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Unit 7: Unsupervised Learning - Practice Quiz

ECAP792 60 Questions
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1 What is the main purpose of clustering?

Introduction to clustering algorithms Easy
A. To group similar data points
B. To label training examples
C. To predict continuous values
D. To remove every outlier

2 Clustering is generally classified as which type of learning?

Introduction to clustering algorithms Easy
A. Reinforcement learning
B. Transfer learning
C. Unsupervised learning
D. Supervised learning

3 What is a cluster?

Introduction to clustering algorithms Easy
A. A table of random predictions
B. A sequence of model errors
C. A collection of labeled variables
D. A collection of similar data points

4 Which information is usually absent from a clustering dataset?

Introduction to clustering algorithms Easy
A. Class labels
B. Object attributes
C. Data records
D. Feature values

5 In K Means, what does represent?

K Means Easy
A. The number of iterations
B. The number of clusters
C. The number of outliers
D. The number of features

6 What represents the center of a cluster in K Means?

K Means Easy
A. The category mode
B. The largest value
C. The arithmetic mean
D. The middle median

7 How does K Means normally assign a data point to a cluster?

K Means Easy
A. By choosing the nearest centroid
B. By choosing the first centroid
C. By choosing a random label
D. By choosing the largest cluster

8 Which type of data is K Means primarily designed to handle?

K Means Easy
A. Categorical data
B. Numerical data
C. Boolean categories
D. Text labels

9 Which type of data is K mode mainly used to cluster?

K mode Easy
A. Categorical data
B. Time-series data
C. Image-pixel data
D. Continuous data

10 What is used as the center of a cluster in K mode?

K mode Easy
A. The arithmetic mean
B. The most frequent category
C. The middle numeric value
D. The maximum numeric value

11 Which comparison is commonly used by K mode for categorical attributes?

K mode Easy
A. Matching and mismatching values
B. Absolute numerical differences
C. Pearson correlation values
D. Squared numerical differences

12 Why is the arithmetic mean generally unsuitable for categorical data?

K mode Easy
A. Categories lack meaningful numeric averages
B. Categories have unlimited possible values
C. Categories require labeled target values
D. Categories always contain missing records

13 What statistic represents a cluster center in K median?

K median Easy
A. The median
B. The range
C. The mode
D. The mean

14 Which distance measure is commonly associated with K median?

K median Easy
A. Jaccard distance
B. Manhattan distance
C. Hamming distance
D. Cosine distance

15 Compared with the mean, the median is generally less affected by what?

K median Easy
A. Repeated values
B. Scaled values
C. Middle values
D. Extreme values

16 For the values , , and , what is the median?

K median Easy
A.
B.
C.
D.

17 What does a high silhouette score generally indicate?

Performance measures of clustering Easy
A. Clusters are compact and separated
B. Clusters contain identical record counts
C. Clusters use many input features
D. Clusters are large and overlapping

18 What does within-cluster sum of squares measure?

Performance measures of clustering Easy
A. Distance between class labels
B. Number of categorical features
C. Accuracy of target predictions
D. Variation inside the clusters

19 For within-cluster sum of squares, which value usually indicates more compact clusters?

Performance measures of clustering Easy
A. A lower value
B. A higher value
C. A negative value
D. An undefined value

20 What is the elbow method commonly used to estimate?

Performance measures of clustering Easy
A. A suitable number of labels
B. A suitable number of records
C. A suitable number of classes
D. A suitable number of clusters

21 A dataset contains customer age in years and annual income in dollars. Before applying a distance-based clustering algorithm, why should these features usually be standardized?

Introduction to clustering algorithms Medium
A. To guarantee that every cluster has equal size
B. To prevent income from dominating the distance calculation
C. To convert the clustering task into classification
D. To remove all correlations between the two features

22 A hierarchical clustering dendrogram is cut at a horizontal level that intersects four vertical branches. How many clusters does this cut produce?

Introduction to clustering algorithms Medium
A. Five clusters
B. Two clusters
C. Four clusters
D. Three clusters

23 Which situation is most suitable for unsupervised clustering?

Introduction to clustering algorithms Medium
A. Classifying emails using manually assigned spam labels
B. Grouping news articles without predefined categories
C. Predicting house prices from labeled sales records
D. Estimating demand from known historical targets

24 Two clusters have irregular, curved shapes and are separated by low-density regions. Which type of clustering approach is generally most appropriate?

Introduction to clustering algorithms Medium
A. A density-based method identifying connected dense regions
B. A supervised regression method fitting curved boundaries
C. A centroid-based method requiring spherical clusters
D. A dimensionality-reduction method that always assigns labels by retaining the components with the greatest variance

25 For the one-dimensional points , , , and , suppose K Means assigns and to one cluster and and to another. What are the updated centroids?

K Means Medium
A. and
B. and
C. and
D. and

26 A point is compared with centroids and using Euclidean distance. To which cluster is the point assigned?

K Means Medium
A. Cluster 2, because its distance is
B. Cluster 1, because its distance is
C. Cluster 1, because its distance is
D. Cluster 2, because its distance is

27 Why can two runs of standard K Means on the same dataset produce different cluster assignments?

K Means Medium
A. The algorithm automatically removes different features during every centroid-update stage
B. Euclidean distance randomly changes for each observation
C. The arithmetic mean changes between separate runs
D. The initial centroids may be selected differently

28 A K Means cluster contains points , , and . What centroid is obtained after the update step?

K Means Medium
A.
B.
C.
D.

29 What is the most likely effect of adding one extremely distant outlier to a dataset clustered with K Means?

K Means Medium
A. All centroids remain fixed because means ignore extremes
B. Every ordinary point is removed before the next assignment step
C. A centroid may shift substantially toward the outlier
D. The number of clusters automatically increases by one

30 A K mode cluster contains the values red, blue, red, green, and red for a categorical feature. What value is used for that feature in the updated mode?

K mode Medium
A. Green
B. Red
C. A numerical average of all category codes
D. Blue

31 Using simple matching dissimilarity, what is the dissimilarity between and ?

K mode Medium
A.
B.
C.
D.

32 Why is K mode generally preferred over K Means for purely nominal attributes?

K mode Medium
A. It converts every category into a continuous probability
B. It uses category modes and mismatch-based dissimilarities
C. It guarantees clusters with identical numbers of records
D. It computes arithmetic means after assigning arbitrary integer codes to categories and then treats those codes as measured quantities

33 A categorical cluster has equal frequencies for the values A and B in one attribute. How should a K mode implementation typically update that component?

K mode Medium
A. Merge every existing cluster into a single cluster
B. Choose one tied mode using a defined tie rule
C. Delete the attribute from the dataset
D. Compute the midpoint between A and B

34 A one-dimensional K median cluster contains , , , , and . What is its updated center?

K median Medium
A.
B.
C.
D.

35 Which objective is most directly minimized by K median clustering?

K median Medium
A. The sum of squared Euclidean distances to centroids
B. The sum of Manhattan distances to cluster centers
C. The count of categorical mismatches with cluster modes
D. The total variance of all features before cluster assignments are produced

36 A two-dimensional cluster contains , , and . What is its coordinate-wise median center?

K median Medium
A.
B.
C.
D.

37 Compared with K Means, why is K median often more robust when a dataset contains extreme numerical outliers?

K median Medium
A. K median increases the number of clusters until each outlier receives a separate cluster
B. Medians always produce perfectly spherical clusters
C. Manhattan distance removes outliers from the dataset
D. Medians are less affected by extreme values

38 A sample has average intra-cluster distance and average distance to its nearest other cluster . What is its silhouette coefficient?

Performance measures of clustering Medium
A.
B.
C.
D.

39 When using the elbow method, the within-cluster sum of squares decreases sharply up to and only slightly afterward. Which value is the most reasonable choice?

Performance measures of clustering Medium
A.
B.
C.
D.

40 Two clustering models have average silhouette scores of and . Assuming the same data and distance measure, which interpretation is most appropriate?

Performance measures of clustering Medium
A. The model has better cohesion and separation
B. Both models have identical cluster quality
C. The model necessarily matches all unknown true labels perfectly and therefore requires no further evaluation
D. The model has better cohesion and separation

41 A dataset contains continuous variables measured in meters and categorical variables with no natural ordering. Which approach most directly avoids imposing arbitrary numeric distances on the categories?

Introduction to clustering algorithms Hard
A. Apply K mode after discretizing every continuous variable
B. Use a mixed-type dissimilarity with an appropriate clustering method
C. Use Euclidean distance after one-hot encoding without rescaling
D. Apply K Means after integer-encoding every categorical value

42 Suppose a clustering method uses only the pairwise rank ordering of dissimilarities. Which transformation leaves its result unchanged, assuming no ties are introduced?

Introduction to clustering algorithms Hard
A. Any strictly increasing transformation of all dissimilarities
B. Any permutation of dissimilarities within each observation
C. Any nonlinear transformation applied separately to each feature
D. Any positive affine transformation of individual coordinates

43 For one-dimensional observations , K Means with is restricted to contiguous partitions after sorting. Which partition minimizes the within-cluster sum of squares?

K Means Hard
A. and an empty cluster
B. and
C. and
D. and

44 A standard Lloyd iteration assigns every observation to its nearest centroid and then replaces each centroid by its assigned-cluster mean. Which statement is guaranteed when ties and empty clusters are handled without increasing the objective?

K Means Hard
A. Each full iteration does not increase the objective
B. Each full iteration preserves all cluster sizes
C. Each full iteration strictly decreases the objective
D. Each full iteration reaches the global optimum

45 In K Means++, one centroid has already been selected at from the candidate points . What is the probability that is selected next?

K Means Hard
A.
B.
C.
D.

46 A feature is multiplied by a constant before Euclidean K Means is run. How does that feature's contribution to the objective change for a fixed partition?

K Means Hard
A. It is multiplied by
B. It remains exactly unchanged
C. It is divided by
D. It is multiplied by

47 A K Means implementation produces an empty cluster during the assignment step. Which response best preserves the intended optimization while allowing the algorithm to continue?

K Means Hard
A. Replace its centroid with the global coordinate-wise median
B. Reinitialize it using a point with large current assignment error
C. Set its centroid equal to the nearest occupied centroid
D. Retain it permanently and exclude it from later assignments

48 For a fixed nonempty cluster, why is its arithmetic mean used as the K Means centroid?

K Means Hard
A. It minimizes the sum of Euclidean distances
B. It minimizes the sum of squared Euclidean distances
C. It minimizes the maximum squared Euclidean distance
D. It minimizes the number of nonzero coordinate deviations

49 Under simple matching dissimilarity, a categorical cluster contains three times, twice, and four times. What is a valid mode vector?

K mode Hard
A.
B.
C.
D.

50 A K mode cluster has category counts , , and for one attribute. Which statement correctly describes the prototype update for that attribute?

K mode Hard
A. Only minimizes the mismatch loss
B. Either or minimizes the mismatch loss
C. Only minimizes the mismatch loss
D. The prototype must remain unchanged because of the tie

51 Two categorical records are and . With simple matching dissimilarity and unit attribute weights, what is their dissimilarity?

K mode Hard
A.
B.
C.
D.

52 A categorical attribute has 1,000 possible values, most of which are rare, while another attribute is binary and balanced. Under unweighted simple matching dissimilarity, what is the main risk?

K mode Hard
A. The high-cardinality attribute may dominate through frequent mismatches
B. Both attributes contribute equally in expected mismatch frequency
C. The high-cardinality attribute becomes irrelevant after mode updates
D. The binary attribute necessarily dominates every assignment

53 For the one-dimensional cluster , which set contains every centroid minimizing the sum of absolute deviations?

K median Hard
A. Only the point
B. Every point in
C. Only the point
D. Every point in

54 For multivariate K median using Manhattan distance, how is the optimal prototype of a fixed nonempty cluster obtained?

K median Hard
A. By taking the arithmetic mean of each coordinate
B. By minimizing squared distance in each coordinate
C. By taking a median independently in each coordinate
D. By selecting the point nearest to the arithmetic mean

55 A one-dimensional cluster consists of , where . As tends to infinity, what happens to the K median prototype and its minimized absolute-deviation objective?

K median Hard
A. The prototype approaches , while the objective remains constant
B. The prototype stays at , while the objective grows linearly
C. The prototype stays at , while the objective remains bounded
D. The prototype approaches , while the objective grows quadratically

56 A weighted one-dimensional K median cluster has observations with respective weights . Which value is a weighted median under the condition that neither side has more than half the total weight?

K median Hard
A.
B.
C.
D.

57 For a point , the mean intra-cluster distance is and the smallest mean distance to another cluster is . What is its silhouette value?

Performance measures of clustering Hard
A.
B.
C.
D.

58 A clustering is compared with ground-truth labels using the Adjusted Rand Index (ARI). Both the cluster identifiers and class identifiers are independently permuted. What happens to the ARI?

Performance measures of clustering Hard
A. It becomes one because permutations imply equivalent labels
B. It becomes zero because the identifiers no longer match
C. It remains unchanged because pair relationships are preserved
D. It changes sign because both label systems are permuted

59 Why can unadjusted cluster purity misleadingly favor solutions with large values of ?

Performance measures of clustering Hard
A. More clusters always increase within-cluster variance
B. Singleton clusters can achieve perfect class homogeneity
C. Purity penalizes every split of a true class
D. Purity becomes negative when clusters are unbalanced

60 Two candidate clusterings have Davies–Bouldin indices and , computed using the same data, distance, and dispersion definition. Which interpretation is correct?

Performance measures of clustering Hard
A. The solution is preferred because lower values indicate better separation
B. The indices cannot be compared unless both solutions have identical centroids
C. The solution is preferred because higher values indicate greater cohesion
D. The solutions are equivalent because the index is invariant to partitions
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