Question

Apply K-Means clustering algorithm to find clusters from dataset 1 and dataset2 which are given below. Choose K as per your wish.

Dataset 1:::{5, 8, 21, 6, 24, 23}

dataset 2:::{(1,2),(1,3),(2,2),(3,2),(3,4),(3,3)}

Finally Implement K-Means clustering using Python.

Answer 1

To perform K-Means clustering on datasets 1 and 2, choose a value for K (e.g., 2), apply the algorithm using Python's sklearn library, and obtain the cluster centers and labels for each dataset.

Step-by-step explanation:

Applying K-Means Clustering Algorithm: Let's say we choose K=2 for the purpose of this example. The following are the general steps for K-Means:

1. Randomly initialize two centers for the two clusters.
2. Assign each data point to the nearest cluster center.
3. Recompute the cluster centers based on the mean of the assigned points.
4. Repeat steps 2 and 3 until the cluster centers do not change significantly or a maximum number of iterations is reached.

Using Python, here is a simple implementation for dataset 1:

from sklearn.cluster import KMeans
# Dataset1
X1 = [[5], [8], [21], [6], [24], [23]]
# Apply KMeans
kmeans1 = KMeans(n_clusters=2, random_state=0).fit(X1)
print("Cluster centers:", kmeans1.cluster_centers_)
print("Labels:", kmeans1.labels_)

As for dataset 2, the implementation would look like this:

# Dataset2
X2 = [(1,2), (1,3), (2,2), (3,2), (3,4), (3,3)]
# Apply KMeans
kmeans2 = KMeans(n_clusters=2, random_state=0).fit(X2)
print("Cluster centers:", kmeans2.cluster_centers_)
print("Labels:", kmeans2.labels_)