Statistics for Data Science & Analytics

Test your knowledge with this Cluster Analysis Quiz featuring MCQs on k-means, k-medoids, k-means++, and k-median algorithms, along with key concepts like Manhattan distance, cosine similarity, CF tree split, and multi-class classification. Perfect for machine learning enthusiasts and data science learners to assess their understanding of unsupervised clustering techniques. Take the Cluster Analysis Quiz now and sharpen your skills!

Online Unsupervised Machine Learning Cluster Analysis Quiz with Answers

1. Which of the following statements is true?

 There are no clustering algorithms that can handle time-series data since we always assume that the data points are temporally independent from each other

 Dimensionality reduction helps make high-dimensional clustering more feasible and scalable

 Since cluster analysis is unsupervised learning, there’s no way to incorporate user preference or guidance into the clustering process

 K-means is an example of a distance-based clustering method

2. What are some common considerations and requirements for cluster analysis?

 In order to perform cluster analysis, we need to have a similarity measure between data objects

 We need to consider how to incorporate user preference for cluster size and shape into the clustering algorithm

 We must know the number of output clusters a priori for all clustering algorithms

 We need to be able to handle a mixture of different types of attributes (e.g.,numerical and categorical)

3. In the k-medoids algorithm, after computing the new center for each cluster, is the center always guaranteed to be one of the data points in that cluster?

 No

 Yes

4. When will a leaf entry in the CF tree split?

 When the number of points in the entry is larger than a threshold

 When the diameter of the entry is larger than a threshold

5. Which of the following statements about k-medoids, k-median, and k-modes algorithms is correct?

 The centroids in the k-medoids algorithm may not be any observed data points

 The centroids in the k-means algorithm may not be any observed data points

 The k-modes algorithm is designed for categorical data

 The k-medoids and k-median algorithms are less sensitive to outliers than k-means

6. For k-means, will different initializations always lead to different clustering results?

 No

 Yes

7. Considering the k- median algorithm, if points (-1, 3), (-3, 1), and (-2, -1) are the only points that are assigned to the first cluster now, what is the new centroid for this cluster?

 (-2, 1)

 (0, 2)

 (0, 0)

 (0, 3)

8. Which of the following statements, if any, is FALSE?

 In divisive clustering, cluster sizes from one iteration to the next may never increase

 In agglomerative clustering, once two objects are grouped into the same cluster, they will never be separated into different clusters again

 In agglomerative clustering, cluster sizes from one iteration to the next may never decrease

 In divisive clustering, it’s possible for two points that are assigned to different clusters to fall into the same cluster later on

9. If you need to choose between clustering and supervised learning for the following applications, which would you choose, clustering over supervised learning?

 A real estate company wants to sell a new house; they need to determine the price for selling the house based on its condition (e.g., size, location), as well as the sales data of their previously sold houses

 Given a large number of web pages, discover the latent topics discussed by those web pages

 Given the historical prices of a group of stocks, predict whether the price of a specific stock will rise or fall in the following week

 Find user communities in online social networks such as Facebook and Twitter

10. Given the two-dimensional points (0, 3) and (4, 0), what is the Manhattan distance between those two points?

 7

 3

 5

 1

11. Considering the k-means algorithm, if points (0, 3), (2, 1), and (-2, 2) are the only points that are assigned to the first cluster now, what is the new centroid for this cluster?

 (-2, 1)

 (0, 0)

 (0, 3)

 (0, 2)

12. Is K-means guaranteed to find K clusters that lead to the global minimum of the SSE?

 Yes

 No

13. Which of the following statements is true?

 A good clustering algorithm should achieve high similarity between the data points within the same cluster

 A good clustering algorithm should achieve low similarity between the data points within the same cluster

14. Suppose $X$ is a random variable with $P(X = -1) = 0.5$ and $P(X = 1) = 0.5$. In addition, we have another random variable $Y=X*X$. What is the covariance between $X$ and $Y$?

 0

 1

 -1

15. Considering the k-means algorithm, after the current iteration, we have three centroids (0, 1), (2, 1), and (-1, 2). Will points (0.5, 0.5) and (-0.5, 0) be assigned to the same cluster in the next iteration?

 Yes

 No

16. The k-means++ algorithm is designed for better initialization for k-means, which will take the farthest point from the currently selected centroids. Suppose $k = 2$, and we have selected the first centroid as (0, 0). Among the following points (these are all the remaining points), which one should we take for the second centroid?

 (0, 2)

 (-2, 1)

 (3, 0)

 (2, 0)

17. Is it possible that the SSE strictly increases after we recompute new centers in the k-means algorithm? Why?

 No, it is impossible. The new center of a cluster comes from the average of all data points in this cluster, which actually minimizes the SSE.

 Yes, it is possible. Because the new centers may be worse than before.

18. Given three vectors $A$, $B$, and $C$, suppose the cosine similarity between $A$ and $B$ is $cos(A, B) = 1.0$, and the similarity between $A$ and $C$ is $cos(A, C) = -1.0$. Can we determine the cosine similarity between $B$ and $C$?

 Yes

 No

19. When dealing with multi-class classification problems, which loss function should be used?

 Binary Cross Entropy

 Categorical Cross Entropy

 Mean Squared Error

 Mean Absolute Error

20. Which of the following statements is true?

 Clustering analysis has a wide range of applications in tasks such as data summarization, dynamic trend detection, multimedia analysis, and biological network analysis

 It is impossible to cluster objects in a data stream. We must have all the data objects that we need to cluster ready before clustering can be performed

 Cluster analysis is considered supervised learning

 When clustering, we want to put two data objects that are similar into the same cluster

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Online Cluster Analysis Quiz with Answers

• Is K-means guaranteed to find K clusters that lead to the global minimum of the SSE?
• When dealing with multi-class classification problems, which loss function should be used?
• Is it possible that the SSE strictly increases after we recompute new centers in the k-means algorithm? Why?
• For k-means, will different initializations always lead to different clustering results?
• In the k-medoids algorithm, after computing the new center for each cluster, is the center always guaranteed to be one of the data points in that cluster?
• Which of the following statements is true?
• What are some common considerations and requirements for cluster analysis?
• Which of the following statements is true?
• If you need to choose between clustering and supervised learning for the following applications, which would you choose, clustering over supervised learning?
• Which of the following statements is true?
• Given the two-dimensional points (0, 3) and (4, 0), what is the Manhattan distance between those two points?
• Given three vectors $A$, $B$, and $C$, suppose the cosine similarity between $A$ and $B$ is $cos(A, B) = 1.0$, and the similarity between $A$ and $C$ is $cos(A, C) = -1.0$. Can we determine the cosine similarity between $B$ and $C$?
• Suppose $X$ is a random variable with $P(X = -1) = 0.5$ and $P(X = 1) = 0.5$. In addition, we have another random variable $Y=X*X$. What is the covariance between $X$ and $Y$?
• Considering the k-means algorithm, after the current iteration, we have three centroids (0, 1), (2, 1), and (-1, 2). Will points (0.5, 0.5) and (-0.5, 0) be assigned to the same cluster in the next iteration?
• Considering the k-means algorithm, if points (0, 3), (2, 1), and (-2, 2) are the only points that are assigned to the first cluster now, what is the new centroid for this cluster?
• The k-means++ algorithm is designed for better initialization for k-means, which will take the farthest point from the currently selected centroids. Suppose $k = 2$, and we have selected the first centroid as (0, 0). Among the following points (these are all the remaining points), which one should we take for the second centroid?
• Considering the k- median algorithm, if points (-1, 3), (-3, 1), and (-2, -1) are the only points that are assigned to the first cluster now, what is the new centroid for this cluster?
• Which of the following statements about k-medoids, k-median, and k-modes algorithms is correct?
• Which of the following statements, if any, is FALSE?
• When will a leaf entry in the CF tree split?

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