CVPR Daily - 2019 Thursday

missing sensor measurements. Like in this case of motion detection. I actually think it might be useful even for motion tracking – I’m wearing a Fitbit right now. We’ve also thought about cases where sensor measurements are corrupted, possibly in chemical system monitoring. It’s not clear, but I think that maybe the broader picture is that any sufficiently complex phenomenon is probably not exactly a low- dimensional subspace. That depends on the coordinates in which you’ve measured it matching something important about the structure of the phenomenon. It’s not clear why that should be true for sufficiently complex phenomena, especially as you collect more and more and more data, you should be able to see that it’s not actually a low-dimensional subspace. It’s not flat. Our method allows you to adapt. As you get more and more data, then you’re allowed to start looking for this non-linear structure . ” Thinking about next steps for this work, Madeleine says she is interested in the deep structure. They know that there are ways that manifolds can wrap back on each other that would confuse this method in high dimensions, but one thing they don’t yet understand very well is when this mapping succeeds and when it fails. Also, when thinking about a low- dimensional manifold, a natural thing to think about is the internal coordinates within that manifold. This method doesn’t give you those. What this method gives you is a completion of the points in the original space, but it can’t tell you, for example, how close together two points are in the natural coordinates of the manifold. For Madeleine, that would be extremely valuable to know, so it would be her next target for this work. 16 DAILY CVPR Thursday Presentation Jicong Fan