mcr-als analysis using initial estimate of concentration profile by efa
Post on 30-Dec-2015
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MCR-ALS analysis using initial estimate of concentration profile by
EFA
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Deducing Chemical Rank(Factor Analysis)
• Scree plot
• Indicator function
• Loading plot
• Eigen-value ratio
• …
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Calculating Initial estimate by EFA
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1.2
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1.2
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1.2
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Source of differences?
Rotational ambiguityPCA: D=TPBeer-Lambert: D=CSIn MCR we want to reach from PCA to Beer-Lambert
• D= TP = TRR-1P, R: rotation matrix• D = (TR)(R-1P)• C=TR, S=R-1P• (R2)(0.5R-1) = RR-1
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How can we overcome this problem?
More extra constraints:
1. Selectivity
2. Peak Shape
3. Matrix augmentation
4. Combined hard model
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Implementation of selectivity in pure spectra
• If we know the pure spectrum of the reactant
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1.2
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Implementation of selectivity in concentration profile
• At the beginning of reaction only reactant is existed and the other species are absent
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1.2
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Two other experiments
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Next step?
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Matrix augmentation
• 3 kinetic experiments
• run at three different experimental conditions
• D1
• D2
• D3
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Steps for column-wise data augmentation
• 1. calculate initial estimate of concentration for each data set
• [e1,ef1,ef2]=efa(d1);• [e2,ef2,ef2]=efa(d2);• [e3,ef3,ef3]=efa(d3);
• 2. produce a matrix of initial estimate• e=[e1;e2;e3];
• 3. collect all data matrices in a single matrix• d=[d1;d2;d3];
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Analysis of a single data matrix Analysis of augmented data matrices
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Original Values: k1=0.2 k2=0.02
Original Calculated
k1 k2 k1 k2
R1 0.20 0.02 0.22 0.017
R2 0.30 0.08 0.31 0.072
R3 0.45 0.32 0.45 0.29
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Row and column wise data augmentation
• If the experiments are also monitored by spectroflourimetric method
Da1
Da2
Da3
Df1
Df2
Df3
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