Frankfurter InformatikBerichte
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 09, 01

Realvalued feature selection for process approximation and prediction
(2009)

Frank Heister
Rüdiger Brause
 The selection of features for classification, clustering and approximation is an important task in pattern recognition, data mining and soft computing. For realvalued features, this contribution shows how feature selection for a high number of features can be implemented using mutual information. Especially, the common problem for mutual information computation of computing joint probabilities for many dimensions using only a few samples is treated by using the Rènyi mutual information of order two as computational base. For this, the GrassbergerTakens correlation integral is used which was developed for estimating probability densities in chaos theory. Additionally, an adaptive procedure for computing the hypercube size is introduced and for real world applications, the treatment of missing values is included. The computation procedure is accelerated by exploiting the ranking of the set of real feature values especially for the example of time series. As example, a small blackboxglassbox example shows how the relevant features and their time lags are determined in the time series even if the input feature time series determine nonlinearly the output. A more realistic example from chemical industry shows that this enables a better approximation of the inputoutput mapping than the best neural network approach developed for an international contest. By the computationally efficient implementation, mutual information becomes an attractive tool for feature selection even for a high number of realvalued features. Key words: feature selection, process approximation, Rènyi mutual information, classification, clustering, TakensGrassberger correlation integral