For arrhythmia detection purpose, I extract some features from ECG signal. Each feature vector (for each beat) has 1*200 size. I used PCA (principle component analysis) to reduce its dimension to 1*20, but the PCs have been set to zero. why?
Should I gather all the feature vectors in a array and then apply the PCA to it?
Yes you should. You won't get anything reasonable from applying PCA to 200 variables with one observation. if you have N heartbeat and each beat has 200 features then you should end up with a matrix of size N by 200. So, you will have 200 variables and N observations. Pay attention to matrix orientation, though, different implementations of PCA may require number variables in columns or rows. Your PCs then will be 200x200 matrix, each column representing one PC consisting of the loadings from all 200 features. Hope that helps.
Dear Valeri
thanks,
But if in the real word, i implement my method in an ICU, i should wait till i record N beats (for example, 6000) and then i diagnose its arrhythmia! i think that this is important to diagnose one beat at a time for giving related cares to the patient.
also there are some publications that have applied PCA on a array with one observation(as i found!), such as:
http://www.sciencedirect.com/science/article/pii/S0957417412006690
LDA (Linear Discriminant Analysis) and PCA (Principal Component Analysis) work very well for your purposes.
Dear Professor Akbar Esmaeelzadeh,
With a single feature vector, you cannot apply PCA. You require to make a array of m*n where m is the number of patterns (no of feature vectors) and n is the number of features in each such vector.
You can follow the following program. It is self explanatory.
===============================================
function [signals,PC,V] = pca1(data)
% PCA1: Perform PCA using covariance.
% data - MxN matrix of input data
% (M dimensions, N trials)
% signals - MxN matrix of projected data
% PC - each column is a PC
% V - Mx1 matrix of variances
[M,N] = size(data);
% subtract off the mean for each dimension
mn = mean(data,2);
data = data - repmat(mn,1,N);
% calculate the covariance matrix
covariance = 1 / (N-1) * data * data’;
% find the eigenvectors and eigenvalues
[PC, V] = eig(covariance);
% extract diagonal of matrix as vector
V = diag(V);
% sort the variances in decreasing order
[junk, rindices] = sort(-1*V);
V = V(rindices);
PC = PC(:,rindices);
% project the original data set
signals = PC’ * data;
================================================
With Kind Regards,
Roshan.
As mentioned by Valeri Tsatsishvili you need to construct the feature vector from all observations. PCA is only used to reduce the dimension of a large dataset and with that said you may loose some information. It is helpful to look at the percent variance that each principal component (PC) represents. For example if you select the first three PCs and find they only represent 70% of the total variance you may want to consider expanding your dimensions. Starting with a quality feature vector is your best start.
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