Machine learning models have been an inevitable tool for analyzing medical images by radiologists. These models provide important information about the contents of these images using extracted radiomic features. However, the dimensionality of the feature space can cause reduction in the accuracy of prediction, a phenomenon known as the curse of dimensionality. In this study we propose a feature selection method using an autoencoder, which incorporates the performance of a classifier within the feature selection process. This is achieved by automatically adjusting a threshold value used for selecting the features fed to the classifier. The contribution of this study is twofold. The first contribution is an improvement to group lasso to include the group size as a cost parameter of the autoencoder. The second contribution is to automate the selection of the threshold value used for eliminating redundant input features. The threshold value in our proposed method is learned during training phase of the proposed model. Our experimental results indicates that the proposed model can successfully converge to appropriate feature selection parameters.