Learning with Similarity Functions: a Tensor-Based Framework

Machine learning algorithms are typically designed to deal with data represented as vectors. Several major applications, however, involve multi-way data, such as video sequences and multi-sensory arrays. In those cases, tensors endow a more consistent way to capture multi-modal relations, which may be lost by a conventional remapping of original data into a vector representation. This paper presents a tensor-oriented machine learning framework, and shows that the theory of learning with similarity functions provides an effective paradigm to support this framework. The proposed approach adopts a specific similarity function, which defines a measure of similarity between a pair of tensors. The performance of the tensor-based framework is evaluated on a set of complex, real-world, pattern-recognition problems. Experimental results confirm the effectiveness of the framework, which compares favorably with state-of-the-art machine learning methodologies that can accept tensors as inputs. Indeed, a formal analysis proves that the framework is more efficient than state-of-the-art methodologies also in terms of computational cost. The paper thus provides two main outcomes: (1) a theoretical framework that enables the use of tensor-oriented similarity notions and (2) a cognitively inspired notion of similarity that leads to computationally efficient predictors.