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Support vector machine is an effective classification and regression method that uses machine learning theory to maximize the predictive accuracy while avoiding overfitting of data.  L2  regularization has been commonly used. If the training dataset contains many noise variables,  L1  regularization SVM will provide a better performance. However, both  L1  and  L2  are not the optimal regularization method when handing a large number of redundant values and only a small amount of data points is useful for machine learning. We have therefore proposed an adaptive learning algorithm using the iterative reweighted  p -norm regularization support vector machine for 0 <  p  ≤ 2. A simulated data set was created to evaluate the algorithm. It was shown that a  p  value of 0.8 was able to produce better feature selection rate with high accuracy. Four cancer data sets from public data banks were used also for the evaluation. All four evaluations show that the new adaptive algorithm was able to achieve the optimal prediction error using a  p  value less than  L1  norm. Moreover, we observe that the proposed  Lp  penalty is more robust to noise variables than the  L1  and  L2  penalties.

Iterative Reweighted Noninteger Norm Regularizing SVM for Gene Expression Data Classification