MS-DS Master of Data science Unsupervised Learning Techniques 2

Question 1

Which linkage criterion in hierarchical clustering tends to produce the most compact, spherical clusters?

Accepted Answer

Ward's method

Answer

Ward's method minimizes the total within-cluster variance at each merge step, producing compact, roughly spherical clusters.

Question 2

In the Expectation-Maximization (EM) algorithm for Gaussian Mixture Models, what does the E-step compute?

Accepted Answer

The posterior probability (responsibility) of each component for each data point

Answer

The E-step computes the responsibility r_{nk}, the posterior probability that component k generated data point n, given current parameters.

Question 3

What is the primary role of the kernel function in kernel PCA?

Accepted Answer

To implicitly map data into a higher-dimensional feature space where linear PCA is applied

Answer

The kernel function computes inner products in a high-dimensional (possibly infinite) feature space without explicitly mapping points there, enabling nonlinear dimensionality reduction.

Question 4

Which of the following is a key assumption made by the DBSCAN algorithm?

Accepted Answer

Clusters are defined by regions of high density separated by low-density regions

Answer

DBSCAN defines clusters as dense regions (cores + reachable points) separated by sparse regions, requiring only epsilon and minPts parameters.

Question 5

In t-SNE, what does the perplexity hyperparameter control?

Accepted Answer

The balance between local and global structure by setting the effective number of neighbors

Answer

Perplexity roughly determines how many neighbors each point considers when constructing the high-dimensional probability distribution, balancing local vs. global structure.

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 2