Dimensionality reduction method for uncorrelated data? In neuroscience it is very common to measure the reaction time (RT) of subjects. Based on the RT conclusions can be made about personal working memory capability, IQ etc.
So I have such data, which came from some neuroscience experiment. In this data I have 180  subjects from two groups  (90 subjects in each group) for simplicity let say boys and girls, and I have a set of 500 RTs for each subject. The difference between the mean RT of each group is statistically significant (t-test). Now, I would like to construct a classifier which will learn the differences between those two groups. I want the classifier to classify new subjects only based on their RT - and I'm talking specifically about classification of RT. 
(A) I'm searching for dimensionality-reduction method which would fit to this case. ( I have tried PCA and it doesn't work well ). Not sure if PCA is the right thing here as there is no difference between the 100th and the 200th RT. Each RT is independent and there is no specific ordering - so there is not any co-variance here that PCA can capture. (right ?)
(B)  Which classifier is recommended in such case ? 
Does anyone aware of such kind of work in general and specific for RT ? Any information on this would be appreciated.
 A: This description is closer to OK, but still you need to describe a lot of things in more detail. 
Since you want to classify, it seems like what you want is LDA (Linear Discriminant Analysis) more than PCA. You want to "dimensionality reduction", possibly because you need to be able to describe the rule you obtain, but more importantly don't forget that you want something that helps you classify boys from girls. 
The most important key step is that you will have to think of a sensible representation for your data that helps achieve this goal. Depending on this: 


*

*what do the 500 RTs mean? Are they repetitions of the same experiment? or

*are they executions of different experiments? Why does it "stand on its own" and "order has no meaning"? 


the representation would be significantly different.
Also when you say PCA does not work well, what exactly do you mean by that? It could be many things: does it give unacceptable accuracy on new data? or does it work reasonably well, just not as well as you had hoped?
What you say in your question (A), is not true you may be seeing the effects of a poor representation for your data.
A: A simple discriminative classifier should train in seconds and generalize well after tuning l1 and l2 regularization parameters on a dataset of this size. There is no need to do dimensionality reduction.
If you still needed to do dimensionality reduction for whatever reason, you could use random projections, independent components analysis, autoencoders, or any number of nonlinear techniques which work well in the absence of obvious linear relationships on the data.
