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 algorithm 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.
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