SQQS5053:Applied Multivariate Data Analysis Assignment, UUM, Malaysia Show that the following matrix A is an orthogonal matrix Then, compute its eigenvalues and eigenvectors.

1.  PCA is a technique for? (note: you can select multiple answers)

variance normalization.

dimensionality reduction.

feature extraction.

data augmentation.

2.  When performing PCA we want to

find orthogonal vectors.

estimate the number of dimensions.

find the components of the dataset.

find the most meaningful basis.

3. The most popularly used dimensionality reduction algorithm is Principal Component Analysis (PCA). Which of the following is/are true about PCA?

i PCA is an unsupervised method.

ii It searches for the directions that data have the largest variance.

III. Maximum number of principal components <= number of features.

iv. All principal components are orthogonal to each other.

I and II

I and III

II and III

I, II and III

I, II III and IV

4. What will happen when eigenvalues are roughly equal?

PCA will perform outstandingly.

PCA will perform badly.

Can’t say.

5. Show that the following matrix A is an orthogonal matrix. Then, compute its eigenvalues and eigenvectors.

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