Intro. & Maths

Question 1

What are n and p?

Answer 1

n: the number of observations or cases in the dataset.
p: the number of variables or features (parameters) in the dataset.
Together, np create the dimensions of the dataset.

Question 2

What topics are covered in the clustering section of the course?

Answer 2

Dissimilarities
Hierarchical clustering
Partitioning methods
Cluster validation

Question 3

What is supervised learning?

Answer 3

Techniques which assume a given structure within the data.

Question 4

What topics are covered in the classification section of the course?

Answer 4

Multivariate normal distributions
Linear and quadratic discriminant analysis
K-nearest neighbors

Question 5

Why do multivariate analyses not (usually) have response variables?

Answer 5

Many variables are recorded, information is then gleaned from the dataset. One specific feature is not usually being measured.

Question 6

What topics are covered in the multidimensional scaling section of the course?

Answer 6

Classical MDS
Metric MDS
Non-metric MDS
Procrustes analysis

Question 7

What are the main topics in the course?

Answer 7

Clustering
Classification
Multidimensional scaling
Model-based clustering
PCA and FA

Question 8

What topics are covered in the model-based clustering section of the course?

Answer 8

Mixture models

Decomposition of covariance matrices

Question 9

What is PCA?

Answer 9

Principle components analysis is where many variables are subgrouped to reduce the amount of autocorrelation in the dataset (implying non-independance).

Question 10

What is FA?

Answer 10

Factor analysis is similar to PCA in that it aims to reduce the number of meaningful features in the dataset. FA usually assumes an equal number of factors to features - but many are discarded because they add no new detail to the analysis.

Question 11

What topics are covered in Principle Components Analysis?

Answer 11

Issues
Interpretation
Mechanics
Solution Validity

Question 12

What topics are covered by factor analysis?

Answer 12

Rotations
Interpretation
Factor Models
PCA Vs FA

Question 13

Column vectors are used…

Answer 13

For individual observations, xi

Question 14

The i-th row of a marix X is also known as…

Answer 14

xi transpose (it’s a single observation)

Question 15

Define variance

Answer 15

The square of the standard deviation

Question 16

Define standard deviation

Answer 16

The sum of the squared differences, divided by N.

Question 17

How is covariance calculated?

Answer 17

Expectation of the product of two variables, minus the product of each expectation.

Question 18

How is correlation calculated?

Answer 18

Covariance of variables divided by the square root of the product of the variances.

Question 19

What is along the diagonal of a covariance matrix?

Answer 19

The variance of each variable.

Question 20

Is the covariance matrix symetric?

Answer 20

Yes.

Question 21

What is along the diagonal of the correlation matrix?

Answer 21

1s.

Question 22

How is the correlation matrix calculated quickly from the sample covariance matrix?

Answer 22

R=(D^-1/2)S(D^-1/2)

Question 23

E[aTx] = …

Answer 23

aTu

Question 24

Var[aTx] = …

Answer 24

aT SIGMA a

Question 25

Cov(U, V) = …

Answer 25

aT SIGMA b

Question 26

What is the notation for the covariance matrix?

Answer 26

SIGMA!

Question 27

What are the three basic dissimmilarity properties?

Answer 27

d(x,y) >= 0,
d(x,y) = d(y,x)
d(x,y) >= d(z,x) + d(y,z)