DSCI 599 Homework 2

1. [10 points] Describe Gaussian Mixture Model clustering. Why is it an instance of the

Expectation Maximization method? What are its advantages over the K-Means

clustering algorithm?

2. [10 points] Describe a multivariate Gaussian along with its parameters (µ and Σ).

What is the geometric interpretation of these two parameters? List some interesting

properties of the eigenvalues and eigenvectors of any covariance matrix.

3. [10 points] Describe the Principal Component Analysis algorithm for dimensionality

reduction along with the time complexity of each of its steps. How does it compare

against FastMap representation-wise, efficiency-wise, and quality-wise?

4. [10 points] What are the steps in the Perceptron Learning algorithm? What do we do

when a constraint is violated in any iteration? Should the learning rate for updating

the weights be high or low; why? What happens if we try running the Perception

Learning algorithm on data that do not have linearly separable positive and negative

labels?

5. [10 points] What is the Constraint Satisfaction Problem (CSP)? Pick a problem of

interest in Data Science which can be solved efficiently using CSP search techniques.

Describe the problem and the application of CSP techniques on it. Elaborate on one

of these techniques.

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