18 may. 2019

set.seed function in R and also in Win ISI

It is common to see how at the beginning of some code the "set.feed" function is fixed to a number. The idea of this is to get reproducible results when working with functions which require random sample generation. This is the case for example in Artificial Neural Networks models where the weights are selected randomly at the beginning and after that are changing during the learning process.

Let´s see what happens if set.seed() is not used:
library(nnet)
data(airquality)

model=nnet( Ozone~Wind, airquality  size=4, linout=TRUE )

The results for the weights are:

# weights:  13
initial  value 340386.755571
iter  10 value 125143.482617
iter  20 value 114677.827890
iter  30 value 64060.355881
iter  40 value 61662.633170
final  value 61662.630819
converged

 
If we repeat again the same process:

model=nnet( Ozone~Wind, airquality  size=4, linout=TRUE )

The results for the weights are different:

# weights:  13
initial  value 326114.338213
iter  10 value 125356.496387
iter  20 value 68060.365524
iter  30 value 61671.200838
final  value 61662.628120
converged
 

 
But if we fit the seed to a certain value (whichever you like) .

set.seed(1)
model=nnet( Ozone~Wind, airquality  size=4, linout=TRUE )

 # weights:  13
initial  value 336050.392093
iter  10 value 67199.164471
iter  20 value 61402.103611
iter  30 value 61357.192666
iter  40 value 61356.342240
final  value 61356.324337
converged

 
and repeat the code with the same seed:

set.seed(1)
model=nnet( Ozone~Wind, airquality  size=4, linout=TRUE )

we obtain the same results:

# weights:  13
initial  value 336050.392093
iter  10 value 67199.164471
iter  20 value 61402.103611
iter  30 value 61357.192666
iter  40 value 61356.342240
final  value 61356.324337
converged


SET.SEED es used in Chemometric Programs as Win ISI to select samples randomly:

2 may. 2019

Using "tecator" data with Caret (part 4)

I add one more type of regression to the "tecator meat data" in this case is the "Ridge Regression".
Ridge Regression use all the predictors, but penalizes their values in order they can not get high values.

We can see that it not get such as best fitting as the PCR or PLS in the case of spectroscopy data, but it is quite common to use it in other data for Machine Learning Application. Ridge Regression is a type of Regularization where we have two types L1 and L2.

In the plot you can see also the RMSE for the validation set:

Of course PLS works better, but we must try other models and see how the affect to the values.

30 abr. 2019

What are the benefits of adding more data to the models?

One of the frequent questions before developing a calibration is: How many samples are necessary to develop a calibration?. The quick answer is: ¡as much as possible!. Of course is obvious that they should content variability and represent as much as possible the new data can appear in the future.
 
The main sources of error are the "Irreducible error" (error from the noise of the instrument itself), the unexplained error (variance) and the Bias and they follow some rules, depending of the number of samples we have. Another thing to take into account is the complexity of the model (the number of coefficients, parameters, or terms we add to the regression).
 
Let´s look to this plot:
Now, if we add more samples tis lines are keep them as dash lines and the Bias, Variance and Total Error improves but the complexity (vertical black line) increase, and this is normal.

 
 
 

25 abr. 2019

Using "tecator" data with Caret (part 3)

This is the third part of the series "Using Tecator data with Caret" , you can read first the posts:
 
 
When developing the regression for protein, Caret select the best option for the number of terms to use in the regression, so in this case that I have developed two regressions (PCR and PLS), Caret select 11 terms for the PLS regression and 14 for the PCR.
 
This  is normal because in the case of PLS all the terms are selected taking in account how the scores (projections over the terms) correlate with the  reference values for  the parameter of interest, so they rotate to increase as much as possible the correlation value of the scores to the reference values. In the case of PCR the terms explain the variability in the spectra matrix and after a multiple linear regression is developed with these scores and is in this moment when the reference values are take it into account.
 
In this plot I show the XY plot of reference values of predictions vs. reference values for PCR and PLS over-plotted, with a validation set (sample removed randomly for testing the regression)
 
 
The error are similar for both:
 
RMSEP  for PCR..................0,654
RMSEP  for PLS...................0,605
 
 

23 abr. 2019

Using "tecator" data with Caret (part 2)

I continue with the exercise of Tecator data from the :
Chapter 6 | Linear Regression and Its Cousins
in the book Applied Predictive Modelling.

In this exercise we have to develop different types of regression and to decide which performs better.
I use for the exercise math treatments to remove the scatter, in particular the SNV + DT with the package "prospectr".

After I use the "train" function from caret to develop two regressions (one with PCR and the other with PLS) for the protein constituent.

Now the best way to decide is a plot showing the RMSE for the different number of components or terms:




Which one do you thinks performs better?.
How many terms would you choose?

I will compare this types of regressions with others in coming posts for this tecator data.

18 abr. 2019

Using "tecator" data with Caret (part 1)


In the Caret package, we have a data set called “tecator” with data from an Infratec for meat. In the book “Applied Predictive Modelling”, is used as an exercise in the Chapter : “Linear Regression and its Cousins”, so I´m going to use it  in this and some coming posts.
When we develop a PLS equation with the function “plsr” in the “pls” package we get several values, and one of them is “validation”, where we get a list with the predictions for the number of terms selected for the samples in the training set. With these values, several calculations will define the best model, so we does not overfit it.
Anyway, to keep apart a random set for validation will help us to adopt the best decision for the selection of terms. For this, we can use the “createDataPartition” from the Caret package. The “predict” using the developed model and the external validation set will give us the predictions for the external validation set and comparing this values with the reference values we will obtain the  RMSE (using the RMSE) function, so we can decide the number of terms to use for the model we use finally in routine.
We normally prefer plots to see performance of a model, but the statistics (numbers) will really decide how the performance is.
In the case I use 5 terms (seems to be the best option), the predictions for the training set are:
train.dt.5pred<-plsFitdt.moi$validation$pred[,,5]
In addition, the predictions for the external validation set are:
test.dt.pred<-predict(plsFitdt.moi,ncomp=5,
                      newdata = test.dt$NIR.dt)
With these values we can plot the performance of the model:
plot(test.dt.pred,test.dt$Moisture,col="green",
     xlim=range.moi,ylim=range.moi,
     ylab="Reference",xlab="Predicted")
 
par(new=TRUE)
 
plot(train.dt.5pred,tec.data.dt$Moisture,col="blue",
     xlim=range.moi,ylim=range.moi,
     xlab="",ylab="")
 
abline(0,1,col="red")

Due to the high range of this parameters we can see plots as this, where we can see area ranges with bias, others with more random noise, or others with outliers.

7 abr. 2019

Reconstruction: Residual vs Dextrose

I tried to explain in several posts how the Residual Matrix that remains after apply a Principal Components Algorithm can show us the residual spectra so we can see what else is in an unknown sample analyzed in routine which can not be explained by the Principal Components model.

In this plot I show the residual for three samples which has an ingredient which was not in the model that we build with samples of different batches of a certain formula.

We can correlate the residual spectra with a database of ingredients to have an idea of what could be the ingredient more similar to that residual.

I compare the residual with the spectra of dextrose (in black), and the correlation is 0,6, so it can be a clue that dextrose can be in the unknown sample analyzed.


31 mar. 2019

Combinando SNV y Segunda Derivada

The video shows the differences between a raw spectra of lactose (where we can se high differences due to the particle size). After applying SNV those differences almost disappear.
 
If we combine SNV and Second Derivative, we increase the resolution but the effect of the particle size is also take it out due to the SNV part, but we see an improvement in the resolution.
 
In case we only apply the Second Derivative we increase the resolution and keep the particle size effect.
 
All these combinations help to find the best option for a quantitative or qualitative model.

29 mar. 2019

DC2 maximun distance Win ISI algorithm (using R)

DC2 maximum distance algorithm is one of the Identification methods where the mean and standard deviation spectra of the training set spectra are calculated.

The unknown spectra is centered with the mean training spectra and after are divided by the standard deviation spectra, so we get a spectra matrix of the distances.
We can see some high distances for the samples with high difference respect to the mean (samples 1,2 and 3)

After we only have to calculate the maximum value (distance) of this matrix for every row (spectrum)

We can determine a cutoff of 3 by default, but it can be different if needed

25 mar. 2019

Reconstruction and RMS

Still working trying to get a protocol with R in a Notebook to detect adulteration or bad manufactured batches of a mixture.

It is important in the reconstruction the selection of the number of principal components. We get two matrices: T and P to reconstruct all the samples in the training set, so if we subtract from the real spectrum the reconstruction we get the residual spectrum.

These residual spectra may have information so we need to continue adding Principal Component terms until no information seems to be on them.
With new spectra batches we can project them on the PC space using the P matrix and get also their reconstructed spectra, and their residual spectra hoping to find patterns in the residual spectra which justify if they are bad batches.

This is the case of some of this batches shown in red over the blue residuals from the training data:

One way to measure the noise and to decide if the samples in red are bad batches respect the training samples is the statistic RMS. I overplot the RMS in blue for the training samples and in red for the test (in theory bad samples). The plot show that some of the test samples have higher RMS values than the training set.
A cutoff value can be fit in order to determine this in routine.



21 mar. 2019

Overploting residual spectra of Training and Test sets (Good Product)

After we have develop a Prediction Model with a certain number of Principal Components, there is always a residual matrix spectra with the noise not explained by the Model. Of course we can add or reduce the number of PCs, but we can overfit or underfit the model increasing the noise in the model or leaving interested variance in the Residual Matrix.
 
This residual matrix is normally called "E".
 
Is interesting to look to this matrix, but specially for detection of adulterants, mistakes in the proportions of a mixture or any other difference between the validation samples (in this case in theory bad samples) and the training matrix residuals.
 
In this case I overplot both for a model with 5 PCs (in red the validation samples residual spectra and in blue the training residual spectra).


We can see interesting patterns that we must study with more detail to answer some questions, about if the model is underfitted, if we see patterns enough to determine if the validation samples have adulterations or changes in the concentrations of the mixture ingredients and so on, or if there are for some reasons in the model samples that should have been considered as outliers and be taken out of the model.


20 mar. 2019

Projecting bad batches over training PC space

Dear readers, along this night this blog will reach the 300.000 visits and I am happy about that. So thanks to all of you for visiting this blog.
 
Along the last posts I am writing about the idea to get a set of samples from several batches of a product which is a mixture of other products in a certain percentage. Of course the idea is to get an homogeneous product with the correct proportions of every product which takes part of the mixture.
 
Anyway there is variability in the ingredients of the mixture itself (different batches, seasons, origins, handling,..), and there are also uncertainty in the measuring of the quantities. It can be much worse if by mistake an ingredient is not added to the mixture or is confused by other.
 
So, to get a set with all the variability that can be allowed is important to determine if a product is correctly mixed or manufacturer.
 
In this plot I see a variability which I considered correct in a "Principal Component Space"
Over this PC Space we project other batches and we check if the projections falls into the limits set during the development of the PC Model. Of course it can appear new variability that we have to add to the model in a future update.
 
But to check it the model performs fine we have to test it with bad building batches, and this is the case in the next plot where we can see clear batches that are out of the limits (specially samples 1,2 and 3) with much more water than the samples in the training model.
 
We have to see the other samples much more in detail and to detect if the are wrong and the reason why.
So coming post about this matter soon.

12 mar. 2019

Over-plotting validation and training data in the Mahalanobis ellipses

One of the great things of R is that we can get the code of the different functions (in this case the function "drawMahal" from the package "Chemometrics" ) and adapt this code to our necessities.
 
I wanted to over-plot the training set scores for the first and second principal components with the scores of the validation set, which are redundant samples taken apart in a selection process with the function "puchwain" from the package "prospectr", but I get problems with the scale due to the way "drawMahal" fix the X and Y limits. But editing the function we can create a personalize function for our case and to compare the redundant samples in red with the training samples in black.
 
Now the next is to over-plot the test samples (in theory bad samples) in another color in a coming post.
 

24 feb. 2019

Scatter Correction Spectra plots with R

These are the spectra of an Infratec 1241 for Soy meal treated with "Multiple Scatter Correction", "Standard Normal Variate" and "Standard Normal Variate  + Detrend", apart from the "Raw Spectra".

All this math treatments are in the new Video Series (in spanish) from the posts last weeks.


In next post we see the effect of derivatives in the spectra, and we continue with Principal Components and Regressions Methods.

27 ene. 2019

An aplication of ANN in Near Infrared (Protein in wheat with Infratec)

This paper shows how the ANN algorithms can be applied to NIR technology:

Artificial Neural Networks and Near Infrared Spectroscopy - A case study on protein content in whole wheat grain

The authors explain why the IFT calibrations are so robust for wheat. This is a case where more than 40000 samples are used with all the variability we can imagine for this type of product.

You can see the videos:

How Deep Neural Networks work?
What do Neural Networks learn?

for a better understanding of how ANN works.

How Deep Neural Networks Work


This is another video from Brandon Rohrer. I add another one two posts ago called "What do Neural Networks learn?  ". I add to these posts the tag "Artificial Neural Networks" to come back to see them whenever needed.

ANN are becoming quite popular and there is more a more interest to see how they work and how to apply them to the NIR spectra.
Meanwhile we try to understand as much as possible what can be considered as a black box. Thanks to Bandon for these great tutorial videos.

23 ene. 2019

Box plot spectra

I have been working this day quite a lot with the concept of good product, and the spectrum with boxplots is a niece example to detect samples which can be contaminated or not to be good product.
 
Always in the case that the good product could be the average spectrum of N samples considered or tested that are good, we can define with all the good samples a boxplot spectra, and over-plot over it new samples and see if they are out of the limits at certain wavelengths, so this can be a clue for a contamination, a confusion in the mixture with the percentages or the components of the mixture.
 
 

18 ene. 2019

Using RMS statistic in discriminant analysis (.dc4)

In the case we want to check if a certain spectrum belongs to a certain product we can create an algorithm with PCA in such a way that this algorithm try to reconstruct the unknown spectrum with the scores of this unknown spectrum on the PCA space of the product, and the loadings of the product. So we have the reconstructed spectrum of the unknown and the original spectrum of the unknown.
 
If we subtract one from the another we get the Residual spectrum which is really informative. We can calculate the RMS value of this spectrum to see if the unknown spectrum is really well reconstructed so the RMS values is small (RMS is used as statistic to check the noise in the diagnostics of the instrument).
 
Find the right cutoff to check if the sample is well reconstructed depends of the type of sample and sample presentation.
 
Win ISI multiply the RMS by 1000, so the default value for this cutoff which is 100 in reality is 0.1, anyway a smaller or higher value can be used depending of the application.
 
This type of discrimination is known as RMS-X residual in Win ISI 4 and create ".dc4" models.
 
We see in next posts other ways to use this RMS residual.

11 ene. 2019

Correcting skewness with Box-Cox

We can use with Caret the function BoxCoxTrans to correct the skewness. With this function we get the lambda value to apply to the Box-Cox formula, and get the correction. In the case of lambda = 0 the Box-Cox transformation is equal to log(x), if lambda = 1 there are not skewness so not transformation is needed, if equals 2 the square transformation is needed and several math functions can be applied depending of the lambda value.

In the case of the previous post (correcting skewness with logs)if we use the Caret function "BoxCoxTrans", we get this result:

> VarIntenCh3_Trans
Box-Cox Transformation

1009 data points used to estimate Lambda
Input data summary:
  Min.  1st Qu.   Median     Mean  3rd Qu.     Max.
0.8693  37.0600  68.1300 101.7000 125.0000 757.0000

Largest/Smallest: 871
Sample Skewness: 2.39

Estimated Lambda: 0.1
With fudge factor, Lambda = 0 will be used for transformations


So, if we apply this transformation, we will get the same skewness value and histogram than when applying logs.



9 ene. 2019

Correcting the skewness with logs

It is recommended to look to the histograms to check if the distributions of the predictors, variables or constituents are skewed in some way. I use in this case a predictor of the segmentation original data from the library "Applied Predictive Modeling". where we can find many predictor to check if the cell are well or poor segmented.
If you want to check the paper for this work you can see this link:
 
One of the predictors for this work is VarIntenChn3, and we can check the histogram:
hist(segData$VarIntenCh3)
skewness(segData$VarIntenCh3)
              [1] 2.391624
As we can see the histogram is skewed to the right, so we can apply a transformation to the data to remove the skewness. There are several transformations, and this time we check applying Logs.
 
VarIntenCh3_log<-log(segData$VarIntenCh3)
hist(VarIntenCh3_log)
skewness(VarIntenCh3_log)    
               [1] -0.4037864
 
As we can see the histogram looks more to a Normal distribution, but a little bit skewed to the left.
 



6 ene. 2019

Correlation Plots (Segmentation Data)

First I would like to wish to the readers of this blog all the best along this 2019.
 
Recently it has been my birthday and I receive as present the book "Applied Predictive Modelling" wrote by Max Kuhn and Kjell Johnson. It is really a great book for those who like R for predictive modelling and to get more knowledge about the Multivariate Analysis. Sure a lot of post will come inspired by this book along this year.
 
I remember when I started with R in this blog I post plots of the correlation matrix to show how the wavelengths in a near infrared spectrum are correlated and why for that reason we have to use techniques like PCA to create uncorrelated predictors.
 
In R there is a package called like the book "Applied Predictive Modelling", where we can find the "Cell Segmentation Data", which Max Kuhn use quite often on his webinars (you can find them available in YouTube).
 
These Cell Segmentation Data has 61 predictors, and we want to see the correlation between them, so with some code we isolate the training data and use only the numeric values of the predictors to calculate the correlation matrix:

library(caret)
library(AppliedPredictiveModeling)

library(corrplot)
data(segmentationData)   # Load the segmentation data set
trainIndex <- createDataPartition(segmentationData$Case,p=.5,list=FALSE)
trainData <- segmentationData[trainIndex,]
testData  <- segmentationData[-trainIndex,]
trainX <-trainData[,4:61]        # only numeric values

M<-cor(trainX)
corrplot(M,tl.cex = 0.3)


This way we get a nice correlation plot:


 This plot is easier to check than the whole correlation matrix in numbers.

Now we can isolate areas of this matrix, like the one which shows higher correlation between the variables:

corrplot(M[14:20,14:20],tl.cex = 0.8