K-Means Clustering Example with K=2

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Which of the following statements about K-means clustering is true?

It may get stuck in local optima. (correct)
It does not require specifying the number of clusters in advance.
It guarantees finding the optimal solution.
It works well on categorical data.

What is a common approach to mitigate the issue of local optima in K-means clustering?

Increase the number of clusters.
Use a different clustering algorithm.
Scale the data before clustering.
Repeat K-means with different initial cluster centers. (correct)

Which of the following is a strength of K-means clustering?

It does not require specifying the number of clusters.
It can handle categorical data.
It always finds the global optimum.
It is easy to use and understand. (correct)

What is a potential disadvantage of K-means clustering?

It is sensitive to outliers. (A) Signup and view all the answers

Which of the following statements about K-means clustering is false?

It can handle categorical data. (C) Signup and view all the answers

What is the primary difference between K-means clustering and hierarchical clustering?

K-means requires specifying the number of clusters, while hierarchical clustering does not. (A) Signup and view all the answers

What is the primary objective of the K-Means Clustering algorithm?

To partition the observations into a pre-specified number of clusters (B) Signup and view all the answers

In the initial step of the K-Means Clustering algorithm, how are the cluster centers (centroids) chosen?

They are randomly assigned from the feature space (A) Signup and view all the answers

What is the criterion used to assign observations to clusters in the K-Means Clustering algorithm?

Euclidean distance (B) Signup and view all the answers

What condition is used to determine the stopping criterion for the K-Means Clustering algorithm?

When the cluster centers no longer move or move within a specified threshold (A) Signup and view all the answers

In the K-Means Clustering algorithm, what property must the cluster sets $C_1, C_2, ..., C_k$ satisfy?

$C_1 \cup C_2 \cup ... \cup C_k = {1, ..., n}$, where each observation belongs to one of the K clusters (D) Signup and view all the answers

What is the primary disadvantage of the K-Means Clustering algorithm?

It is sensitive to the initial choice of cluster centers (C) Signup and view all the answers

What is the fundamental principle behind K-Means clustering?

Minimizing the within-cluster variation (D) Signup and view all the answers

What is the optimization problem that K-Means clustering aims to solve?

Minimize $\sum_{k=1}^K \sum_{x \in C_k} ||x - \mu_k||^2$ (D) Signup and view all the answers

Which statement about the clusters in K-Means clustering is true?

The clusters are always disjoint (C) Signup and view all the answers

How is the within-cluster variation for a cluster $C_k$ defined in K-Means clustering?

$W(C_k) = \sum_{x \in C_k} ||x - \mu_k||^2$ (D) Signup and view all the answers

What is a potential weakness of K-Means clustering mentioned in the text?

It is difficult to choose the correct value of K (B) Signup and view all the answers

Which statement about the strengths of K-Means clustering is true?

It is a simple iterative method where the user provides the number of clusters (C) Signup and view all the answers