A New Two-Sided Sketching Algorithm for Large-Scale Tensor Decomposition Based on Discrete Cosine Transformation
arxiv(2024)
摘要
Large tensors are frequently encountered in various fields such as computer
vision, scientific simulations, sensor networks, and data mining. However,
these tensors are often too large for convenient processing, transfer, or
storage. Fortunately, they typically exhibit a low-rank structure that can be
leveraged through tensor decomposition. Despite this, performing large-scale
tensor decomposition can be time-consuming. Sketching is a useful technique to
reduce the dimensionality of the data. In this study, we introduce a novel
two-sided sketching method based on the t-product decomposition and the
discrete cosine transformation. We conduct a thorough theoretical analysis to
assess the approximation error of the proposed method. Specifically, we enhance
the algorithm with power iteration to achieve more precise approximate
solutions. Extensive numerical experiments and comparisons on low-rank
approximation of color images and grayscale videos illustrate the efficiency
and effectiveness of the proposed approach in terms of both CPU time and
approximation accuracy.
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