无法找到具有相同内部尺寸的两个矩阵（来自 NMF 的 W 和 H）的点积

Question

我正在对 R 中的矩阵 A 进行非负矩阵分解 (NMF)。它的行上有基因，列上有样本。对于 NMF，我使用的是 CRAN package NMF。一旦计算出基础矩阵 W 和系数矩阵 H ，我想检查因式分解是否足够准确。为此，我正在尝试计算 W 和 H 的点积，以检查我是否可以获得原始矩阵 A回.

虽然基矩阵W和系数矩阵H的内部维度相同(rank = 3)，但我无法将它们相乘。我不断收到以下错误。这一行错误不是很有帮助。

Error in x * y : non-conformable arrays

可重现代码

# Make a 10 * 10 matrix
ranVal= sample(1:10,100,replace =T)
M=matrix(ranVal,nrow=10)

# Rename the rows and columns
rownames(M) <-  paste(rep("gene", 10),c(1:10), sep = "_")
colnames(M) <-  paste(rep("sample", 10),c(1:10), sep = "_")

# See how it looks
M

# NMF
library(NMF)
tempRes <- nmf(x = M, rank = 3, .options = c("pv"))

# NMF implementation from Brunet et al. (2004)
result <- nmf_update.brunet_R(i = 1, v = M, x = tempRes, eps=.Machine$double.eps)

# Basis Matrix
W <- .basis(result); 

# Coeff Matrix
H <- .coef(result)

# Checking dimensions
dim(W)
dim(H)

# Dot product
A <- W*H # Error: non-conformable arrays
A <- geometry::dot(W,H) # Error: non-conformable arrays

我该怎么办？有没有不同的方法来检查它？谢谢！

Answer 1

W %*% H呢？

W %*% H
        sample_1 sample_2   sample_3 sample_4  sample_5 sample_6
gene_1  4.406480 6.392739  9.5742884 5.164528  5.074363 3.549958
gene_2  7.165909 4.960877  2.3608356 5.718255  8.405870 5.817709
gene_3  5.070350 3.804750  3.2464367 3.906296  6.383760 4.810851
gene_4  8.356959 4.181312  0.9964025 5.167783 10.955091 8.533261
gene_5  4.671284 5.157582 11.0938515 3.059027  7.946619 7.730591
gene_6  5.899437 6.666820  6.0368747 6.705011  5.718862 2.998982
gene_7  7.801179 7.052729  1.3482074 8.775604  6.398204 2.076385
gene_8  3.501642 4.410587  9.1595473 2.720517  5.693630 5.401830
gene_9  5.271008 7.975740  9.1787413 7.358409  4.472696 1.753683
gene_10 5.855654 4.396895  1.0050132 5.424544  5.950780 3.326661
        sample_7 sample_8  sample_9 sample_10
gene_1  6.781347 5.909006  8.431049  4.716241
gene_2  4.884002 6.815600  4.339132  4.531809
gene_3  4.015448 5.548575  3.376917  2.836615
gene_4  4.446931 8.554956  1.793168  3.014138
gene_5  6.644475 8.692351  5.003496  1.000724
gene_6  6.364861 5.479570  8.536569  6.593015
gene_7  5.804209 4.769660  8.798081  9.175741
gene_8  5.469769 6.475237  4.801630  1.365611
gene_9  7.673524 5.183927 11.371303  7.760969
gene_10 3.915477 4.571069  4.548770  5.005138

无法找到具有相同内部尺寸的两个矩阵（来自 NMF 的 W 和 H）的点积

Unable to find dot product of two matrix (W and H from NMF ) with same inner dimensions

r

matrix-multiplication

dimensionality-reduction

nmf