The quality and quantity of learning samples are very important for intelligent data classification systems. But there is no general good method for finding meaningful samples in data classification systems. For this reason, the concept of convex boundary of dataset was proposed, and a fast method of discovering meaningful sample set was given. Firstly, abnormal and incomplete samples in the learning sample set were cleaned by box-plot function. Secondly, the concept of data cone was proposed to divide the normalized learning samples into cones. Finally, each cone of sample subset was centralized, and based on convex boundary, samples with very small difference from convex boundary were extracted to form convex boundary sample set. In the experiments, 6 classical data classification algorithms, including Gaussian Naive Bayes (GNB), Classification And Regression Tree (CART), Linear Discriminant Analysis (LDA), Adaptive Boosting (AdaBoost), Random Forest (RF) and Logistic Regression (LR), were tested on 12 UCI datasets. The results show that convex boundary sample sets can significantly shorten the training time of each algorithm while maintaining the classification performance. In particular, for datasets with many noise data such as caesarian section, electrical grid, car evaluation datasets, convex boundary sample set can improve the classification performance. In order to better evaluate the efficiency of convex boundary sample set, the sample cleaning efficiency was defined as the quotient of sample size change rate and classification performance change rate. With this index, the significance of convex boundary samples was evaluated objectively. Cleaning efficiency greater than 1 proves that the method is effective. The higher the numerical value, the better the effect of using convex boundary samples as learning samples. For example, on the dataset of HTRU2, the cleaning efficiency of the proposed method for GNB algorithm is over 68, which proves the strong performance of this method.