TODO.md

In linxihui/NNLM: Fast and Versatile Non-Negative Matrix Factorization

Other thoughts on bioinformatics applications (DONE)

When the microarray contents multiple tumour, and $H_0$ is set to a 0/1 matrix represent tumour types, with number of rows equals to number of tumour, $W_1$ can be intepretted as tmuour type specific common profiles, which can be used to characterise and distinguish tumours.

If $W$ is designed according to some known gene subnetworks, i.e., each column of $W$ represents a gene subnetwork, by assigning 0 to genes not in the subnetwork and an unknown (and to be determined from $A$) non-negative number to genes within the subnetwork. One can solve the optimization problem to get the expression amount of each gene within the subnetwork. A gene can appear in different functional subnetwork, and the amonts in those different subnetwork represent the different functionalities of the gene. (partial information)

-- to be implemented

$$ A = WH + W0 H1 + W1 H0 + W2 H3 + W3 H2 $$

$W, H$ are completely unknow $W0, H0$ are completely known $W2, H2$ are partially known (a mask, 0 or unkonw to be determined)

A careful design of $W0, H0, W2, H2$ may give disired result.

Systematic bias, or batch effect can be adjust by adding a column of 1 to $W_0$, and the correspondent coefficent vector will capture the biasness. In addtion, NMF has a natural property to elimate noise, which is not necessary to be Gaussian noise.

number of iteration can stop criterion of NNLS within NMF (DONE)

One don't need a very precise NNLS result in the early NMF iteration

better regularization (DONE)

The current regularization has a weird behavior: RMSE converged but the targetted-error, which is penalized-RMSE, keeps minizing the penalized-RMSE, probably by simply rescalling/distributing $W$ and $H$ matrix. $W$ is intialized to have unit normal on each column, is there way to determine the optimal scale (minizing the penalized-RMSE) of $W$ and $H$ assuming that RMSE is minized?

$$A = W PDP^T H^T$$

where $W$ and $H$ has unit column norm. and $P$ is a permation matrix and $D$ is a diagonal matrix (scaling). Can we sort columns of $W$ via magnitude of $D$?

Can the sequential NNLS be extented to KL divergence? (DONE)

Add support to user-specified inintialized $W$ matrix. (DONE)

A = WH with nonnegative W, and unconstraint. Or both unconstraint

Support for sparse matrix A

Plotting

Automatic Rank Tuning

Probabilit like: p(a) = $\sum_{a=0} = p(a|b) p(b)}$$

linxihui/NNLM documentation built on Oct. 15, 2021, 8:59 a.m.