Support Tensor Regression (STR)

Support Vector Regression (SVR) is a pow-erful kernel-based method for regressiontasks on vector data. However, many mod-ern datasets, such as images, videos, or medi-cal scans, possess an inherent multi-modal ortensor structure. Vectorizing such data dis-rupts this intrinsic structure and often leads tohigh-dimensional feature spaces, posing chal-lenges for traditional learning algorithms, es-pecially in small sample size regimes. Inspiredby the success of Support Tensor Machines(STM) for classification, we propose SupportTensor Regression (STR), a novel algorithmthat directly performs regression on tensor-structured data. STR learns a regressor inthe tensor space by factorizing the parametertensor into a set of vectors, significantly reduc-ing the number of parameters to be estimated.This approach not only preserves the under-lying data structure but also demonstratesrobustness against the curse of dimensionality,making it particularly suitable for high-orderdata.