12.10: Exercises
- Page ID
- 138504
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)Part A: Conceptual Questions
K-Means Clustering
- What is the objective function minimized by the K-Means algorithm?
- How does the choice of K affect the clustering output?
- What is the elbow method and how is it used to determine the optimal number of clusters?
- What are the limitations of K-Means in terms of cluster shape and scale sensitivity?
- How does the initial placement of centroids influence final clusters in K-Means?
Hierarchical Clustering
- What is the difference between agglomerative and divisive hierarchical clustering?
- What are linkage methods in hierarchical clustering, and how do they affect results?
- How do dendrograms help in identifying natural clusters?
- What are the advantages and disadvantages of hierarchical clustering compared to K-Means?
- Can hierarchical clustering be used with categorical data? If so, how?
DBSCAN
- What are the key parameters of DBSCAN, and how do they influence the result?
- How does DBSCAN handle noise and outliers?
- Compare DBSCAN to K-Means in terms of assumptions and scalability.
- What is a core point versus a border point in DBSCAN?
- In what situations is DBSCAN preferred over K-Means or hierarchical clustering?
Gaussian Mixture Models (GMM)
- How does GMM differ from K-Means in terms of cluster assignment?
- What is the role of the Expectation-Maximization (EM) algorithm in GMM?
- How are soft assignments useful in GMM clustering?
- What assumptions do GMMs make about data distribution?
- How can model selection criteria like BIC or AIC be used in choosing the number of components in GMM?
Part B: Interpretation Questions
K-Means Clustering
- How would you interpret the centroid of a cluster in a business context?
- What does a low within-cluster sum of squares (WCSS) suggest about the clustering?
- If two clusters have overlapping data points, what might that indicate about your choice of K?
- How do standardized variables affect K-Means clustering outcomes?
- What does the distance between centroids imply about cluster separation?
Hierarchical Clustering
- How do you decide the optimal number of clusters using a dendrogram?
- What does it imply if clusters merge at very high linkage distances?
- How would you explain the difference between single and complete linkage visually?
- If hierarchical clusters don’t match known group labels, what could be the issue?
- How do dendrogram height and shape reflect data structure?
DBSCAN
- What does a high number of noise points suggest about your DBSCAN parameter settings?
- How would you interpret the presence of small clusters in DBSCAN output?
- If DBSCAN returns one large cluster and many outliers, what might that indicate?
- How can you visualize the effectiveness of DBSCAN clustering?
- What does it mean if DBSCAN identifies more clusters than expected?
Gaussian Mixture Models (GMM)
- - How do you interpret soft clustering assignments in a GMM context?
- - What does the shape of a GMM ellipse represent in a plot?
- - If two Gaussian components overlap, what business insights might that provide?
- - How does the log-likelihood of the GMM help evaluate clustering quality?
- - Why might BIC be preferred over AIC when evaluating GMMs in large datasets?
Part C: Hands-On Data Exercises
K-Means Clustering Applications
- Marketing: Use K-Means clustering to segment customers based on recency, frequency, monetary value (RFM), website behavior, and demographics. (Dataset: marketing_segments.xlsx)
- Finance: Use K-Means clustering to group financial instruments based on volatility, liquidity, market cap, sector, and price momentum. (Dataset: financial_instruments.xlsx)
- Operations: Use K-Means clustering to segment warehouse inventory items by turnover rate, unit cost, reorder frequency, lead time, and item category. (Dataset: inventory_clusters.xlsx)
- Sales: Use K-Means clustering to group sales reps based on total sales, average deal size, sales cycle length, product mix, and close rate. (Dataset: sales_team_clusters.xlsx)
- Customer Service: Use K-Means clustering to cluster support tickets by issue complexity, resolution time, escalation count, communication channel, and customer satisfaction score. (Dataset: service_ticket_clusters.xlsx)
- Quality Control: Use K-Means clustering to segment manufactured parts based on dimension measurements, weight, temperature tolerance, surface finish, and inspection outcomes. (Dataset: quality_metrics_clusters.xlsx)
- Credit Risk Management: Use K-Means clustering to group borrowers by income level, debt-to-income ratio, number of credit lines, credit history length, and payment behavior. (Dataset: borrower_profiles.xlsx)
- Entertainment: Use K-Means clustering to cluster users based on streaming habits, such as average watch time, preferred genres, binge frequency, device type, and watch time of day. (Dataset: viewer_segments.xlsx)
- Manufacturing: Use K-Means clustering to segment machines by downtime frequency, maintenance hours, age, energy use, and failure types. (Dataset: equipment_profiles.xlsx)
- Accounting: Use K-Means clustering to group expense categories or departments based on transaction volume, average transaction size, vendor diversity, and budget variance. (Dataset: expense_patterns.xlsx)