1

Multivariate Data Analysis (MVDA)•Any investigation of a real process or system is based on datameasurements•The data collected in science, technology and almost everywhere elseare multivariate; with multiple variables measured on multiple samplesor at multiple time points cannot be analyzed by simple graphs•More sophisticated, computer based methods such as PrincipleCompenent Analysis are required for a multivariate data set•New information and facts can be seen using MVDA•PCA is one of the most popular MVDA technique

Convert data tables to plots

2

with 104 observations, K = 34 X variables,and M = 1 Y‐variable

X3

X1

X2

X Y104 104

K=34 M=1

observations

factors response

Provides an overview of therelationships among all X‐variables and Y variables at the same time.

PLS

3

Projection methods (PCA and PLS)

X X Y

Overview andSummary

• PCA, PrincipalComponents Analysis

Relation between blocksof variables, X & Y• PLS analysis• PLS‐DA

• PCA models the correlationstructure of a data set

Partial Least Squares Projections to Latent Structures (PLS)‐Relating X to Y

Principal Component Analysis (PCA)Overview of data tables

• PLS find relationships betweensets of multivariate data X and Y

PLS differences to PCA*Projection of X that  *Projection of X thatis an optimal both

approximation of X approximates X well, (least squares fit) and correlates well with Y 

4

Case Study 2Gini (1999) used a  back propagation neural network to predict the

carcinogenicity of aromatic Nitrogen compounds.34 Descriptors 104 Molecules

Carcinogenicity

Y

Y=f(x)

Molecular Descriptors

X

QSAR

Gini. G. Et al. (1999). Predictive carcinogenicity: A model for aromatic compounds with nitrogen-containing substituents, based on moleculardescriptors using an artifical neural network. J.of Che. Inf. Com. Sci., 1076-1080

5

Variables close to each other correlateObservations close to each other are similar.