Towards Minimizing k-Submodular Functions
نویسندگان
چکیده
In this paper we investigate k-submodular functions. This natural family of discrete functions includes submodular and bisubmodular functions as the special cases k = 1 and k = 2 respectively. In particular we generalize the known Min-Max-Theorem for submodular and bisubmodular functions. This theorem asserts that the minimum of the (bi)submodular function can be found by solving a maximization problem over a (bi)submodular polyhedron. We define and investigate a k-submodular polyhedron and prove a Min-MaxTheorem for k-submodular functions.
منابع مشابه
Algorithms for Optimizing the Ratio of Submodular Functions
We investigate a new optimization problem involving minimizing the Ratio of two Submodular (RS) functions. We argue that this problem occurs naturally in several real world applications. We then show the connection between this problem and several related problems including minimizing the difference between submodular functions (Iyer & Bilmes, 2012b; Narasimhan & Bilmes, 2005), and to submodula...
متن کاملAlgorithms for Approximate Minimization of the Difference Between Submodular Functions, with Applications
We extend the work of Narasimhan and Bilmes [30] for minimizing set functions representable as a difference between submodular functions. Similar to [30], our new algorithms are guaranteed to monotonically reduce the objective function at every step. We empirically and theoretically show that the per-iteration cost of our algorithms is much less than [30], and our algorithms can be used to effi...
متن کاملSubmodular Optimization with Submodular Cover and Submodular Knapsack Constraints
We investigate two new optimization problems — minimizing a submodular function subject to a submodular lower bound constraint (submodular cover) and maximizing a submodular function subject to a submodular upper bound constraint (submodular knapsack). We are motivated by a number of real-world applications in machine learning including sensor placement and data subset selection, which require ...
متن کاملOn the Convergence Rate of Decomposable Submodular Function Minimization
Submodular functions describe a variety of discrete problems in machine learn-ing, signal processing, and computer vision. However, minimizing submodularfunctions poses a number of algorithmic challenges. Recent work introduced aneasy-to-use, parallelizable algorithm for minimizing submodular functions thatdecompose as the sum of “simple” submodular functions. Empirically, this ...
متن کاملSymmetric Submodular Clustering with Actionable Constraint
Clustering with submodular functions has been of interest over the last few years. Symmetric submodular functions are of particular interest as minimizing them is significantly more efficient and they include many commonly used functions in practice viz. graph cuts, mutual information. In this paper we propose a novel constraint to make clustering actionable which is motivated by applications a...
متن کامل