Image classification using local tensor singular value decompositions
This work addresses storage and computational efficiency issues in image classification, particularly for applications like object recognition with varying poses, but it appears incremental as it builds on existing tensor methods.
The paper tackles the problem of high storage costs and computational complexity in image classification by proposing a novel nonlinear classification approach using local tensor singular value decompositions (tSVD) truncation, which offers accurate results while maintaining manageable storage costs, as demonstrated on the MNIST dataset.
From linear classifiers to neural networks, image classification has been a widely explored topic in mathematics, and many algorithms have proven to be effective classifiers. However, the most accurate classifiers typically have significantly high storage costs, or require complicated procedures that may be computationally expensive. We present a novel (nonlinear) classification approach using truncation of local tensor singular value decompositions (tSVD) that robustly offers accurate results, while maintaining manageable storage costs. Our approach takes advantage of the optimality of the representation under the tensor algebra described to determine to which class an image belongs. We extend our approach to a method that can determine specific pairwise match scores, which could be useful in, for example, object recognition problems where pose/position are different. We demonstrate the promise of our new techniques on the MNIST data set.