The cultivation of counselors’ core literacy under the background of big data networks is the inheritance and development of the traditional core literacy ability based on the development of network technology. This paper focuses on the construction of a scientific and reasonable core literacy evaluation system for college counselors in the core literacy cultivation path. For the factor analysis model under the cluster data component form structure, expressed in the form of a diagonal matrix. After disassembling the covariance matrix and other steps, the parameter estimation of the factor analysis model for cluster data is obtained. Based on this model, a new model compression method is proposed. Using a step-by-step factor analysis algorithm, the parameters of the convolutional layer are added to complete the iteration of the model, and the performance is improved while reducing the training time of the model. The overall fitness situation of the model is examined, and the values of GFI, CFI, IFI, and TLI are 0.9265, 0.9454, 0.9866, and 0.9855, respectively, which are higher than the ideal value of 0.9 for fitness, which indicates that the model is of good quality and has a high degree of fitness. Different counselors have different core literacy structures, and the score range for A3 counselors is between 70 and 90, which is exceptional in political literacy.