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**Examiner:** Prof. Nöth

**Atmosphere:** Friendly.

**Questions:**

K Nearest Neighbor (from exercises)

- Q: He drew a coordinate system with some points. What step is necessary before applying KNN itself?
- A: Normalize the data, e.g. to [-1, 1].
- Q: How does it work?
- Q: How did we implement it?
- Q: We learned of something that is related to KNN …
- A: Bayes Classifier.

Bayes

- Q: Formulate the Bayes rule and name all parts.
- Q: Formulate Decision Function.
- Q: Relation to KNN:
- A: Error is at most twice of Bayes (not the classifier) Error Rate (see http://cseweb.ucsd.edu/~elkan/151/nearestn.pdf for more info).
- A: Bayes Classifier with the identity covariance matrix is the same as Nearest Neighbour.
- Q: How can you calculate the class conditional pdf?
- A: Assume gaussian distribution and perform Maximum Likelihood.
- Q: What do you do if the distribution is not known?
- A: GMM.

Gaussian Mixture Models

- Q: What are the parameters?
- A: Mean, covariance matrix and relative portion of samples for every distribution.
- Q: How can you initialize the parameters?
- A: Take random samples and calculate parameters with their help.
- Q: To what can this lead?
- A: GMM may only converge to a local maximum.
- Q: What can you do then?
- A: Try other random samples and take the largest found maximum.
- Q: Is there a better way to initialize the parameters?
- A: Apply k-means clustering before and calculate parameters for every cluster. This way you'll probably almost get the correct parameters.

SVM

- Q: Formulate the optimization problem of hard margin and soft margin SVM.
- Q: What are the slack variables for?
- A: Slack variables move samples onto the border of the margin. This way they'll become support vectors.