L3_LDA

Question 1

Solution for Correlated Data

Answer 1

(Fisher’s) Linear Discriminant Analysis LDA

Question 2

What measures the Correlation?

Answer 2

the linear relationship between X and Y
1,0 monotonic increasing
-1,0 monotonic decreasing
0,0

Question 3

Goal of Linear Discriminant Analysis - View classification in terms of dimensionality reduction

Answer 3

Find a (normal vector of a linear decision boundary) w that showing the greatly improved class separation by Maximizes mean class difference, and
Minimizes variance in each class

Question 4

LDA is the optimal classifer

Answer 4

If data is Gaussian with equal class covariances

Question 5

The goal of classification is

Answer 5

generalization: Correct categorization/prediction of new data

Question 6

How can we estimate generalization performance?

Answer 6

Cross-validation

Question 7

Characteristic of Cross-validation:

Answer 7

• Train model on part of data
• Test model on other part of data
• Repeat on different cross-validation folds
• Average performance on test set across all folds

Question 8

Algorithm 1: Cross-Validation (6)

Answer 8

Require: Data (x1,y1)...,(xN,yN), Number of CV
        folds F
1.# Split data in F disjunct 
2. folds for folds f = 1,...,F do
3.# Train model on folds {1,...,F} \ f
4.# Compute prediction error on fold f 
5.end for
6.# Average prediction error

Question 9

BCI Based on Event-Related Potentials (ERPs)

Answer 9

• User concentrates on a symbol
• Rows and columns are intensified
randomly
• Target rows and columns elicit specific ERPs
• BCI detects target ERPs (averaged over few repetitions)

Question 10

Linear Discriminant Algorithm (4)

Answer 10

Computes: Normal vector w of decision hyperplane, threshold (der Entscheidungs-Hyperebene, Schwelle) β
1. Compute class mean vectors
2. Compute within-class covariance matrices SW
Compute normal vector w
3. Compute normal vector w
4. Compute threshold