Abstract: The existing filtering feature selection algorithm ignores the correlation between features.This paper proposes a new filtering feature selection algorithm —the feature selection algorithm based on persistent homology(Rel-Betti algorithm),which can consider the correlation between features and the combined effect.This paper gives a new definition named by relevant Betti numbers,which can filter out the important topological features in the dataset.The algorithm first preprocesses the data set,classifies the data set according to the class labels,calculates the relevant Betti numbers in different classes,obtains the feature mean of the data information,and uses the feature mean difference to sort the importance of the features.Using eight data in UCI,the algorithm is compared with other common algorithms under four learning models:decision tree,random forest,K-nearest neighbor and support vector machine.Experimental results show that the Rel-Betti algorithm is an effective method that can improve classification accuracy and F1 value,and does not depend on a specific machine learning model.

Key words: Feature selection, Persistent homology, Barcode, Betti number, Machine learning