Exploring the heritage of Chinese traditional festival culture is to enhance the national identity of the people better. This paper introduces the classification principle of support vector machines using support vector machines as an entry point in the big data perspective and shows that support vector machines are all optimized by introducing Lagrangian functions and then finding their optimal classification decision functions. Then, the principle and steps of the artificial fish swarm algorithm are introduced and explained, and the artificial fish swarm algorithm is used to optimize the support vector machine and rank the fitness values. Finally, the AFSA-SVM algorithm is used to classify and analyze two aspects of Chinese traditional festival culture inheritance, i.e., the spiritual value and inheritance mode of Chinese traditional festival culture. From the viewpoint of spiritual value, the harmonious concept of the unity of heaven and man and the self-practice of pursuing ideals are more embodied in the Lantern Festival, accounting for 32.96% and 38.09%, respectively. Regarding inheritance methods, 61.43%, 50.15%, and 55.28% of the people use the Internet, TV, and movies to inherit traditional festivals, respectively. Based on the big data perspective, the AFSA-SVM algorithm can be used to effectively classify and analyze the cultural heritage of traditional Chinese festivals, and the data can be used better to understand the spiritual connotation of traditional Chinese festivals and enhance the sense of national identity.