Canonical Correlation Analysis The objective of CCA is to identify and measure the association between two sets of random variables using a specific matrix function of the variance-covariance matrix of these variables.
1 11 X1 X = ~ N , X 2 2 21
12 22
Principal Component Analysis: Linear reduction technique.
Example (Johnson and Wichern):
Weekly return of five stocks (Allied Chemical, du Pont, Union Carbide, Exxon, Texaco). Let x1 , x 2 ,.x5 denote observed weekly rates. x ' = [.0054 .0048 .0057 .0063
Vector Space A vector consisting of m elements may be regarded geometrically as a point in mdimensional space.
A vector consisting of p elements can also be regarded geometrically as a line from the origin to a point in p-dimensional space.
Length of a ve
Factor Analysis
The factor analysis model assumes that there is a smaller set of uncorrelated variables (underlying factors or underlying characteristics) that will give a better understanding of the data being analyzed. Objectives: 1) To determine whethe
Discriminant Analysis Discrimination and classification are multivariate techniques concerned with separating distinct sets of observations (objects) and with allocating new observations (objects) to previously defined groups. Goal of discrimination is to
Inferences about a mean vector Readings from Johnson 10.2 The Central Limit Theorem: Let ( x1 , x2 ,.xN ) be independent observations for a population with mean and variance covariance Then:
N ( ) is approximately N p (0, ) and
2 N ( ) 1 ( ) is approxima
Cluster Analysis Cluster analysis attempts to address a very different problem from a different point of view when compared with discriminant analysis. Given a set of observations we want to form smaller subgroups of similar observations, so that in each