Non nega:ve matrix factoriza:on (NMF) Masked Non Nega6ve Matrix Factoriza6on (MNMF)  Mask:  the base matrix W is defined by a user-­‐provided mask matrix  data in the subspace are described by the parts  New objec:ve func:on : constrains the columns in W to contain only few non-­‐zero elements  New itera:ve upda:ng rules: objec:ve func:on non-­‐increasing under the upda:ng rules  MNMF improves NMF for IDA " Unique decomposi:on " W and H very sparse => easy to bring out useful knowledge Iris Dataset Part 1 Part 2 Sepal length Sepal width Petal length Petak witdth Query Mask MNMF NMF could be a good tool for Intelligent Data Analysis (IDA) " Capable of represen:ng data as an addi:ve combina:on of parts " Dimensionality reduc:on helps to understand data " Ability of interpre:ng factors in the problem domain " Not unique decomposi:on " W and H very dense => difficult to bring out useful knowledge What is a part? We define a part as a small selec:on of features that present a local linear rela:onship in a subset of data * € X ∈ R + nxm ,W ∈ R + mxr ,H ∈ R + rxn