In this paper, we define a semi-tensor product for third-order tensors. Based on this definition, we present a new type of tensor decomposition strategy and give the specific algorithm. This decomposition strategy actually generalizes the tensor SVD based on semi-tensor product. Due to the characteristic of semi-tensor product for compressing the data scale, we can therefore achieve data compression in this way. Numerical comparisons are given to show the advantages of this decomposition.
翻译:在本文中, 我们定义了三等高压的半电压产品。 基于此定义, 我们提出一种新的高压分解策略, 并给出了特定的算法 。 这种分解策略实际上以半电压产品为基础, 概括了高压 SVD 。 由于压缩数据比例的半电压产品特性, 因此我们可以以这种方式实现数据压缩。 数字比较可以显示这种分解的优点 。