Non-Negative Matrix Factorization, NMF
Updated 2026-08-13
INTRODUCTION
English translation pending.
CORE DEFINITION
Popularized by Lee and Seung, Non-Negative Matrix Factorization (NMF) factorizes a non-negative matrix V into two non-negative matrices W and H such that V is approximately W times H. The core claim is that the non-negativity constraint makes the decomposition additive and interpretable, since parts sum to form a whole. It is commonly applied to topic extraction from term-document matrices and to image decomposition, where basis vectors represent parts such as eyes or noses. The constraint is that the input data itself must be non-negative.
SCAFFOLDING EFFECT
Reduce cognitive load
- Interpretable decomposition: read H's columns as topics and W as sample compositions, since non-negative parts sum to a whole. - Dimension reduction with meaning: reduce data while keeping basis vectors as understandable parts rather than arbitrary signed axes.
Anchor fast decisions
Constraining W and H entries to be non-negative means the approximation V is roughly W times H is built from positive combinations of additive parts, which yields part-whole interpretability and tends toward sparse representations unlike the canceling components of PCA.
MINIMUM ACTION
In progress 0/1Practice this model in one real situation:
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Source support: Explicit
- en.wikipedia.orghttps://en.wikipedia.org/wiki/Non-negative_matrix_factorizationverified
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