IRTF: A new tensor factorization for irregular multidimensional data recovery

Tensor factorizations, although serving as paramount tools for exploiting prior knowledge of multidimensional data, are unsuitable for emerging irregular multidimensional data with the arbitrary shape spatial domain (i.e., spatial-irregular tensor), such as superpixels and spatial transcriptomics. Developing new tensor factorizations suitable for spatial-irregular tensors poses a compelling challenge. To meet this challenge, we introduce a novel Irregular Tensor Factorization (IRTF), which can fully capture the intrinsic spatial and channel information behind the spatial-irregular tensor. Concretely, a spatial-irregular tensor can be decomposed into the product of an intrinsic regular tensor, learnable channel transform matrices, and a learnable spatial transform matrix. Accompanying IRTF, we suggest the Total Variation on Channel and Spatial Transforms (TV-CST) to exploit the local information of spatial-irregular tensors, which is hardly excavated by traditional total variation methods. Combining the proposed IRTF and TV-CST, we built a spatial-irregular tensor recovery model. Extensive experiments on real-world spatial-irregular tensors demonstrate the promising performance of our IRTF and its significant advantages on downstream tasks.