GEORGIA TECH OMSCS
CS 7641 — Machine Learning
Unsupervised Learning
Unit Quiz V2 — Problems and Solutions
2026/2027 Updated Edition
100% Correct — Verified Solutions with Worked Steps
Total Questions 85 (Verified)
Sections 9 Comprehensive Modules
Cognitive Mix 25% Recall / 55% Application / 20% Analysis
Format 4-Option Multiple Choice (A–D)
Scope K-Means, Hierarchical, EM/GMM, PCA, ICA, MF
Audience CS 7641 OMSCS Candidates
This study aid is independently prepared for examination preparation and is not affiliated with, endorsed by, or sponsored by the Georgia Institute of
Technology or the OMSCS program. Content reflects current CS 7641 unsupervised learning unit coverage including K-Means, hierarchical
clustering, EM/GMM, PCA, ICA, and matrix factorization.
, SECTION 1 — Unsupervised Learning Fundamentals and Problem Formulation
Problem Formulation | Clustering vs. DR vs. Density Estimation | Q1–Q8
Q1. A data scientist has a dataset of 10,000 customer purchase histories with no labels. The goal is to identify
natural groupings of customers with similar buying patterns. Which type of learning problem is this?
A. Supervised classification — predict group labels from features.
B. Unsupervised clustering — discover inherent group structure without labels. [CORRECT]
C. Reinforcement learning — optimize a reward signal through trial and error.
D. Semi-supervised learning — use a small labeled subset to propagate labels.
Correct Answer: B
Rationale: Unsupervised learning deals with unlabeled data, seeking to discover inherent structure (clusters, low-dimensional
manifolds, or density). Clustering groups similar instances; dimensionality reduction finds a low-dimensional embedding
preserving structure; density estimation models the data distribution. Supervised learning requires labeled targets; reinforcement
learning uses reward signals; semi-supervised combines a few labels with many unlabeled points. Since no labels exist and the
goal is grouping, this is unsupervised clustering.
Q2. Which of the following BEST distinguishes unsupervised learning from supervised learning?
A. Unsupervised learning always produces a single output; supervised learning produces many.
B. Supervised learning optimizes a loss against ground-truth labels, while unsupervised learning discovers
structure (clusters, low-dimensional representations, or densities) without labeled targets. [CORRECT]
C. Unsupervised learning is computationally cheaper than supervised learning.
D. Supervised learning requires less data than unsupervised learning.
Correct Answer: B
Rationale: The fundamental distinction is the presence or absence of labels. Supervised learning fits f: X → Y using labeled (xᵢ,
yᵢ) pairs to minimize a loss such as MSE or cross-entropy. Unsupervised learning only has X and seeks structure — clusters
(K-Means, hierarchical), low-dimensional embeddings (PCA, ICA), or density models (GMM, KDE). Cost and data size are not
defining features. Many unsupervised methods (e.g., EM for GMM) are as expensive as or more expensive than supervised
methods.
Q3. A researcher applies PCA to reduce 200-dimensional gene expression data to 10 dimensions, then applies
K-Means on the reduced data. Which statement BEST characterizes the relationship between the two techniques?
A. PCA is supervised clustering; K-Means is unsupervised dimensionality reduction.
B. PCA is unsupervised dimensionality reduction; K-Means is unsupervised clustering. They are complementary
but address different goals. [CORRECT]
C. Both techniques are forms of density estimation.
D. PCA requires labels; K-Means does not.
Correct Answer: B
Rationale: PCA is a dimensionality reduction technique that finds orthogonal directions of maximum variance, projecting data
onto a lower-dimensional subspace while preserving global structure. K-Means is a clustering algorithm that partitions data into
k groups by minimizing within-cluster sum of squares (WCSS). Both are unsupervised. They are often combined: PCA first (to
denoise/compress), then K-Means (to cluster). Neither is density estimation; that role belongs to GMMs, KDEs, and similar
methods. Neither requires labels.
Q4. A data scientist has three goals: (1) discover natural groups in customer data, (2) compress images by
representing them with fewer numbers, (3) estimate the probability density of feature vectors for anomaly
detection. Which sequence of unsupervised techniques is MOST appropriate?
, CS 7641 — UNSUPERVISED LEARNING UNIT QUIZ V2 — 85 QUESTIONS 2026/2027 Update | 100% Correct - GT
A. K-Means for (1), PCA for (2), GMM/density estimation for (3). [CORRECT]
B. PCA for (1), K-Means for (2), GMM for (3).
C. GMM for (1), K-Means for (2), PCA for (3).
D. K-Means for all three goals.
Correct Answer: A
Rationale: (1) Discovering natural groups is clustering → K-Means (or hierarchical, GMM). (2) Compression via
low-dimensional representation is dimensionality reduction → PCA finds orthogonal components maximizing variance, enabling
low-rank reconstruction. (3) Estimating p(x) for anomaly detection is density estimation → GMM provides a parametric mixture
density p(x) = Σ π N(x | μ , Σ ). K-Means cannot estimate densities (it produces hard assignments and centroids, not p(x)).
PCA does not cluster or estimate density. Each goal maps to its appropriate technique.
Q5. A colleague claims "K-Means is a special case of a Gaussian Mixture Model." Which statement is MOST
accurate?
A. The claim is false — K-Means and GMM are completely unrelated.
B. The claim is essentially correct: K-Means is the limit of a GMM with shared spherical covariances Σ = εI as ε
→ 0, yielding hard assignments via squared Euclidean distance. [CORRECT]
C. The claim is correct: GMM is a special case of K-Means.
D. The claim is correct only when K-Means uses Mahalanobis distance.
Correct Answer: B
Rationale: K-Means is the hard-assignment limit of EM on a GMM with identical isotropic covariances Σ = εI as ε → 0. Under
this limit, the GMM responsibility r = π N(x |μ ,εI) / Σ π N(x |μ ,εI) degenerates to a 1-of-K encoding (hard
assignment), and the M-step update μ = (Σ r x ) / (Σ r ) reduces to the K-Means centroid update. The GMM
log-likelihood reduces to negative WCSS. Thus K-Means ≈ GMM with spherical covariances and ε→0. K-Means is NOT a
density model in itself (no proper p(x)).
Q6. A researcher has data that lies on a curved manifold (e.g., the "Swiss roll"). They apply PCA. Which
limitation of PCA does this scenario BEST illustrate?
A. PCA fails because it is supervised and the data has no labels.
B. PCA assumes linear structure: it projects onto a global linear subspace, so it cannot "unroll" a curved
nonlinear manifold, even though the data may have low intrinsic dimensionality. [CORRECT]
C. PCA fails because it requires Gaussian data.
D. PCA fails because the data has too many dimensions.
Correct Answer: B
Rationale: PCA is a linear method: it finds the orthogonal directions of maximum variance, equivalent to projecting onto the
leading eigenvectors of the covariance matrix. It cannot capture nonlinear manifold structure like the Swiss roll, which is
intrinsically 2D but embedded in 3D in a curled way. Manifold learning methods (ISOMAP, LLE, t-SNE, UMAP) are designed
for such cases. PCA does not strictly require Gaussianity (it is optimal under Gaussian assumptions but works on any data via
SVD). It is unsupervised. The issue is linearity, not dimensionality.
Q7. In unsupervised learning, the "no free lunch" theorem implies which of the following?
A. No single clustering or dimensionality reduction algorithm is universally best for all datasets; algorithm choice
depends on data structure and assumptions. [CORRECT]
B. K-Means is always the best clustering algorithm.
C. PCA is always the best dimensionality reduction method.
D. All unsupervised algorithms converge to the same solution.
Correct Answer: A
CS 7641 Machine Learning — Georgia Tech OMSCS Page 3
CS 7641 — Machine Learning
Unsupervised Learning
Unit Quiz V2 — Problems and Solutions
2026/2027 Updated Edition
100% Correct — Verified Solutions with Worked Steps
Total Questions 85 (Verified)
Sections 9 Comprehensive Modules
Cognitive Mix 25% Recall / 55% Application / 20% Analysis
Format 4-Option Multiple Choice (A–D)
Scope K-Means, Hierarchical, EM/GMM, PCA, ICA, MF
Audience CS 7641 OMSCS Candidates
This study aid is independently prepared for examination preparation and is not affiliated with, endorsed by, or sponsored by the Georgia Institute of
Technology or the OMSCS program. Content reflects current CS 7641 unsupervised learning unit coverage including K-Means, hierarchical
clustering, EM/GMM, PCA, ICA, and matrix factorization.
, SECTION 1 — Unsupervised Learning Fundamentals and Problem Formulation
Problem Formulation | Clustering vs. DR vs. Density Estimation | Q1–Q8
Q1. A data scientist has a dataset of 10,000 customer purchase histories with no labels. The goal is to identify
natural groupings of customers with similar buying patterns. Which type of learning problem is this?
A. Supervised classification — predict group labels from features.
B. Unsupervised clustering — discover inherent group structure without labels. [CORRECT]
C. Reinforcement learning — optimize a reward signal through trial and error.
D. Semi-supervised learning — use a small labeled subset to propagate labels.
Correct Answer: B
Rationale: Unsupervised learning deals with unlabeled data, seeking to discover inherent structure (clusters, low-dimensional
manifolds, or density). Clustering groups similar instances; dimensionality reduction finds a low-dimensional embedding
preserving structure; density estimation models the data distribution. Supervised learning requires labeled targets; reinforcement
learning uses reward signals; semi-supervised combines a few labels with many unlabeled points. Since no labels exist and the
goal is grouping, this is unsupervised clustering.
Q2. Which of the following BEST distinguishes unsupervised learning from supervised learning?
A. Unsupervised learning always produces a single output; supervised learning produces many.
B. Supervised learning optimizes a loss against ground-truth labels, while unsupervised learning discovers
structure (clusters, low-dimensional representations, or densities) without labeled targets. [CORRECT]
C. Unsupervised learning is computationally cheaper than supervised learning.
D. Supervised learning requires less data than unsupervised learning.
Correct Answer: B
Rationale: The fundamental distinction is the presence or absence of labels. Supervised learning fits f: X → Y using labeled (xᵢ,
yᵢ) pairs to minimize a loss such as MSE or cross-entropy. Unsupervised learning only has X and seeks structure — clusters
(K-Means, hierarchical), low-dimensional embeddings (PCA, ICA), or density models (GMM, KDE). Cost and data size are not
defining features. Many unsupervised methods (e.g., EM for GMM) are as expensive as or more expensive than supervised
methods.
Q3. A researcher applies PCA to reduce 200-dimensional gene expression data to 10 dimensions, then applies
K-Means on the reduced data. Which statement BEST characterizes the relationship between the two techniques?
A. PCA is supervised clustering; K-Means is unsupervised dimensionality reduction.
B. PCA is unsupervised dimensionality reduction; K-Means is unsupervised clustering. They are complementary
but address different goals. [CORRECT]
C. Both techniques are forms of density estimation.
D. PCA requires labels; K-Means does not.
Correct Answer: B
Rationale: PCA is a dimensionality reduction technique that finds orthogonal directions of maximum variance, projecting data
onto a lower-dimensional subspace while preserving global structure. K-Means is a clustering algorithm that partitions data into
k groups by minimizing within-cluster sum of squares (WCSS). Both are unsupervised. They are often combined: PCA first (to
denoise/compress), then K-Means (to cluster). Neither is density estimation; that role belongs to GMMs, KDEs, and similar
methods. Neither requires labels.
Q4. A data scientist has three goals: (1) discover natural groups in customer data, (2) compress images by
representing them with fewer numbers, (3) estimate the probability density of feature vectors for anomaly
detection. Which sequence of unsupervised techniques is MOST appropriate?
, CS 7641 — UNSUPERVISED LEARNING UNIT QUIZ V2 — 85 QUESTIONS 2026/2027 Update | 100% Correct - GT
A. K-Means for (1), PCA for (2), GMM/density estimation for (3). [CORRECT]
B. PCA for (1), K-Means for (2), GMM for (3).
C. GMM for (1), K-Means for (2), PCA for (3).
D. K-Means for all three goals.
Correct Answer: A
Rationale: (1) Discovering natural groups is clustering → K-Means (or hierarchical, GMM). (2) Compression via
low-dimensional representation is dimensionality reduction → PCA finds orthogonal components maximizing variance, enabling
low-rank reconstruction. (3) Estimating p(x) for anomaly detection is density estimation → GMM provides a parametric mixture
density p(x) = Σ π N(x | μ , Σ ). K-Means cannot estimate densities (it produces hard assignments and centroids, not p(x)).
PCA does not cluster or estimate density. Each goal maps to its appropriate technique.
Q5. A colleague claims "K-Means is a special case of a Gaussian Mixture Model." Which statement is MOST
accurate?
A. The claim is false — K-Means and GMM are completely unrelated.
B. The claim is essentially correct: K-Means is the limit of a GMM with shared spherical covariances Σ = εI as ε
→ 0, yielding hard assignments via squared Euclidean distance. [CORRECT]
C. The claim is correct: GMM is a special case of K-Means.
D. The claim is correct only when K-Means uses Mahalanobis distance.
Correct Answer: B
Rationale: K-Means is the hard-assignment limit of EM on a GMM with identical isotropic covariances Σ = εI as ε → 0. Under
this limit, the GMM responsibility r = π N(x |μ ,εI) / Σ π N(x |μ ,εI) degenerates to a 1-of-K encoding (hard
assignment), and the M-step update μ = (Σ r x ) / (Σ r ) reduces to the K-Means centroid update. The GMM
log-likelihood reduces to negative WCSS. Thus K-Means ≈ GMM with spherical covariances and ε→0. K-Means is NOT a
density model in itself (no proper p(x)).
Q6. A researcher has data that lies on a curved manifold (e.g., the "Swiss roll"). They apply PCA. Which
limitation of PCA does this scenario BEST illustrate?
A. PCA fails because it is supervised and the data has no labels.
B. PCA assumes linear structure: it projects onto a global linear subspace, so it cannot "unroll" a curved
nonlinear manifold, even though the data may have low intrinsic dimensionality. [CORRECT]
C. PCA fails because it requires Gaussian data.
D. PCA fails because the data has too many dimensions.
Correct Answer: B
Rationale: PCA is a linear method: it finds the orthogonal directions of maximum variance, equivalent to projecting onto the
leading eigenvectors of the covariance matrix. It cannot capture nonlinear manifold structure like the Swiss roll, which is
intrinsically 2D but embedded in 3D in a curled way. Manifold learning methods (ISOMAP, LLE, t-SNE, UMAP) are designed
for such cases. PCA does not strictly require Gaussianity (it is optimal under Gaussian assumptions but works on any data via
SVD). It is unsupervised. The issue is linearity, not dimensionality.
Q7. In unsupervised learning, the "no free lunch" theorem implies which of the following?
A. No single clustering or dimensionality reduction algorithm is universally best for all datasets; algorithm choice
depends on data structure and assumptions. [CORRECT]
B. K-Means is always the best clustering algorithm.
C. PCA is always the best dimensionality reduction method.
D. All unsupervised algorithms converge to the same solution.
Correct Answer: A
CS 7641 Machine Learning — Georgia Tech OMSCS Page 3
