Abstract
We clarify the equivalence between second-order tensor principal component analysis and two-dimensional singular value decomposition. Furthermore, we show that the two-dimensional discrete cosine transform is a good approximation to two-dimensional singular value decomposition and classical principal component analysis. Moreover, for the practical computation in two-dimensional singular value decomposition, we introduce the marginal eigenvector method, which was proposed for image compression. To evaluate the performances of the marginal eigenvector method and two-dimensional discrete cosine transform for dimension reduction, we compute recognition rates for image patterns. The results show that the marginal eigenvector method and two-dimensional discrete cosine transform have almost the same recognition rates for images in six datasets.
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Itoh, H., Imiya, A., Sakai, T. (2015). Low-Dimensional Tensor Principle Component Analysis. In: Azzopardi, G., Petkov, N. (eds) Computer Analysis of Images and Patterns. CAIP 2015. Lecture Notes in Computer Science(), vol 9256. Springer, Cham. https://doi.org/10.1007/978-3-319-23192-1_60
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DOI: https://doi.org/10.1007/978-3-319-23192-1_60
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