一种三维矩阵的奇异值分解算法

Abstract

提出了一种三维矩阵的奇异值分解算法,该法适合处理具有三维矩阵数据的模式识别和分类模型等领域实际问题,该算法与二维矩阵奇异值分解算法类似,通过求解约束条件极值问题获得,该算法与已有的三线性分解算法比较,相对简单,计算速度快,适合处理数据量大的实际问题,该算法也很容易推广到更高维阵列的光谱数据。

A algorithm of the singular value decomposition for three-way array is proposed in this paper.The algorithm is suitable to deal with the actual problems of pattern recognition and classification model with three-way array data.Similar to the al gorithm of the singular value decomposition for matrix,the algorithm is obtained by saving the problem of extremum subject to constraint conditions.Comparing with the existent algorithms of trilinear decomposition the algorithm is simple and fast in calculation,suitable to deal with the actual bigger data problems.The algorithm is easy to expand into the situation for multi-way array spectral data.