Guidance/Brainstorming for a mapping/classification problem
You need to be certain that your feature vector is capturing the properties you are looking for. Using the mean and median for dimension reduction (i.e. extracting the features) is not a good choice unless your problem is really simple. Better choices are: PCA, ICA, and SVM's. Capturing the features in the frequency domain can also be a great tool if your signal is sparse in the FFT or DCT domain.