Etydhv

I came across this picture and I would like to know if you could give me a hand with it. I know how to draw the rectangles but, when it comes to the labeling thing, I am a total mess. Not to mention the sigma in the diagonal in the middle matrix.

So far, I've tried this:

 documentclass[border=0.1cm]standalone
 usepackage[utf8]inputenc

 usepackagetikz
 usepackageamsfonts
 usepackageamsmath,amssymb
 usepackagesysteme,mathtools
 usetikzlibrarypositioning,arrows.meta,quotes
 usetikzlibraryshapes,snakes
 usetikzlibrarybayesnet
 tikzset>=latex

begindocument
begintikzpicture
draw (-1.8,0.6) node colorblueMF explained:;
draw [very thick] (0,0) rectangle (3.6/2,2.4/2);
filldraw [fill=green!20!white,draw=green!40!black] (0,0) rectangle (3.6/2,2.4/2);
filldraw [fill=white] (0.4/2,0.4/2) rectangle (0.8/2,0.8/2);
filldraw [fill=white] (2.4/2,0.4/2) rectangle (2.8/2,0.8/2);
filldraw [fill=white] (0.8/2,1.2/2) rectangle (1.2/2,1.6/2);
filldraw [fill=white] (2.0/2,1.6/2) rectangle (2.4/2,2.0/2);
filldraw [fill=white] (0.4/2,2.0/2) rectangle (0.8/2,2.4/2);
filldraw [fill=white] (2.4/2,2.0/2) rectangle (2.8/2,2.4/2);
filldraw [fill=white] (2.8/2,1.2/2) rectangle (3.2/2,2.0/2);
draw [step=0.4/2, very thin, color=gray] (0,0) grid (3.6/2,2.4/2);
draw (1.8/2,-0.3) node colorredscriptsize$YinmathbbR^mtimes f$;
draw (4.4/2,1.2/2) node colorblacklarge$approx$;
draw [very thick] (5.2/2,0) rectangle (6.0/2,2.4/2);
filldraw [fill=green!20!white,draw=green!40!black] (5.2/2,0) rectangle (6.0/2,2.4/2);
draw [step=0.4/2, very thin, color=gray] (5.2/2,0) grid (6.0/2,2.4/2);
draw (5.6/2,-0.3) node colorblackscriptsize$WinmathbbR^mtimes r$;
draw (6.8/2,1.2/2) node colorblacklarge$times$;
draw [very thick] (7.6/2,0.8/2) rectangle (11.2/2,1.6/2);
filldraw [fill=green!20!white,draw=green!40!black] (7.6/2,0.8/2) rectangle (11.2/2,1.6/2);
draw [step=0.4/2, very thin, color=gray] (7.6/2,0.8/2) grid (11.2/2,1.6/2);
draw (9.4/2,0) node colorredscriptsize$X^TinmathbbR^rtimes f$;
endtikzpicture
enddocument

How about the following? It uses only TikZ along with the baseline key in an ordinary equation (and contour for the Sigma). The dimensions of these blocks are controlled by inner xsep and inner ysep. And overlay is used to avoid that the FEATURES node above U does not introduce additional horizontal space.

documentclassarticle
usepackagecontour
contourlength1pt
usepackagetikz
begindocument
[ tikz[baseline=(X.base)]
node[draw,inner xsep=2.5em,inner ysep=2em,outer sep=0pt] (X)$mathsfX$;
draw ([yshift=0.4ex]X.north west) -- ++ (0,1ex) -~=~
tikz[baseline=(U.base)]
node[draw=yellow!80!black,inner xsep=0.5em,inner ysep=2em,outer sep=0pt] (U)$mathsfU$;
draw([yshift=0.4ex]U.north west) -- ++ (0,1ex) -
~times~
tikz[baseline=(S.base)]
node[draw=blue!80,inner xsep=0.5em,inner ysep=0.5em,font=sffamilysmall,path
picture=draw (path picture bounding box.north west) --
(path picture bounding box.south east);,outer sep=0pt] (S)contourwhite$Sigma$;

~times~
tikz[baseline=(V.base)]- ([xshift=0.4ex]V.north east)
node[pos=0.25,font=sffamilysmall,right]FEATURES

]
enddocument