Clustering

This exercise involves working with K-means clustering, Mean-shift clustering, and Agglomerative clustering on the poses data used for the exercises in week 2 and week 10 . The task includes applying and experimenting with each method and then comparing their outcomes. The comparison will be conducted by clustering a sequence of human poses using these three methods in similar steps.

The dataset tensor contains 1403 pose sequences. Each sequence is a 100-frames time series capturing human poses. Each pose consists of 25 skeletal joints, where each joint is defined by an x and y coordinate ($25*2$). The shape of the dataset tensor is $(1403, 100, 25*2)$. For this exercise, you will use a single pose sequence of 100 frames and apply clustering to the sequence.

Task overview

For each clustering method you will:

• Implement the method.
• Plot the clusters in the sequence.
• Plot the cluster centers.

# write reflections here

The following cells import libraries and provide functions for plotting the poses:

import numpy as np
import matplotlib.pyplot as plt
import warnings
import seaborn as sns
from sklearn.cluster import MeanShift
from sklearn.cluster import KMeans
from sklearn.cluster import AgglomerativeClustering
from scipy.spatial.distance import pdist, squareform
import scipy.cluster.hierarchy as shc
from scipy.cluster.hierarchy import dendrogram, linkage
from clustering_utils import *


# Suppress the specific warning
warnings.filterwarnings("ignore")

data = np.load('poses_norm.npy')
N,T,D,C = data.shape
reshaped_data = data.reshape(N,T,D*C)
sequence = reshaped_data[191]
print(sequence.shape)

(100, 50)

K-means Clustering

In this exercise you will use k-means clustering on a pose sequence.

# Specify the number of clusters (k)
k = 3  

# Create KMeans 
kmeans = KMeans(n_clusters=k, random_state=42)

# Fit to the data
kmeans.fit(sequence)

# Write your solution here

# You can now use 'cluster_labels' to see which cluster each frame belongs to
# 'centroids' contains the coordinates of the cluster centers

colors = {0: 'red', 1: 'blue', 2: 'green', 3: "orange", 4: "black", 5: "brown", 6: "yellow", 7: "cyan"}  # Map cluster labels to colors
plt.figure(figsize=(25,15))
for i in range(len(sequence)):
    plt.subplot(10, 10, i + 1)
    plot_single_pose(sequence[i], c=colors[cluster_labels[i]], head=False)
    plt.ylim(1, 0)
    plt.xlim(-1, 1)

num_centroids = len(centroids)
# Set up subplots
fig, axes = plt.subplots(1, num_centroids, figsize=(num_centroids * 3, 3))

# Assuming you have a function plot_single_pose defined
for i in range(len(centroids)):
    plt.subplot(1, len(centroids), i+1)
    plt.title(f'Cluster center {i+1}')
    plot_single_pose(centroids[i], c=colors[i], head=False)
    plt.ylim(1, 0)
    plt.xlim(-1, 1)

plt.tight_layout()
plt.show()


# write your reflection here

# Find the optimal k using the elbow method
k_range = range(2, 30) # values for the number of clusters `k`
inertia = []

for k in k_range:
    kmeans = KMeans(n_clusters=k, random_state=42)
    kmeans.fit(sequence)
    inertia.append(kmeans.inertia_)

# Plot the elbow curve
plt.figure(figsize=(10, 5))
plt.plot(k_range, inertia, marker='o')
plt.xlabel('Number of Clusters (k)')
plt.ylabel('WCSS')
plt.title('Elbow Method for Optimal k')
plt.show()

# Write your reflections here...

Mean-shift Clustering

This exercise is about applying mean-shift clustering to the sequence of human poses.

# Perform Mean Shift clustering
mean_shift = MeanShift(bandwidth=0.629)
mean_shift.fit(sequence)

# Write your solution here

# Write your solution here

Agglomerative Clustering

This exercise is about applying hierarchical clustering to the human poses dataset.

colors = {0: 'black', 1: 'blue', 2: 'green', 3: 'red'}
sns.set_palette([colors[i] for i in range(len(colors))])
shc.set_link_color_palette(None)
plt.figure(figsize=(10,10))
plt.title('Dendrogram for Agglomerative Clustering')
plt.xlabel('Pose Index')
plt.ylabel('Distance')
linkage_matrix = shc.linkage(sequence, method ='ward', metric="euclidean")
Dendrogram = shc.dendrogram(linkage_matrix)

agg_clustering = AgglomerativeClustering(n_clusters=k, metric='euclidean', linkage='ward')

# Write your solution here (agglomerative clustering and cluster centers)

# Write your solution here

Comparison

# write your relfection here