MS-DS Master of Data science Unsupervised Learning Techniques 4

Question 1

What problem does the k-means++ initialization scheme address compared to random initialization?

Accepted Answer

It reduces the chance of poor convergence to local optima by spreading initial centroids

Answer

k-means++ selects each subsequent initial centroid with probability proportional to its squared distance from the nearest existing centroid, leading to better spread and faster convergence.

Question 2

In spectral clustering, what is the graph Laplacian used for?

Accepted Answer

To embed data into a low-dimensional space where standard clustering is applied

Answer

Spectral clustering computes the eigenvectors of the graph Laplacian to embed the data into a space that reveals cluster structure, then applies k-means on this embedding.

Question 3

Which of the following is a core limitation of PCA for dimensionality reduction in the context of unsupervised learning?

Accepted Answer

PCA only captures linear relationships and misses nonlinear structure in the data

Answer

PCA finds orthogonal directions of maximum variance using linear projections, so it cannot capture curved manifolds or other nonlinear structure in high-dimensional data.

Question 4

A data scientist applies k-means to customer transaction data and observes that the algorithm assigns all points to one cluster in the first iteration. What is the most likely cause?

Accepted Answer

All initial centroids were placed in the same region of the feature space

Answer

If all centroids are initialized very close together, all points become nearest to one centroid, causing a degenerate solution; k-means++ initialization mitigates this.

Question 5

In autoencoders used for anomaly detection, what serves as the anomaly score for a data point?

Accepted Answer

The reconstruction error between input and decoder output

Answer

An autoencoder trained on normal data learns to reconstruct normal patterns well; anomalies have high reconstruction error because the model cannot encode and decode them accurately.

MS-DS Master of Data science Practice Test

MS-DS Master of Data science Practice Test

MS-DS Master of Data science Unsupervised Learning Techniques 4