I had a look at the fiddle Gerrat set-up but doesn't look to have worked the way I thought it should. In that fiddle the names of dimensions have been removed, but the link or lines between the dimension still represent the original data. This behaviour seems odd to me and it might be a bug.
Anyway, I've set-up a fiddle that pre-filters the data using:
data.forEach( function (e,j) {
var temp ={};
filteredDimensions.forEach ( function (d,i) {
temp[d] = e[d]
})
filteredData.push(temp)
})
With a working fiddle here