Tensor Valued Common and Individual Feature Extraction: Multi-dimensional Perspective
This addresses a major bottleneck in modern data science for applications like image classification, though it appears incremental as it builds on existing tensor decomposition approaches.
The paper tackled the curse of dimensionality in large-scale multi-block data by proposing a tensor decomposition method for common and individual feature extraction, which dramatically reduced search space dimensionality and greatly enhanced classification accuracy in simulations on real-world images.
A novel method for common and individual feature analysis from exceedingly large-scale data is proposed, in order to ensure the tractability of both the computation and storage and thus mitigate the curse of dimensionality, a major bottleneck in modern data science. This is achieved by making use of the inherent redundancy in so-called multi-block data structures, which represent multiple observations of the same phenomenon taken at different times, angles or recording conditions. Upon providing an intrinsic link between the properties of the outer vector product and extracted features in tensor decompositions (TDs), the proposed common and individual information extraction from multi-block data is performed through imposing physical meaning to otherwise unconstrained factorisation approaches. This is shown to dramatically reduce the dimensionality of search spaces for subsequent classification procedures and to yield greatly enhanced accuracy. Simulations on a multi-class classification task of large-scale extraction of individual features from a collection of partially related real-world images demonstrate the advantages of the "blessing of dimensionality" associated with TDs.