High-dimensional and sparse (HiDS) matrices are commonly encountered in many big-data-related and industrial applications like recommender systems. When acquiring useful patterns from them, nonnegative matrix factorization (NMF) models have proven to be highly effective owing to their fine representativeness of the nonnegative data. However, current NMF techniques suffer from: 1) inefficiency in addressing HiDS matrices; and 2) constraints in their training schemes. To address these issues, this paper proposes to extract nonnegative latent factors (NLFs) from HiDS matrices via a novel inherently NLF (INLF) model. It bridges the output factors and decision variables via a single-element-dependent mapping function, thereby making the parameter training unconstrained and compatible with general training schemes on the premise of maintaining the nonnegativity constraints. Experimental results on six HiDS matrices arising from industrial applications indicate that INLF is able to acquire NLFs from them more efficiently than any existing method does.

中文翻译：

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工业应用中高维稀疏矩阵的固有非负潜在因子模型


高维稀疏 (HiDS) 矩阵在许多大数据相关和工业应用（例如推荐系统）中经常遇到。当从中获取有用的模式时，非负矩阵分解（NMF）模型由于其对非负数据的良好代表性而被证明是非常有效的。然而，当前的 NMF 技术存在以下问题：1）寻址 HiDS 矩阵效率低下； 2) 培训计划的限制。为了解决这些问题，本文提出通过一种新颖的固有 NLF（INLF）模型从 HiDS 矩阵中提取非负潜在因子（NLF）。它通过单元素相关映射函数连接输出因子和决策变量，从而使参数训练不受约束，在保持非负性约束的前提下与一般训练方案兼容。工业应用中产生的六个 HiDS 矩阵的实验结果表明，INLF 能够比任何现有方法更有效地从中获取 NLF。