principal+componentanalysis+ par$al+leastsquare++...

Mul$variate Data Analysis

•  Data characteris$cs •  Data analysis types •  Methods

–  Principal component analysis –  Par$al least square –  PLS-‐DA/SIMCA

Covariance

Correla$on

Data Characteris$cs

Data Analysis Purpose

•  Summary •  Regression •  Classifica$on

Issues with engineering data

What is a latent variable?

•  Visualizing mul$variate data •  Geometric interpreta$on of PCA •  Mathema$cal interpreta$on •  Example(s)

Principal Component Analysis

Principal Component Analysis

Visualizing Mul$variate Data

Geometric Interpreta$on

Mathema$cal Deriva$on

Predicted value for each observa$ons

More about direc$on vector

Preprocessing

Square Predic$on Error

Square Predic,on Error

Column Residual

Whole Matrix Residual

Example

Hotelling’s T2

Preprocessing Data

How is PCA calculated?

How many components?

Principal Component Regression

Higher Dimension Data

Improved Process Understanding

Troubleshoo$ng Process Problem

Process Monitoring

•  Reference: Eigenvector

Projec$on to Latent Structure (PLS)

How is PLS model determined

•  Reference: Eigenvector

NIPALS algorithm

Projec$on to Latent Structure (PLS)

PLS: Geometric Interpreta$on

Interpre$ng scores in PLS

Defla$on

PLS: R2 Values

Classifica$on

Supervised vs. Unsupervised

Unsupervised Classifica$on: PCA

Supervised Classifica$on: SIMCA SoX Independent Modeling of Class Analogy

Supervised Classifica$on: PLS-‐DA

Tutorial with Raw material NIR data

Raw Material, NIR Spectra

PCA Modeling with Raw Data

PCA Modeling with 1st Deriva$ve

PCA with Cell Growth Data

PLS-‐DA (Score Plot)

Scores on LV1 (71.66%)

-0.010 -0.005 0.000 0.005 0.010

Sco

res

on L

V2

(9.8

1%)

-0.004

-0.002

0.000

0.002

0.004

8H0284B

8E0258

6L0359

9C0230

8E0330

8K0237

8K0067

8E0574

1038147910462698

M031114

1320005528

8008

10033

KA7HN3007

KA9CN6012

DMV

Kerry Milipore

Organo

PLS-‐DA (Loading Plot)

wavenumber (cm-1)

40005000600070008000900010000

Load

ing

for L

V1

-0.20

-0.15

-0.10

-0.05

0.00

0.05

0.10

wavenumber (cm-1)

40005000600070008000900010000Lo

adin

g fo

r LV2

-0.20

-0.15

-0.10

-0.05

0.00

0.05

0.10

0.15

0.20(a) (b)

PLS with Cell Growth Data

•  Figure 11. True vs. es$mated values by each PLS model for (a) IVCD of K1 (b) IgG of K1 (c) IVCD of GS (d) IgG of GS (e) IVCD of EB66

PLS Predic$on

true value

0.0 0.4 0.8 1.2 1.6 2.0

estim

ated

val

ue

0.0

0.4

0.8

1.2

1.6

2.0

Calibrationcross-validation

true value

0.8 1.2 1.6 2.0 2.4

estim

ated

val

ue

0.8

1.2

1.6

2.0

2.4


true value

0.4 0.8 1.2 1.6

estim

ated

val

ue0.4

0.8

1.2

1.6


true value

0.4 0.8 1.2 1.6

estim

ated

val

ue

0.4

0.8

1.2

1.6


true value

0.0 0.5 1.0 1.5

estim

ated

val

ue

0.0

0.5

1.0

1.5


(a) (b)

(c) (d)

(e)

PLS and PLS-‐DA •  What are good applica$ons of PLS? •  What are good applica$ons of PLS-‐DA? •  Disadvantages?

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