A new implementation of the canonical polyadic decomposition (CPD) is presented. It features lower computational complexity and memory usage than the available state of art implementations available. The CPD of tensors is a challenging problem which has been approached in several manners. Alternating least squares algorithms were used for a long time, but they convergence properties are limited. Nonlinear least squares (NLS) algorithms - more precisely, damped Gauss-Newton (dGN) algorithms - are much better in this sense, but they require inverting large Hessians, and for this reason there is just a few implementations using this approach. In this paper, we propose a fast dGN implementation to compute the CPD. In this paper, we make the case to always compress the tensor, and propose a fast damped Gauss-Newton implementation to compute the canonical polyadic decomposition.
翻译:演示了一种新的Canonical 多元分解(CPD) 。 它的计算复杂性和记忆用量都比现有的艺术实施状态要低。 发声器的CPD是一个具有挑战性的问题, 已经以几种方式处理过。 交替的最小方程式算法被长期使用, 但它们的趋同性是有限的。 非线性最低方程式算法―― 更确切地说, 被拖动的高斯- 牛顿算法( dGN) 算法―― 在这个意义上要好得多, 但是它们需要倒置大赫塞西亚人, 但由于这个原因, 只有少数执行者使用这个方法。 在本文中, 我们建议快速地执行 dGN 来计算CPD 。 在本文中, 我们提出一个理由, 总是要拼写高方程式, 并提议快速修整高方格- 牛顿算出大方形多方形解剖。