Abstract

Two closely related problems—stability of the solution to the topic modeling problem and uniqueness of the stochastic matrix factorization are considered. A theorem describing an analytical method for finding out if the stability of the solution to a given stochastic matrix factorization problem is formulated and proved. The practical usefulness of this theorem is investigated by applying it to real-life data.

中文翻译：

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随机矩阵分解的稳定性和唯一性问题

摘要

考虑了两个密切相关的问题-主题建模问题的解决方案的稳定性和随机矩阵分解的唯一性。一个定理描述了一种分析方法，用于找出和证明给定随机矩阵分解问题的解的稳定性。通过将该定理应用于实际数据来研究其实用性。