Robust MCR for Problem Images FACSS 2006

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Robust Multivariate Analysisfor Problem Images

Jeremy M. ShaverEigenvector Research, Inc., Wenatchee, WA

Lei PeiGuilin Jiang

Matthew C. AsplundMatthew R. Linford

Department of Chemistry and Biochemistry,Brigham Young University, Provo, UT 84602

Robust Methods Multivariate Curve Resolution (MCR)

Quantitative/Qualitative analysis method of choice in many situations

Highly influenced by outliers!

Statistically proven robust methods exist for performing standardanalyses

Minimum Covariance Determinant Robust PCA

Trimmed Least Squares Robust MCR

Methods require several phases and can be slow for images (10k+samples per image!)

Exploring various methods for quick, qualitative and quantitativesurvey of images.

Go old school


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k-Means Clustering

Find natural clusters in data.Samples grouped by proximityto a class mean

Gives average spectrum ofeach cluster (akin to loadings).

Exceptionally fast relative toMultivariate Curve Resolution(MCR).

Can handle rank-deficientsituations.

x

x

x = cluster mean

Does NOT handle mixture data well (e.g. when image spatial

resolution is poor).

Sensitive to initial guess.

Various modifications exist in literature to temper algorithm.

MCR & Cluster have as goal tolocate Pure ComponentSpectra

Samples which are farthest outin multivariate space provideprototypical target spectra

Pure pixel as k-Means initial

guess provides method forstabilization! (Deterministic)

Pure Pixels(a.k.a. SIMPLISMA, purity)


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Pure Pixel k-Means

Clusteringk-Means clustering with pure

pixels:

1. Identify n most unusualpixels

2. Classify all other pixels bytheir closest pure pixel(projection)

3. Iterate with class mean asnew pure pixel basis

Purest pixels

TOF-SIMS of Time ReleasedDrug Delivery System

Multilayer drug beads serve as controlled-release

delivery system

TOF-SIMS taken of cross section of bead

Evaluate integrity of layers, distribution of

ingredients

Thanks again to Physical Electronics and AnnaBelu for the data!

Reference: A.M. Belu, M.C. Davies, J.M. Newton and N. Patel, TOF-SIMS Characterization andImaging of Controlled-Release Drug Delivery Systems, Anal. Chem., 72(22), pps 5625-5638, 2000


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Avicel Pure-Pixel k-MeansClustering

False-color MCR Results Pure Pixel Clusters

(3 clusters)

Satellite Image of Mississippi RiverFalse-Color ScaleBlue = Short Vis. (red)Green = NIRRed = SWIR-1

Seven-Slab Image: Red (vis), Green (vis),Blue (vis), NIR, SWIR-1, SWIR-2, Thermal

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Pure Pixel k-Means Clustering

Pure pixel clusteringwith 5 classes

identified.

Can identify different

land feature groupsfairly well

False-color image

Blue = Short Vis. (red)Green = NIRRed = SWIR-1

(region 1)

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?

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!

!

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WHAT HAPPENED?

Obvious classdifferences are missed

because classes 1 and5 are wasted on bad

pixels (in orange region)

Pure-Pixel K-Means Clustering

5-class k-means cluster

False-color image(region 2)


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Scores on PC 1 (56.06%)

ScoresonPC2(34.4

2%)

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PCA Scores (PCs 1 and 2)

Because outliers fall on theoutside edges of

multivariate space, they are

almost always selectedearly by Pure-Pixel

selection algorithm

They are not similar to

many other pixels

THEREFORE: Exclude a

pure point (and all like it) ifit classifies < specified % of

pixels then select new

pure points.

NOTE: can save these for

analysis of outliers! Mightbe what is of interest!

Robust Pure-Pixel k-Means Clustering

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5-class k-means clusterWITHsmall-class exclusion

Bad pixels are discardedfrom pure spectrumselection when classesfrom them do not capture >1% of pixels. Result isbetter classification ofvariations.

False-color image


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NMR Image of Brain

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robustpure-pixelselection

standardpure-pixelselection

Total IonImage

m/z 13Image

Laser

hydrocarbonliquid

Silicon Substrate

Laser-Activation Modification ofSemiconductor Surfaces (LAMSS)

Time ofFlight Mass

Spec


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C8 Solution C14 Solution

CombinedRaw Data

Clustering

Combined Image Data

TOF-SIMS

Non-Robust Pure-PixelClustering

4 Clusters

C8 C14

Neither the spatial distribution of the clusters, nor the recovered clustering basisspectra make sense with raw spectra recovered from the data.


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Robust Pure-Pixel Clustering

4 Clusters

C8 C14

RobustClustering of

CombinedImages

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MultipleItems

(seeLegend)

-CH

-O -OH

-F

C8 C14


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leItems(seeLegend)

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2C H 35 -Cl37 -

Cl

C8 C14Robust

Clustering ofCombined

Images

Conclusions

Pure-Pixel Robust k-Means a fast methodfor clustering (can also use results as evenbetter initial guess for MCR!)

Other robust methods on images

PLS_Toolbox and LIBRA toolbox

Documents

Robust MCR for Problem Images FACSS 2006