a variant of the standard Cholesky decomposition) and it allows for down-dates.That means we can remove from a decomposition a previously-added vector.I then fit a multivariate normal distribution to the points in the set, and compute the entropy of this distribution.I also run some other computations, which involve evaluating the density at various points.we just read in corrupted points), we might even get away by simply storing the past couple decompositions and retrieving them.The Melenchon and Martinez paper outlines a relatively simple implementation if you are inclined to try your hand (in which case please publish it! Update on the matter: I looked around the Eigen library offers a rank update for their $LDL^T$ decomposition (ie.2008) are well-cited papers than can offer a good starting point.The whole idea is the "forgetting vector" to something very small will lead us to obtain essentially a new eigen-decomposition for $n 1$ points given we already have seen $n$ points.
It offers an online PCA implementation using incremental SVD (function functions if you want to take matters in your own hands more (for PCA-purposes incremental SVD will be much faster though).They have nice application papers that explain the relevant mechanics without getting to heavy into the numerics side of things.The papers "Incremental singular value decomposition of uncertain data with missing values" (Brand, 2002) and "Incremental learning for robust visual tracking" (Ross et al.However, it is well known that this formula can lead to serious instabilities in the presence of roundoff error.
If the system matrix is symmetric positive definite, it is almost always possible to use a representation based on the Cholesky decomposition which renders the same results (in exact arithmetic) at the same or less operational cost, but typically is much more numerically stable.What's needed is a way to iteratively update the decomposition of the covariance matrix, given the data point added to or removed from the set. If the data points had constant mean, this problem could be formulated in terms of rank one updates.