How to create NxM Corr matrix from Column 2 of 2xN signals in R?

Question

I have 2x N amount of 1D Signals in files where Column 1 is Signal 1 and Column 2 Signal 2. Code 1 is simplified example about 1x N amount of 1D signals, whil

Answer 1

I am still not sure of your question, so I will first try to make sure of the data structure that you have in mind.

I have created a list of length M (= 100) each element of which with an N x 2 matrix (where N = 1000) which represents the 2D signals.

library(dplyr)
library(ggplot2)

N = 1000
li_matrices = setNames(
  lapply(paste("Improved", 1:100), function(x) matrix(rnorm(N*2), nrow = N, ncol = 2, byrow = TRUE)),
  paste("Improved", 1:100))

> str(li_matrices, list.len = 5, max.level = 1)
List of 100
 $ Improved 1  : num [1:1000, 1:2] 0.228 -0.44 0.713 -0.118 -0.918 ...
 $ Improved 2  : num [1:1000, 1:2] 0.928 0.362 -0.105 -0.1 0.165 ...
 $ Improved 3  : num [1:1000, 1:2] 0.0881 -0.1466 1.8549 -0.3376 -1.1626 ...
 $ Improved 4  : num [1:1000, 1:2] 0.0575 -0.7809 0.4221 0.5378 -0.7882 ...
 $ Improved 5  : num [1:1000, 1:2] 0.6739 1.4515 -0.0704 -0.1596 0.2157 ...
  [list output truncated]

Then, I have extracted the second dimension of the signals from each of the M list elements, and computed their correlations across the M replicates.

> cor(sapply(li_matrices, function(x) x[, 2]))
                Improved 1    Improved 2    Improved 3    Improved 4    Improved 5    Improved 6    Improved 7
Improved 1    1.0000000000 -0.0181724914  0.0307864778 -0.0235266506  0.0681155904 -0.0654758679 -0.0416660418
Improved 2   -0.0181724914  1.0000000000  0.0837086793 -0.0310760562  0.0035757641 -0.0303866471 -0.0345608009
Improved 3    0.0307864778  0.0837086793  1.0000000000 -0.0093528744  0.0282039040 -0.0525328267  0.0410787784
Improved 4   -0.0235266506 -0.0310760562 -0.0093528744  1.0000000000 -0.0139707732 -0.0145970712 -0.0022037703
Improved 5    0.0681155904  0.0035757641  0.0282039040 -0.0139707732  1.0000000000 -0.0406468255  0.0381800143
Improved 6   -0.0654758679 -0.0303866471 -0.0525328267 -0.0145970712 -0.0406468255  1.0000000000 -0.0534592829
Improved 7   -0.0416660418 -0.0345608009  0.0410787784 -0.0022037703  0.0381800143 -0.0534592829  1.0000000000
Improved 8   -0.0320972342 -0.0344929079 -0.0204718584 -0.0007383034  0.0223386392 -0.0361548831  0.0090484961
Improved 9    0.0068743021 -0.0109232340  0.0071627901  0.0102613137  0.0265829001 -0.0443782611  0.0266421500
Improved 10  -0.0228804070 -0.0163596866  0.0066448268  0.0137962914  0.0357421845  0.0403325013 -0.0391002841

---

Edit:

Here is the plotting code requested by OP:

m_corr = cor(sapply(li_matrices, function(x) x[, 2])) 

    m_corr %>% 
  as.data.frame() %>% 
  rownames_to_column(var = "Var1") %>% 
  as_data_frame() %>% 
  gather(key = Var2, value = Value, -Var1) %>% 
  ggplot(
    aes(
      x = reorder(Var1, as.numeric(gsub("Improved ", "", Var1))), 
      y = reorder(Var2, as.numeric(gsub("Improved ", "", Var2))), 
      fill = Value
    )
  ) + 
  geom_tile() + 
  theme_bw() + 
  theme(
    axis.text.x = element_text(angle = 90, size = 5, hjust = 1),
    axis.text.y = element_text(size = 5)
  ) + 
  xlab("Variable 1") + 
  ylab("Variable 2")

This gives: