Computer Vision News - July 2019

She points out that there was some really nice work done by Laura Balzano , Rebecca Willett , Rob Nowak and Greg Ongie . They essentially had the same idea, but it’s too slow, and you can’t scale it to the kinds of sizes of data sets that are interesting in computer vision. To improve on that, this method adds a couple of critical components. One component that’s really important is that they don’t represent these vectors in this high- dimensional space explicitly. Instead they use a kernel map, because writing them down in this high-dimensional space would be too large. Then once they’ve kernelized, they’re able to rewrite the objective and rewrite all the penalties in a way so that it decomposes over the data points, and it allows them to train it online. One of the most interesting things about the online training is it means that they can adapt to a changing manifold. Imagine you’re watching someone run, or they’re running and they transition to walking and then they transition to jumping jacks. Their motion is quite complex. You might imagine that all of human motion lives in some low-dimensional manifold, in the space of all possible coordinates of every point in the body, but it’s a much lower-dimensional manifold if you just look at jumping jacks or if you just look at running. By learning online, they’re able to learn this transition and figure out, for example, if they started jumping jacks, they learn the jumping jacks manifold, or if they’ve started running, they learn the running manifold. Because of this they can learn much lower-dimensional manifolds and learn it much faster and get better accuracy than offline methods. Normally online methods don’t perform as well as offline methods because they’re using the information less efficiently, but for them, the online method performs better because they can adapt to quick changes in the kind of motion. How can this be applied practically in the real world? Madeleine explains: “ Some of the things that we’ve considered are using it to adapt to 29 DAILY CVPR Thursday Online High Rank Matrix Completion " 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." “… this method adds a couple of critical components"