Spectral Clustering Quiz

Answers and explanations appear as you take the quiz.

1. Which representation does spectral clustering commonly construct before computing a Laplacian?
   • A similarity or affinity graph
   • A decision tree of class labels
   • A density histogram with fixed bins
   • A linear regression residual matrix
2. Why can spectral clustering help with nested-ring data?
   • It turns rings into normally distributed classes automatically
   • Graph connectivity can represent non-convex groups beyond centroid partitions
   • It always selects two clusters without user input
   • It removes the need to define similarity
3. What role do selected Laplacian eigenvectors play?
   • They set all pairwise distances to zero
   • They are the original class labels
   • They form an embedding used for subsequent cluster assignment
   • They estimate the number of observations
4. What may happen if an affinity graph is too sparse?
   • All observations receive equal similarity
   • Every region becomes one connected component
   • The graph becomes an RBF kernel automatically
   • A true group may break into disconnected fragments
5. Why can the final labels vary even with the same embedding?
   • Eigenvectors contain the true semantic names
   • The label-assignment step has its own choices and initialization
   • Every labeling method is mathematically identical
   • The affinity matrix becomes asymmetric
6. What does a graph degree represent in the Laplacian construction?
   • The coordinate's squared distance from zero
   • The number of clusters supplied
   • The sum of an observation's edge weights
   • The eigenvector's class probability
7. How does an RBF kernel width affect graph affinities?
   • It changes the response variable's units
   • It sets the true number of clusters
   • It guarantees a connected graph
   • It controls how quickly similarity decreases with distance
8. Why should a disconnected graph be examined before interpreting spectral labels?
   • The normalized-cut result may not match the intended connected-cluster interpretation
   • It proves all clusters are invalid
   • Disconnected graphs cannot have eigenvectors
   • It means every point has an identical affinity