Breast cancer is the second most common cancer among women worldwide, and the diagnosis by pathologists is a time-consuming procedure and subjective. Computer-aided diagnosis frameworks are utilized to relieve pathologist workload by classifying the data automatically, in which deep convolutional neural networks (CNNs) are effective solutions. The features extracted from the activation layer of pre-trained CNNs are called deep convolutional activation features (DeCAF). In this paper, we have analyzed that all DeCAF features are not necessarily led to higher accuracy in the classification task and dimension reduction plays an important role. We have proposed reduced DeCAF (R-DeCAF) for this purpose, and different dimension reduction methods are applied to achieve an effective combination of features by capturing the essence of DeCAF features. This framework uses pre-trained CNNs such as AlexNet, VGG-16, and VGG-19 as feature extractors in transfer learning mode. The DeCAF features are extracted from the first fully connected layer of the mentioned CNNs, and a support vector machine is used for classification. Among linear and nonlinear dimensionality reduction algorithms, linear approaches such as principal component analysis (PCA) represent a better combination among deep features and lead to higher accuracy in the classification task using a small number of features considering a specific amount of cumulative explained variance (CEV) of features. The proposed method is validated using experimental BreakHis and ICIAR datasets. Comprehensive results show improvement in the classification accuracy up to 4.3% with a feature vector size (FVS) of 23 and CEV equal to 0.15.