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My data looks like this (F=Features)

        F1     F2     F3     F4     F5     F6     F7     F8....
ID1     0.67   0.76   0.3    0.54   0.21   0.88   0.97   0.45....
ID2     0.76   0.68   0.10   0.45   0.12   0.44   0.79   0.54....
ID3     0.67   0.76   0.3    0.54   0.21   0.88   0.68   0.76....
ID4     0.67   0.10   0.3    0.45   0.3    0.88   0.97   0.45....
...
...
...

I have about 40 features (I have just put 8 here). If I set a threshold for, say 4 features, what I am looking for is a combination of 4 features which, together, are most relevant and significant in the dataset. I need some kind of score that measures how good a combination of features is. This is what I meant by the confidence score (or whatever score we may call it). So instead of selecting 1 feature I want to select a combination of 4 features. For example.

F1-F4-F9-F12 = 0.92
F2-F3-F7-F6 = 0.85
F5-F3-F4-F8 = 0.667

Here, F1-F4 is not subtraction. I am just attaching the two features together. The scores above, I do not know how to get it. That is my question? So I do not know what kind of a test to use or can be used.

How can I go about it? Thanks

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  • $\begingroup$ @yO2gO What would/should your confidence score reflect? What is the purpose of the analysis? (You added the feature-selection tag, but what are those features?) $\endgroup$ – chl Apr 9 '11 at 18:57
  • $\begingroup$ @chl this is from the biology domain. For each ID, how important each feature is, is the score (tf-idf) given to it in the sample table above. The confidences reflects, statistically how significant the combination of features are in the whole dataset and not just for one ID. $\endgroup$ – y2p Apr 9 '11 at 19:11
  • $\begingroup$ @yO2gO (1) What do you mean by tf and idf? (2) I checked your example for no pair of F5 and F3 values holds that F5-F3 = 0.667, could you explain this? $\endgroup$ – GaBorgulya Apr 9 '11 at 19:21
  • $\begingroup$ @GaBorgulya The values in the table are calculated using tf-idf (term frequency - inverse document frequency). When I say F5-F3=0.667, I mean the two features (F5 and F3) together are 0.667 significant $\endgroup$ – y2p Apr 9 '11 at 19:40
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    $\begingroup$ I'm not sure this question deserves so many downvotes. Although it lacks some information, some clarifications are given as comments, upon request -- @yO2gO, maybe you could now update your question and just add a rough definition of what you think of or expect from such a confidence score? $\endgroup$ – chl Apr 10 '11 at 10:26
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As I understand (see comments to the original question) you want to select a subset of the features by two criteria:

  1. the subset covers most of the information content of the dataset,
  2. the subset includes as few features as possible.

The paper Variable selection in large environmental data sets using principal components analysis by King and Jackson in Environmetrics, 1999 compares the methods for this problem.

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