Non-negative matrix factorization

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  • 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