Right order of doing feature selection, PCA and normalization?

If I were doing a classifier of some sort I would personally use this order

1. Normalization
2. PCA
3. Feature Selection

Normalization: You would do normalization first to get data into reasonable bounds. If you have data (x,y) and the range of x is from -1000 to +1000 and y is from -1 to +1 You can see any distance metric would automatically say a change in y is less significant than a change in X. we don't know that is the case yet. So we want to normalize our data.

PCA: Uses the eigenvalue decomposition of data to find an orthogonal basis set that describes the variance in data points. If you have 4 characteristics, PCA can show you that only 2 characteristics really differentiate data points which brings us to the last step

Feature Selection: once you have a coordinate space that better describes your data you can select which features are salient.Typically you'd use the largest eigenvalues(EVs) and their corresponding eigenvectors from PCA for your representation. Since larger EVs mean there is more variance in that data direction, you can get more granularity in isolating features. This is a good method to reduce number of dimensions of your problem.

of course this could change from problem to problem, but that is simply a generic guide.

Good answers here. One point needs to be highlighted. PCA is a form of dimensionality reduction. It will find a lower dimensional linear subspace that approximates the data well. When the axes of this subspace align with the features that one started with, it will lead to interpretable feature selection as well. Otherwise, feature selection after PCA, will lead to features that are linear combinations of the original set of features and they are difficult to interpret based on the original set of features.

Generally speaking, Normalization is needed before PCA. The key to the problem is the order of feature selection, and it's depends on the method of feature selection.

A simple feature selection is to see whether the variance or standard deviation of the feature is small. If these values are relatively small, this feature may not help the classifier. But if you do normalization before you do this, the standard deviation and variance will become smaller (generally less than 1), which will result in very small differences in std or var between the different features.If you use zero-mean normalization, the mean of all the features will equal 0 and std equals 1.At this point, it might be bad to do normalization before feature selection

Feature selection is flexible, and there are many ways to select features. The order of feature selection should be chosen according to the actual situation