In recent years, cancer can be detected and recognized by analyzing the sample's expression profile. The cancer gene expression data are high dimensional, high variable dependent, and very noisy. The dimension reduction method is often used for processing the high dimensional data. In this study, a new statistical dimension reduction method called Expressive Value Distance (EVD) is developed and proposed for the practical high-dimensional gene expression cancer data. The feature genes data extracted by EVD are arranged for training the optimally trained Artificial Neural Network (ANN). The trained ANN is then used to classify whether the unseen gene data is cancer or not. In comparison of ANN classification with and without EVD, it is found that both of the ANN can classify the cancer data in good accuracy. With the EVD method, the great amount of data (2000 genes) can be effectively reduced to 16 genes. Therefore, EVD is an effective dimension reduction method. Even the EVD method is not used, the optimally trained ANN is also an advanced method for classifying the high dimensional and complicated cancer data. Briefly, it proves that optimally trained ANN is a very robust classification technique.