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This document discusses matrix factorization and describes how a matrix X can be approximated as the product of two lower-rank matrices U and V. It also defines accuracy as the number of correct predictions divided by the total number of predictions and provides equations for computing probability and joint probability distributions based on counts.

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u11 u12 ··· u1k v11 v12 ··· vk1
? u21 u22 ··· u2k ? ?v21 v22 ··· vk2 ?
? ?? ?
X≈? . . .. . ?? . . .. . ?
? .. .
. . . ?? .
. . .
. . . ?
.
um1 um2 ··· umk vk1 vk2 ··· vkn

|ci |
p(ci ) = n
|ci ∩c |
p(ci , c ) =
j n
j

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NMF

11. T X ≈ UV

15. ? ?? ? u11 u12 ··· u1k v11 v12 ··· vk1 ? u21 u22 ··· u2k ? ?v21 v22 ··· vk2 ? ? ?? ? X≈? . . .. . ?? . . .. . ? ? .. . . . . ?? . . . . . . . ? . um1 um2 ··· umk vk1 vk2 ··· vkn

19. accuracy = 6 8

20. |ci | p(ci ) = n |ci ∩c | p(ci , c ) = j n j

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