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WON-PARAFAC
Weighted orthogonal non-negative (WON) parallel factor analsyis (PARAFAC)
WON-PARAFAC is a variant of parallel factor analysis (PARAFAC), a tensor factorization method. WON-PARAFAC impose the following three constraints on the standard PARAFAC:
- Weighting scheme
- For balanced integration of the multiple data types
- Orthogonality constraint
- To reduce overlapping between a factor (originally used on gene mode). This also introduces extra sparcity on the mode.
- Non-negativity
- To induce sparse and parts-based representation.
Implementation / Dependency
A multiplicative update rule was used to derive the algorithm, as in the original NMF implementation from Lee & Seung (Nature, 1999). The code requires tensor toolbox version 2.6 (by Tamara Kolda), freely available for non-commercial use upon registration.
For running the code, tenstor toobox must be avilable on the path environment, using addpath command in MATLAB.
Demo code and data
You can load demo data, which contains pan-cancer multiomics data produced in GDSC1000 project (Sanger). You can load the data by:
load Demo.mat
The command will load a varialbe X, a 3-way tensor (1815 gene by 935 cell lines and 5 data types).
Note that the 5 data types corresponds to below:
- positive gene expression levels (non-negative continuous; GE(+))
- absolute value of negative gene expression levels (non-negative continuous; GE(-))
- mutation (binary; MT)
- copy number gain (binary; CN(+))
- copy number loss (binary; CN(-))
The list of genes names in X is indicated in genenames, which will also be loaded together with X.
Demo.m will perform WON-PARAFAC analysis using random 100 genes by default, and varying number of factors and strength of orthogonal constraint on gene factor matrix.
- Number of basis: 10, 20, 30, ..., 200
- Strength of orthogonal constraint: 0 (no constraint), 0.2, 0.5, 1
Finally, a plot will be generated to show the performance of WON-PARAFAC for reconstructing input tensor (see below for an example).
