改进非负矩阵分解算法，支持正则化与加权范数，提升数据降维精度。

An Iterative Algorithm for Regularized Non-negative Matrix Factorizations

• 将乘法更新改为加法更新，避免零值陷阱。
• 引入岭回归与Lasso正则化，提升模型泛化能力。
• 适用于高维数据库降维，如鸡尾酒配方分析。

我们扩展了Lee和Seung的非负矩阵分解算法，使其可接受加权范数，并支持岭回归与Lasso正则化。将原算法的乘法更新机制重构为加法更新，有效避免在零值处陷入局部最优。我们使用配套的R包rnnmf对鸡尾酒数据库进行低秩表示学习，实现高效特征提取与数据压缩。

原文摘要 · Abstract (English)

We generalize the non-negative matrix factorization algorithm of Lee and Seung to accept a weighted norm, and to support ridge and Lasso regularization. We recast the Lee and Seung multiplicative update as an additive update which does not get stuck on zero values. We apply the companion R package rnnmf to the problem of finding a reduced rank representation of a database of cocktails.

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