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High dimensional sequential regression on manifolds using adaptive hierarchical trees

We address nonlinear sequential regression in high dimensional settings when the data lies on a time varying manifold. We solve the curse of dimensionality by tracking the subspace of the underlying manifold using a hierarchical tree structure. Therefore, instead of using the original feature vectors as the input, we use the projections of the high dimensional feature space onto the underlying manifold. We provide significantly enhanced regression performance with considerably reduced computational complexity as well as memory requirement. We reduce the computational complexity to the order of the depth of the tree and the memory requirement to to the order of the intrinsic dimension of the manifold. We provide several experiments that validate the proposed algorithm and compare it with the other state of the art techniques.