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[1701.08381] Random Forest regression for manifold-valued responses
An increasing array of biomedical and computer vision applications requires the predictive modeling of complex data, for example images and shapes. The main challenge when predicting such objects lies in the fact that they do not comply to the assumptions of Euclidean geometry. Rather, they occupy non-linear spaces, a.k.a. manifolds, where it is difficult to define concepts such as coordinates, vectors and expected values. In this work, we construct a non-parametric predictive methodology for manifold-valued objects, based on a distance modification of the Random Forest algorithm. Our method is versatile and can be applied both in cases where the response space is a well-defined manifold, but also when such knowledge is not available. Model fitting and prediction phases only require the definition of a suitable distance function for the observed responses. We validate our methodology using simulations and apply it on a series of illustrative image completion applications, showcasing superior predictive performance, compared to various established regression methods.
machine-learning  representation  to-understand  regression  metrics  distance-measures 
yesterday by Vaguery
[0806.1416] Highway Hull Revisited
A highway H is a line in the plane on which one can travel at a greater speed than in the remaining plane. One can choose to enter and exit H at any point. The highway time distance between a pair of points is the minimum time required to move from one point to the other, with optional use of H.
The highway hull HH(S,H) of a point set S is the minimal set containing S as well as the shortest paths between all pairs of points in HH(S,H), using the highway time distance.
We provide a Theta(n log n) worst-case time algorithm to find the highway hull under the L_1 metric, as well as an O(n log^2 n) time algorithm for the L_2 metric which improves the best known result of O(n^2).
We also define and construct the useful region of the plane: the region that a highway must intersect in order that the shortest path between at least one pair of points uses the highway.
metrics  computational-geometry  optimization  rather-interesting  mathematical-recreations  to-write-about  consider:planning  consider:highway-positioning 
3 days ago by Vaguery
Open source Java APM
java  apm  metrics  logging  monitoring 
3 days ago by wjy

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