Gender$"])$

# Calculate true and false labelings for Hierarchical clustering

true$\_$label$\_$hierarchical $=$ sum$($df$["$Hierarchical$\_$Clusters"$]==$ df$["$Gender$"])$

false$\_$label$\_$hierarchical $=$ sum$($df$["$Hierarchical$\_$Clusters"$]!=$ df$["$Gender$"])$

import matplotlib.pyplot as plt

plt$.$figure$($figsize$=(10,5))$

plt$.$subplot$(1,2,1)$

plt$.$scatter$($true$\_$label$\_$kmeans, false$\_$label$\_$kmeans, color$=$'blue'$)$

plt$.$title$(\text{'}$K$-$Means Clustering'$)$

plt$.$xlabel$(\text{'}$True Labels'$)$

plt$.$ylabel$(\text{'}$False Labels'$)$

plt$.$subplot$(1,2,2)$

plt$.$scatter$($true$\_$label$\_$hierarchical, false$\_$label$\_$hierarchical, color$=$'red'$)$

plt$.$title$(\text{'}$Hierarchical Clustering'$)$

plt$.$xlabel$(\text{'}$True Labels'$)$

plt$.$ylabel$(\text{'}$False Labels'$)$

plt$.$tight$\_$layout$()$

plt$.$show$()$

print$("$K$-$Means Clustering Results:"$)$

print$("$# of True Labeling:", true$\_$label$\_$kmeans$)$

print$("$# of False Labeling:", false$\_$label$\_$kmeans$)$

print$("$

Hierarchical Clustering Results:"$)$

print$("$# of True Labeling:", true$\_$label$\_$hierarchical$)$

print$("$# of False Labeling:", false$\_$label$\_$hierarchical$)$

Code$2$:

import numpy as np

import matplotlib.pyplot as plt

from sklearn.datasets import fetch$\_$olivetti$\_$faces, load$\_$digits

from sklearn.cluster import KMeans, AgglomerativeClustering

from sklearn.metrics import silhouette$\_$score

try:

# Try to fetch the Olivetti faces dataset

data $=$ fetch$\_$olivetti$\_$faces$()$

X $=$ data.data

y $=$ data.target

dataset$\_$name $=$ "Olivetti Faces"

except Exception as e:

print$("$Failed to fetch Olivetti Faces dataset:", e$)$

# Fallback to a different dataset, e$.$g$.,$ load$\_$digits

data $=$ load$\_$digits$()$

X $=$ data.data

y $=$ data.target

dataset$\_$name $=$ "Digits"

# Apply k$-$means clustering

kmeans $=$ KMeans$($n$\_$clusters$=2,$ random$\_$state$=42)$

kmeans$\_$labels $=$ kmeans.fit$\_$predict$($X$)$

# Apply hierarchical clustering

hierarchical $=$ AgglomerativeClustering$($n$\_$clusters$=2)$

hierarchical$\_$labels $=$ hierarchical.fit$\_$predict$($X$)$

# Evaluate clustering performance using silhouette score

kmeans$\_$score $=$ silhouette$\_$score$($X$,$ kmeans$\_$labels$)$

hierarchical$\_$score $=$ silhouette$\_$score$($X$,$ hierarchical$\_$labels$)$

# Print the silhouette scores

print$($f$"$Silhouette Score for K$-$Means on $\{$dataset$\_$name$\}$:$",$ kmeans$\_$score$)$

print$($f$"$Silhouette Score for Hierarchical Clustering on $\{$dataset$\_$name$\}$:$",$ hierarchical$\_$score$)$

# Visualize the clustering results

plt$.$figure$($figsize$=(12,6))$

plt$.$subplot$(1,2,1)$

plt$.$scatter$($X$[$:$,0],$ X$[$:$,1],$ c$=$kmeans$\_$labels, cmap$=$'viridis', s$=10)$

plt$.$title$($f$"$K$-$Means Clustering on $\{$dataset$\_$name$\}")$

plt$.$xlabel$("$Feature $1")$

plt$.$ylabel$("$Feature $2")$

plt$.$subplot$(1,2,2)$

plt$.$scatter$($X$[$:$,0],$ X$[$:$,1],$ c$=$hierarchical$\_$labels, cmap$=$'viridis', s$=10)$

plt$.$title$($f$"$Hierarchical Clustering on $\{$dataset$\_$name$\}")$

plt$.$xlabel$("$Feature $1")$

plt$.$ylabel$("$Feature $2")$

plt$.$tight$\_$layout$()$

plt$.$show$()$

Please use the dataset of Code$1($the link$)$ for Code$2,$ combine the $2$ codes together, and give me the complete code. Thank you!:$)$