Transformations and algorithms for least sum of squares hypersphere fitting
نویسندگان
چکیده
A problem from shape fitting is finding the sphere which has the least sum of squares fit to a set of points. Most current algorithms for this use an iterative process, with randomized restarting. We present, instead, two geometric transformations, and algorithms derived using them, which present alternate methods of solving the problem. We discuss running of these algorithms in three dimensions, and note the algorithms have favorable time complexities in high dimension. Finally, we present directions for future work.
منابع مشابه
Least-Squares Fitting of Circles and Ellipses∗
Fitting circles and ellipses to given points in the plane is a problem that arises in many application areas, e.g. computer graphics [1], coordinate metrology [2], petroleum engineering [11], statistics [7]. In the past, algorithms have been given which fit circles and ellipses in some least squares sense without minimizing the geometric distance to the given points [1], [6]. In this paper we p...
متن کاملLeast Squares Fitting of Circle and Ellipse
Fitting circles and ellipses to given points in the plane is a problem that arises in many application areas, e.g. computer graphics [1], coordinate metrology [2], petroleum engineering [11], statistics [7]. In the past, algorithms have been given which fit circles and ellipses in some least squares sense without minimizing the geometric distance to the given points [1], [6]. In this paper we p...
متن کاملAn Incremental DC Algorithm for the Minimum Sum-of-Squares Clustering
Here, an algorithm is presented for solving the minimum sum-of-squares clustering problems using their difference of convex representations. The proposed algorithm is based on an incremental approach and applies the well known DC algorithm at each iteration. The proposed algorithm is tested and compared with other clustering algorithms using large real world data sets.
متن کاملNew Approach in Fitting Linear Regression Models with the Aim of Improving Accuracy and Power
The main contribution of this work lies in challenging the common practice of inferential statistics in the realm of simple linear regression for attaining a higher degree of accuracy when multiple observations are available, at least, at one level of the regressor variable. We derive sufficient conditions under which one can improve the accuracy of the interval estimations at quite affordable ...
متن کاملPEDOMODELS FITTING WITH FUZZY LEAST SQUARES REGRESSION
Pedomodels have become a popular topic in soil science and environmentalresearch. They are predictive functions of certain soil properties based on other easily orcheaply measured properties. The common method for fitting pedomodels is to use classicalregression analysis, based on the assumptions of data crispness and deterministic relationsamong variables. In modeling natural systems such as s...
متن کامل