Machine learning is predominantly employed to classify or cluster image and video data, leveraging the similarities among their inherent features. Amidst the profound surge in the scale of image and video data, identifying appropriate similarity metrics has become paramount for both machine learning and deep learning tasks. Mutual information, rooted in Shannon entropy, stands as a prevalent similarity metric across disciplines like statistics and deep learning. Notably, extracting mutual information between tensors while preserving the integrity of tensor space information is of significant value. In the paper, we extend the concept of mutual information between random variables to higher-order tensors, formulating definitions for tensor mutual information and entropy. Furthermore, we delve into the properties of tensor mutual information, exploring its concavity and convexity within the context of average tensor mutual information. In the realm of evolutionary algorithms, tensor mutual information introduces innovative elements: an internal radius parameter r and an embedded function f(x), distinguishing it from conventional mutual information. To ensure the meaningfulness of tensor mutual information, it suffices for f(x) to be a continuous function. Notably, when  \(r=0\)  and f(x) represents the identity mapping, tensor mutual information reduces to the conventional form defined by Shannon entropy. Experimental simulations underscore the remarkable performance of this metric, both in supervised and unsupervised learning contexts, showcasing its effectiveness and potential applications.