how can i select the important features from a set of features? Is there any mathematical technique
There are a number of statistical softwares that perform best subset selection (SPSS, Statistica, Minitab, etc.). A segment of Functional Networks could do the trick too.
However, if the feature dimension is large running into thousands, PCA would be more appropriate to reduce it to, say, hundreds or tens.
Think of it as a search across feature-space. Whether you use one technique or another, your search is to some extent bound by the number of features within the space. Due to combinational complexity, we can predict that the number of tests needed to resolve the set completely will be some factor of at least logrithmic increase in comparison to the size of the space. To speed the search, you will need to manage your tests, so as to limit the time taken to testing to a reasonable reaction time for the device. You can do this by throwing processing power at it, or by using a heuristic that gives you more leverage on the search, but may reduce your certainty that you have the right answer at the end of the search. Which you choose depends on the expectations you have for the quality factor of your choices and how long you are willing to wait for the search to complete.
PCA, SVD, LVD, ICA etc. are some of the methods which you can use for dimension reduction and feature extraction...
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