Monthly Archives: March 2010

I recently read articles on paleomagnetism. It is common to make the assumption of antipodal symmetry for the distribution of the dispersion of the directions. Two such spherical distributions (directional statistics) with such an antipodal symmetry are the Bingham and

Olivier was kind enough to provide this report trip on the French computational geometry days, as known as JGA 2010. The plenary speaker slides are online and worth a check. The Journées de Géométrie Algorithmique are the main French-speaking meeting about computational

Tensors are square symmetric positive-definite matrix. They are surprisingly in 1-to-1 mapping with symmetric matrices through matrix exponentiation (exp.log computed on the diagonal elements of the spectral decomposition). I said surprisingly because tensors are symmetric and therefore a proper subset

Shannon entropy is said additive in the sense that the entropy of the joint distribution H(X*Y) is the sum of the entropies: H(X*Y) = H(X)+H(Y). This property is not true for the quadratic entropy (sum of squares). The Java program

How do we visualize relationships in the jungle of (statistical) distances? I tried to give insights at a glance with this poster.

A long time ago, well in 1996, I investigated output-sensitive algorithms. I then designed an algorithm for peeling iteratively the convex hulls of a 2D point set. This yields the notion of depth of a point set, and is a

The center of mass (=centroid) is defined as the center point minimizing the squared of the Euclidean distances (=variance). If one of the source point is an outlier corrupting your dataset, and if that outlier goes to infinity, then your

They are only 6 exponential family distributions that admit variance as a quadratic function (QVF=quadratic variance function) of the parameter. For the multivariate case, it is a bit more complex but well defined and studied: The $2d+4$ simple quadratic natural