If I understood the question right, there are plenty of things that fit your description. One is random forest, for example. In random forest it's called "random feature selection". But I doubt that random feature selection as it is might increase accuracy. On my mind, It's done mostly for robustification of predictions, not for improving accuracy. Systematic selection of features with good historical prediction accuracy might lead to overfitting the model.
@Arash, how do you want to increase the prediction accuracy? in this way you can't increase accuracy at all,
you can select some features which don't have overlap for your classes but you should consider all your training data samples.
It depends what you mean by input, and whether you are selecting samples / rows or features / columns.
For samples / rows, the word you are looking for is "bagging" - you select overlapping subsets of your samples, and train a classifier on each subset, then combine the classifiers.
For features, it is indeed feature selection or feature resampling techniques, such as random subspace / random forest, as Alexander already mentioned.
You may also be talking about "Windowing" which was used by Ross Quinlan in ID3
Perhaps you are looking for the term: dimension reduction? Ideally, you want to select a subset of dimensions that are orthogonal to each other to get the best results.
And in that case it could be achieved with something like PCA, isn't it?
if you read further, you approach is actually applying embedded/wrapper feature selection approach which integrate classifier/predictor for the search and evaluation of the feature subset. The training in this case is for assist in evaluating the relevancy of the features & selection of features for subsequent steps which is the real classification.
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