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Convex piecewise-linear fitting
We consider the problem of fitting a convex piecewise-linear function, with some specified form, to given multi-dimensional data. Except for a few special cases, this problem is hard to solve exactly, so we focus on heuristic methods that find locally optimal fits. The method we describe, which is a variation on the K-means algorithm for clustering, seems to work well in practice, at least on d...
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We consider the problem of fitting a continuous piecewise linear function to a finite set of data points, modeled as a mathematical program with convex objective. We review some fitting problems that can be modeled as convex programs, and then introduce mixed-binary generalizations that allow variability in the regions defining the best-fit function’s domain. We also study the additional constr...
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Given a set of n data points (xi, yi, zi) ∈ [0, 1] , two methods are established for constructing two piecewise linear copulas, respectively denoted CA(x, y) and CB(x, y), in such a way that CA(xi, yi) and CB(xi, yi) both yield an approximation of zi for all i. If the data points are (randomly) sampled from an unknown copula C, i.e. zi = C(xi, yi), then CA and CB provide two piecewise linear es...
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ژورنال
عنوان ژورنال: Optimization and Engineering
سال: 2008
ISSN: 1389-4420,1573-2924
DOI: 10.1007/s11081-008-9045-3