using PCA as feature extraction

I use PCA as a feature extraction tool. in the learning stage I trained the system to choose the best principal component for the training data, for each class(lets say 5 classes ) the system learned for each class what is best principal component to represent the trained data(take the most variance) So I have 5 different principal components(or 5 different sets),So each class will has it's own principal components.

In the testing stage, I think to project the testing data into each principal components, since I have 5 classes which means 5 principal components sets, then I will have 5 feature vector, I will pass those 5 feature vector to classification algorithm one by one, which means I will run the classification 5 times, then I will see what is the best(or maximum) classification result in those 5 classification results, And I will make the decision about. my question is: Is what I do correct?

Answer 1

[Image Analyst]

I'm not following the numbers, like why everything is 5. Okay, you have 5 classes but why do you think that that means you have 5 principal components? For example, let's say you're classifying faces into race and sex. And you have 2 sexes and 4 races and 1000 faces to be classified. Well, you have 8 classes (4 races x 2 sexes) but you could have dozens of eigenface images, not just 8. Let's say I'm using 20 eigenfaces so for a given face I'd have a vector of 20 weights of those 20 images. Then you need to take those 20 feature vector values and figure out which of the 8 sex/race combinations the image actually is (each class/PC would have 20 weights that define the class). So not everything has to be the same number.

[hassan hyt]

you misunderstand my question, I don't say I have 5 principal components, I say I will have 5 "sets" each class will have it's own "set" or (it's own principal components). Is it clear now, or do you need more clarification?

[Image Analyst]

We still need more clarification. Sometimes when you try to be too general, it's not clear, whereas it will become more clear if you use specific situation. What are the 5 classes and what are the measurements made on each sample? And how many PCs are in each class?