The L1-norm best-fit hyperplane problem
نویسندگان
چکیده
منابع مشابه
The L1-norm best-fit hyperplane problem
We formalize an algorithm for solving the L(1)-norm best-fit hyperplane problem derived using first principles and geometric insights about L(1) projection and L(1) regression. The procedure follows from a new proof of global optimality and relies on the solution of a small number of linear programs. The procedure is implemented for validation and testing. This analysis of the L(1)-norm best-fi...
متن کاملDynamic Point Selection for the L1 Norm Hyperplane Separation Problem
L1 norm discrimination consists in finding the hyperplane that minimizes the sum of L1 norm distances between the hyperplane and the points that lie on the wrong side of the hyperplane. This problem is difficult for datasets containing more than 100,000 points. Since few points are needed to obtain the optimal hyperplane, we propose a point selection algorithm which iteratively adds the necessa...
متن کاملBest one-sided approximation of polynomials under L1 norm
In this paper, we develop an analytic solution for the best one-sided approximation of polynomials under L1 norm, that is, we 0nd two polynomials with lower degree which bound the given polynomial such that the areas between the bounding polynomials and the given polynomial attain minimum. The key ingredient of our technique is a characterization for one-sided approximations based on orthogonal...
متن کاملSolving the Graph Cut Problem via l1 Norm Minimization
Graph cuts have become an increasingly important tool for solving a number of energy minimization problems in computer vision and other fields. In this paper, the graph cut problem is reformulated as an unconstrained l1 norm minimization. This l1 norm minimization can then be tackled by solving a sequence of sparse linear systems involving the Laplacian of the underlying graph. The proposed pro...
متن کاملL1-norm Kernel PCA
We present the first model and algorithm for L1-norm kernel PCA. While L2-norm kernel PCA has been widely studied, there has been no work on L1-norm kernel PCA. For this non-convex and non-smooth problem, we offer geometric understandings through reformulations and present an efficient algorithm where the kernel trick is applicable. To attest the efficiency of the algorithm, we provide a conver...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Applied Mathematics Letters
سال: 2013
ISSN: 0893-9659
DOI: 10.1016/j.aml.2012.03.031