Novel Alternating Least Squares Algorithm for Nonnegative Matrix and Tensor Factorizations
Novel Alternating Least Squares Algorithm for Nonnegative Matrix and Tensor Factorizations
复制标题
非负矩阵和张量分解的新型交替最小二乘算法
DOI：
10.1007/978-3-642-17537-4_33
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发表时间：
2010
期刊：
影响因子：
--
通讯作者：
Thanh Vu Dinh
中科院分区：
文献类型：
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作者：
A. Phan;A. Cichocki;R. Zdunek;Thanh Vu Dinh
另一种最小二乘(ALS)算法被认为是一般张量分解的“苦力”算法。对于非负张量分解(NTF)，我们通常在迭代过程中使用非线性投影(整流器)来去除负条目。然而，这种ALS算法经常失败，不能收敛到期望的解。本文通过递归求解非负二次规划问题，提出了一种求解非负二次规划问题的新算法。该算法在高难度基准测试中的有效性和高性能得到了验证，并在目标分类应用中得到了验证。
Alternative least squares (ALS) algorithm is considered as a "work-horse" algorithm for general tensor factorizations. For nonnegative tensor factorizations (NTF), we usually use a nonlinear projection (rectifier) to remove negative entries during the iteration process. However, this kind of ALS algorithm often fails and cannot converge to the desired solution. In this paper, we proposed a novel algorithm for NTF by recursively solving nonnegative quadratic programming problems. The validity and high performance of the proposed algorithm has been confirmed for difficult benchmarks, and also in an application of object classification.