With advances in data collection technologies, tensor data is assuming increasing prominence in many applications and the problem of supervised tensor learning has emerged as a topic of critical significance in the data mining and machine learning community. Conventional methods for supervised tensor learning mainly focus on learning kernels by flattening the tensor into vectors or matrices, however structural information within the tensors will be lost. In this paper, we introduce a new scheme to design structure-preserving kernels for supervised tensor learning. Specifically, we demonstrate how to leverage the naturally available structure within the tensorial representation to encode prior knowledge in the kernel. We proposed a tensor kernel that can preserve tensor structures based upon dual-tensorial mapping. The dual-tensorial mapping function can map each tensor instance in the input space to another tensor in the feature space while preserving the tensorial structure. Theoretically, our approach is an extension of the conventional kernels in the vector space to tensor space. We applied our novel kernel in conjunction with SVM to real-world tensor classification problems including brain fMRI classification for three different diseases (i.e., Alzheimer's disease, ADHD and brain damage by HIV). Extensive empirical studies demonstrate that our proposed approach can effectively boost tensor classification performances, particularly with small sample sizes.
Another recent work by @cite_2 , although not directly performs supervised tensor learning, is worth mentioning in this context. They introduced the so-called tensor kernels to analyze neuroimaging data from multiple sources, which demonstrated that the tensor product feature space is useful for modeling interactions between feature sets in different domains. In this study, we make use of the tensor product feature space to derive our kernels in vivo the incorporation of CP model. The tensor kernels can be cast as a special case of our framework.
@cite_2
2072248825
The tensor kernel has been used across the machine learning literature for a number of purposes and applications, due to its ability to incorporate samples from multiple sources into a joint kernel defined feature space. Despite these uses, there have been no attempts made towards investigating the resulting tensor weight in respect to the contribution of the individual tensor sources. Motivated by the increase in the current availability of Neuroscience data, specifically for two-source analyses, we propose a novel approach for decomposing the resulting tensor weight into its two components without accessing the feature space. We demonstrate our method and give experimental results on paired fMRI image-stimuli data.