Context Sensitive Formatting for a Table

Question

Suppose I am calculating the correlation of a a set of vectors.

Correlation[RandomReal[1, {5,5}]]

I would like to display the output using TableForm or Grid and use either Style or Background to highlight the entries that exceed some threshold (say > .5 and < -.5)

I found How can I add row and column header images to my TableForm output? which highlights the minimum in each row using:

    TableForm[With[{min = Min[#]}, # /. min -> Style[min, Red]] & /@ data, 
TableHeadings -> {ConstantArray[lena, 3], ConstantArray[lena, 9]}]

Can someone help me adapt this for my purpose?

Edit:

Of course I can do it this way:

 data = RandomReal[1,{5,5}];
 cors = Round[Correlation[data], .01];
 Table[Style[cors[[i, j]], 
 If[Abs[cors[[i, j]]] > .35, Red, Black]], {i, 1, 5}, {j, 1, 5}] // TableForm

but I would like to understand how to do it in one line

Edit #2:

Here is the inelegant solution I came up with:

 cors = Correlation[RandomReal[1, {5, 5}]];
 headers = Table["Header " <> ToString[j], {j, 1, 5}];
 backs = Table[ If[cors[[i, j]] > .35, {i + 1, j + 1} -> Green, 
 If[cors[[i, j]] < -.35, {i + 1, j + 1} -> Red]], {i, 1, 
 Length[cors]}, {j, 1, Length[cors]}] // Flatten;

 Grid[MapThread[Prepend[#2, #1] &, {Join[{""}, headers], Prepend[
(Round[cors, .01]), headers]}], 
 Background -> {LightGray, LightGray, backs}, Frame -> All]

Which produces

Answer 1

Not a one liner but a little bit more straight forward than what you are doing:

1: Get your data and make your headers.

cors = Correlation[RandomReal[1, {5, 5}]];
headers = Table[{"Header " <> ToString[j]}, {j, 1, 5}];

2: I am assuming that your columns will always be the same as the headers as per your example. In that case:

Grid[
 grid = Join[{Flatten[{"", headers}]}, Join[headers, cors, 2]],
 Background -> {White, White, 
   Flatten[{Thread[Position[grid, x_Real /; x > 0.35] -> Green], 
     Thread[Position[grid, x_Real /; x < -0.35] -> Red]}]}
 ]

This code makes the table/grid (called grid) and then finds the positions in grid that match the criteria.

You can turn this into something dynamic that adjusts whenever you change cors:

Dynamic[
 Grid[
  grid = Join[{Flatten[{"", headers}]}, Join[headers, cors, 2]],
  Background -> {White, White, 
    Flatten[{Thread[Position[grid, x_Real /; x > 0.35] -> Green], 
      Thread[Position[grid, x_Real /; x < -0.35] -> Red]}]}
  ],
 TrackedSymbols :> {cors}]

Answer 2

Not really that different, the ReplaceAll approach together with PatternTest and Condition is quite versatile...

m = MapIndexed[Prepend[#, "Row " <> ToString@#2[[1]]] &, 
   Correlation[RandomReal[1, {5, 5}]]];

Grid[m /. {x_?NumericQ /; x < -.35 :> Style[x, Red], 
   x_?NumericQ /; x > .35 :> Style[x, Green]}, Frame -> All, 
 Background -> LightGray]

Should be adaptable for the Grid backgrounds - the contrast here is really awful.