There are many ways to play "LIVE" electronica, some methods being more live than others.... A few years back, my act, Mantrix used to jam every individual sound live, meaning we'd trigger each sound loop individually on the sequencer, and mute each sound individually as well. If you heard a sound it was because we'd told it to play. This method (combined with all the other things we'd do on stage) was as live as I've ever seen, but it also had its disadvantages. You couldn't (very easily) make full on changes in the music unless you placed all your fingers on the appropriate buttons and BAM! triggered the change and hope to God you hadn't forgotten one of the key elements... maybe a little hard to explain in a few words but lets just say it wasnt as powerful on the dancefloor compositionally.
We've recently compromised between that method and playing mastered material. Our current method is as follows...
We write a track, master it, then chop it up into loops (say 16 bar loops).
We place each loop into Ableton on seperate clips. This means we can recompose the mastered signal, like keep this part going for a while longer, skip the next part, jump back to a previous part, jump ahead to the climax of the track etc
We also have certain parts of the tracks which aren't the mastered stereo signal... They are separated groups of sounds which can be jammed. Like, kick in to just the kick and bass, filter in the lead sound, drop in the hi hats, do a fill by muting the kick, dropping in the percussion and other sounds, then dopping the kick back in.
We also feature live electronic drum kit which is triggering samples from each track, with effects controls over the samples, live guitar, we run certain sounds and loops through an Air FX, we run live mic over acoustic percussion.
Also with the sequencing of Ableton, we've nailed it so that we dont have to touch the laptop.... everything is controlled by knobs and buttons on a midi controller, as well as having various filters, and manipulative plugins which can be used to fuck with the signals creatively, and to filter the tracks together while beatmixing...
Our method also allows us to mix various parts of other tracks into the current track which really creates spontaneous psychedelic moments... we end up hearing things which we've never heard before, let alone the audience.
So at the end of the day, no backing tracks or cds are used at all, we have complete control of where the music is at at any moment, but we don't ALWAYS have control of every sound within each part. I think this compromise has been a good decision to make, as it means we can rock the dancefloor harder than we could in the past due to compositional ease.
We're always developing our live method so I'm sure soon enough we'll sort out ways to get even more control over each individual sound without losing the ability to easily slam into a fat change... The other limitation is CPU power. while computers are pretty stable these days we dont like to risk the chance of having a crash or glitch while playing so we go easy on how hard we push the cpu.
So i think you can add Mantrix to your live list
