My advice is to check covariance matrix, specially if you have a huge number of variables, probably you have a quasi-singular matrix, thus you could use sparse covariance estimation as Ledoit-Wolf method.

Another advice is to use a stable PCA algorithm.

But someone more expert than me could enrich the discussion.

I am not sure that you should be using PCA. If ECG data is a sample of regular pulse then perhaps you should be processing it to find the frequencies that make up that pulse (fourier transform) , The PCA may find orthogonal basis vectors (which are also likely to be related to the frequencies ) but you would need to relate that to a sampling rate (depending of what data you feed in). Classification in terms of frequencies present is the obvious. But you may need to decide on what characteristics you are looking for if its not frequency

Dear Qazvin,

As far as I can see your code is OK for computing PCA. It seems like your problem suffers from overtraining. When you use featureVector=max(PC), you select values for all principle components, even the very noisy ones. In general only the first N components are taken to make sure that the noisy components are left out. N is often determined as the number of components with the largest variance that are needed to cover 90% or 95% of the variance.

In this way you reduce the number of features drastically and do not suffer from overtraining anymore. Another solution could be to use different components, such as from Independent Component Analysis. They have shows good results for these kind of problems in the past.

Best regards,

Martijn

Which is your sampling rate ? That is crucial in order to take into consideration, in any case it is important to know what you are interested in, if for example you are only interested in RR intervals, PCA on the emebedding matrix of the RR series allows you for a drastic reduction of dimensionality and to discrimnate very well fractal and periodic component of the signals (I have some publications posted in research gate on this issue). On the contrary if you want to study the 'basic morphological elements' of the QRS complex the best way is to work in a way similar to metabolomics research on NMR or GC spectra: each specific QRS sample is a statistical unit of your raw data matrix and the original variables correspond to RESCALED reference points along each QRS (something like subdividing the spectrum into 200 equispaced bins and considering these bins as variables whose value is the corresponding rescaled height of the signal). In this way you loose the entire dynamics but you focus on ECG morphology, on the contrary , if you are interested in the dynamics over the long signal it is much better to use RR...but agin is apt to you, it dpends on what you are interested into.

If data is the raw ECG, you are too optimist when you are expecting good results without any other previous processing.

I suppose there is a mistake in understanding.

PCA is suitable for discrete data sets. while ECG in itself is a wave function and not a set of discrete data. If you want to convert a continuos wave function of ECG to a rendered discrete data set, PCA is not the right choice. Hope following links help you.

http://www.aueb.gr/users/mgia/cvforWEB/D3.pdf

http://www.hcs.harvard.edu/~weber/HomePage/Papers/ECGCompression/

however PCA can reduce the number of ECGs you want to process, what it usually does, working on datasets.

just let me know if i understood the problem right.

You can render anything discrete by sampling it with a sufficiently strict grid. Look at example how you can work it out with nMR spectra:

http://www.sciencedirect.com/science/article/pii/S1359644605036093

the same binning strategy can in principle be applied to any continuous signal..

PCA is for multivariate data analysis. How many channels have you considered ? or how are you considering single lead ECG data to create multivariate data matrix ? Picking up the eigen values (so, eigen vector) for processing matter .

I suggest you can go for multiscale PCA analysis.

This may be helpful to you:

http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=6187729

I would go with ICA. It seems to be better than PCA when dealing with ECG. I would also suggest FA.

Dear friends, thank you all for your helpful answers.

I think that i should tell some details of my problem. I use MIT-BIH arrhythmia dataset that has sampling frequency of 360 Hz. (but i don't know that how the frequency rate can be related to PCA?) I segmented each signal into one beat length and then i applied WT to each beat to get it's feature vector. each feature vector has variable dimensions between 6*600 to 6*800 . I reduced each beats dimension using some dimension reduction methods other than PCA and i achieved the classifications accuracy over 99%. now i wanna try the PCA algorithm. there are some publications (such as http://onlinelibrary.wiley.com/doi/10.1111/j.1468-0394.2011.00606.x/abstract) that claimed that by using PCA they get over 99% classification accuracy.

why i get such a poor result? is there any mistakes in my code? how can i improve the results?

Thanks

I've been looking at people who have had successful ECG arrhythmia beat classification. More than a few are using SVM (and there ~is~ matlab support): http://ecs.utdallas.edu/research/researchlabs/QoLT/files/pdfs/lissa11_st.pdf

Look at page 124 left column where they describe their classification and results

When using PCA, it is considered that data have a gaussian distribution, which is not always correct. I recommend you use a combination of wavelet decomposition and neural networks for ECG classification. Try to make a stronger analysis of the type of component frecuencies and other properties that can help in the classification process.

if you are familiar with linear algebra, try to deal you data with the method described in this presentation

https://www.researchgate.net/publication/235624054_projection

this is the paper with the alghoritms and the code :

https://www.researchgate.net/publication/235623992_Three-Dimensional_Representation_of_Geochemical_Data_from_a_Multidimensional_Compositional_Space?ev=prf_pub

Data projection

Article Three-Dimensional Representation of Geochemical Data from a ...

Hi Akbar

How about implementation PCA in matlab? You can perform PCA easily and get the coefficient matrix. Before performing PCA try a normalization method like Z-Score or Min-Max normalization.

Dear Sajjad

Thank you for your help.

I tried the min-max normalization on my data, but it decreased the classification accuracy from 47% to 32% !!! my PCA code is shown above, what do you think about it? is it correct?

I've used the code below. Try it. Might be beneficial:

data=Your data; % for example: xlsread('path of .xlsx data');

mn=mean(data);

sdx=std(data);

for i=1:SIZE OF YOUR DATA

dataNormal(i,:)=(data(i,:)-mn)./(sdx+(sdx==0));

end;

[COEFF,SCORE,latent,tsquare] = princomp(dataNormal);

coeff=COEFF(:,1:THE PROPER NUMBER OF DIMENSIONS );

newdata=dataNormal * coeff;

May be following implementation will be beneficial:

feature=data; % data is n X f dimension with n as samples and f is number of % %features

% substracting mean from data

for c=1:size(feature,1)

feature(c,:)=feature(c,:)-mean(feature);

end

DataCov=cov(feature); % covariance matrix

[PC,~,explained] = pcacov(DataCov);

[~, ie]=max(explained);

[~, ipc]=max( PC(:,ie));

[temp,IX] = sort( PC(:,ie),'descend' );

% let 4 features is to be extracted from f features

no_of_features=4;

feature_New=data(:,IX(1:no_of_features)); % it will extract those features which gives maximum variance explained by first principal component.

Also see: http://stackoverflow.com/questions/13309387/selection-of-features-using-pca where the implementation in MATLAB is explained

Dear friends,

Thank you all for your helps.

but, Which part of PCA outputs should be consider as feature vector to feed into a classifier (for ex. NN)?suppose that i have a 10*150 data and i reduced it's dimensions to 10*7, here i have Coefficient, Scores, Latent and NewData (by Sajjad's code) , now which of them should i feed into NN and how?

i use featureVector=var(NewData), is it true?

Thanks

If your purpose is to do the classification, better go for LDA which preserves both inter and intra class variations.

You should use component scores or, equally NewDta (that I suppose are again scores), and clearly you could apply on them LDA

The Feature_New matrix in the code I have provided is the subset of original feature set or you can say is dominant features from whole original feature set . I have also used PCA in one of my project where I have used Feature_New (whose dimension is n X fs , where fs is reduced subset and fs

Yes it is true. But it is worth noting that by choosing 7 dimension how much variance will be produced. The Latent is sorted descending. use the code below:

s=0;

l=0;

for i=1:150 % 150 is entire dimension

s=s+latent(i);

end

for i=1:7 % You've chosen 7 dimension

l=l+latent(i);

end

l/s

Usually l/s should be over 90 present.

Maybe your could use svd function in matlab to perform PCA. This will largely reduce your program.

PCA is a non-supervised method. it may be insufficient to classify your data. you can select a supervised classification method such as LDA, SVM, Random Forset, Boosting, Decision tree etc.

Before performing prediction, maybe your need to select some useful or informative variables.

In my opinion, Random Forest is a good machine learning algorithm. You can try to use it!

sparse PCA is also a suitable choice for your problem.

What classifier are you using to perform the classification?  PCA is not designed to perform classification, really for exploratory data analysis.  How much data are you training on and what is the size of your data set?

Hello. As noted, your method should use singular value decomposition (SVD) and not an eigenvalue routine. The latter is very ill conditioned. SVD works regardless of the matrix you need to decompose.

What about this approach? Address: https://www.researchgate.net/publication/319469038_New_Interpretation_of_Principal_Components_Analysis

Article New Interpretation of Principal Components Analysis

Here is a very good source of PCA including presentation and source code Presentation Principal Component Analysis (PCA) : An Overview Article Principal component analysis - a tutorial Alaa