Incremental (N) -Mode SVD for Large-Scale Multilinear Generative Models

摘要

Tensor decomposition is frequently used in image processing and machine learning for its ability to express higher order characteristics of data. Among tensor decomposition methods, (N) -mode singular value decomposition (SVD) is widely used owing to its simplicity. However, the data dimension often becomes too large to perform (N) -mode SVD directly due to memory limitation. An incremental method to (N) -mode SVD can be used to resolve this issue, but existing approaches only provide a result, which is just enough to solve discriminative problems, not the full factorization result. In this paper, we present a complete derivation of the incremental (N) -mode SVD, which can be applied to generative models, accompanied by a technique that can reduce the computational cost by reordering calculations. The proposed incremental (N) -mode SVD can also be used effectively to update the current result of (N) -mode SVD when new training data is received. The proposed method provides a very good approximation of (N) -mode SVD for the experimental data, and requires much less computation in updating a multilinear model.