With the popularity of electronic commerce, there are increasing requirements on product comparison services, which collect the similar products information on different platforms for a user reference. Since there are a large quantity of products on each platform, it is necessary to classify the products based on their short descriptions and to learn the relationships between the different categories on multiple platforms. In this paper, we propose the Rectified Topic Classification model to classify products into hierarchical categories based on their short text descriptions. We adopt the topic model to capture the latent features of products from the noisy short descriptions generated by merchants. To reduce the uncertainty of the inferring topic features of a new product, we invoke the topic model several times to get a set of probabilistic feature results and adopt the convolutional neural network for classification. To learn the correlations between two platform categories, the mapping matrix is learned by using a set of seed products. We crawled several real datasets from popular e-commerce platforms and perform experiments to verify our methods. The results show that our method outperforms the related methods.