inmf: Perform Integrative Non-negative Matrix Factorization

Description

Performs integrative non-negative matrix factorization (iNMF) (J.D. Welch, 2019) to return factorized $H$, $W$, and $V$ matrices. The objective function is stated as

$$\arg\min_{H\ge0,W\ge0,V\ge0}\sum_{i}^{d}||E_i-(W+V_i)Hi||^2_F+ \lambda\sum_{i}^{d}||V_iH_i||_F^2$$

where $E_i$ is the input non-negative matrix of the $i$'th dataset, $d$ is the total number of datasets. $E_i$ is of size $m \times n_i$ for $m$ features and $n_i$ sample points, $H_i$ is of size $k \times n_i$, $V_i$ is of size $m \times k$, and $W$ is of size $m \times k$.

inmf optimizes the objective with ANLS strategy, while onlineINMF optimizes the same objective with an online learning strategy.

Usage

inmf(
  objectList,
  k = 20,
  lambda = 5,
  niter = 30,
  nCores = 2,
  Hinit = NULL,
  Vinit = NULL,
  Winit = NULL,
  verbose = FALSE
)

Value

A list of the following elements:

H - a list of result $H_i$ matrices of size $n_i \times k$
V - a list of result $V_i$ matrices
W - the result $W$ matrix
objErr - the final objective error value.

Arguments

objectList: list of input datasets. List elements should all be of the same class. Viable classes include: matrix, dgCMatrix, H5Mat, H5SpMat.
k: Integer. Inner dimensionality to factorize the datasets into. Default 20.
lambda: Regularization parameter. Larger values penalize dataset-specific effects more strongly (i.e. alignment should increase as lambda increases). Default 5.
niter: Integer. Total number of block coordinate descent iterations to perform. Default 30.
nCores: The number of parallel tasks that will be spawned. Default 2
Hinit: Initial values to use for $H$ matrices. A list object where each element is the initial $H$ matrix of each dataset. Each should be dense matrix of size $n_i \times k$. Default NULL.
Vinit: Similar to Hinit, but each should be of size $m \times k$.
Winit: Initial values to use for $W$ matrix. A matrix object of size $m \times k$. Default NULL.
verbose: Logical scalar. Whether to show information and progress. Default FALSE.

Author

Yichen Wang

References

Joshua D. Welch and et al., Single-Cell Multi-omic Integration Compares and Contrasts Features of Brain Cell Identity, Cell, 2019

Examples

Run this code

library(Matrix)
set.seed(1)
result <- inmf(list(ctrl.sparse, stim.sparse), k = 10, niter = 10, verbose = FALSE)

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