# Non-negative matrix factorization

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## General

- Original data must be non-negative
- for K latent variables << min(m,n)
- W is a tall matrix, H is the wide matrix
- For image analysis, W is the "basis images", like the topic centroid

- Label is based on the H matrix
- Works well with images since pixels are always non-negative

## Compare vs PCA

- PCA can have negative values
- Items are in the rows
- Topics are linear combinations of words, documents are linear combinations of topics
- sparse ( non-smooth NMF)

## Compare vs K-Means

- K means are bad at unbalanced problems
- K means implies K centroids mu_i where you minimize the cost function
- Class membership matrix, one hot encoded