Results 1  10
of
17
www.pharmacypractice.org (ISSN: 18863655) 59
"... Deterioration of the medication adherence for elderly could result in wasteful medical expenditure in a longterm span as well as aggravating the patient's medical condition. Objective: This study surveyed the effect of onedose package medication made up by a pharmacist on the patient's b ..."
Abstract
 Add to MetaCart
's behavior towards medication, what is expected to be one of the measures to improve the medication adherence for elderly. Methods: With support activity of the Pharmacist Association in Uedacity in Nagano Prefecture, Japan, the survey form of onedose package was sent to 86 pharmacy directors located
Minimizing Discrete Convex Functions with Linear Inequality Constraints
, 2008
"... A class of discrete convex functions that can efficiently be minimized has been considered by Murota. Among them are L♮convex functions, which are natural extensions of submodular set functions. We first consider the problem of minimizing an L ♮convex function with a linear inequality constraint h ..."
Abstract
 Add to MetaCart
extension can be solved in polynomial time by using a binary search for an optimal Lagrange multiplier and by adopting Nagano’s algorithm for the intersection of line and a base polyhedron. The latter can also be solved in polynomial time by an approach similar to that for L♮convex functions, based on a
Sizeconstrained Submodular Minimization through Minimum Norm Base
"... A number of combinatorial optimization problems in machine learning can be described as the problem of minimizing a submodular function. It is known that the unconstrained submodular minimization problem can be solved in strongly polynomial time. However, additional constraints make the problem intr ..."
Abstract

Cited by 10 (1 self)
 Add to MetaCart
A number of combinatorial optimization problems in machine learning can be described as the problem of minimizing a submodular function. It is known that the unconstrained submodular minimization problem can be solved in strongly polynomial time. However, additional constraints make the problem intractable in many settings. In this paper, we discuss the submodular minimization under a size constraint, which is NPhard, and generalizes the densest subgraph problem and the uniform graph partitioning problem. Because of NPhardness, it is difficult to compute an optimal solution even for a prescribed size constraint. In our approach, we do not give approximation algorithms. Instead, the proposed algorithm computes optimal solutions for some of possible size constraints in polynomial time. Our algorithm utilizes the basic polyhedral theory associated with submodular functions. Additionally, we evaluate the performance of the proposed algorithm through computational experiments. 1.
A Strongly Polynomial Algorithm for Line Search in Submodular Polyhedra
 Proceedings of the 4th JapaneseHungarian Symposium on Discrete Mathematics and Its Applications
, 2005
"... A submodular polyhedron is a polyhedron associated with a submodular function. This paper presents a strongly polynomial time algorithm for line search in submodular polyhedra with the aid of a fully combinatorial algorithm for submodular function minimization. The algorithm is based on the parametr ..."
Abstract

Cited by 9 (1 self)
 Add to MetaCart
A submodular polyhedron is a polyhedron associated with a submodular function. This paper presents a strongly polynomial time algorithm for line search in submodular polyhedra with the aid of a fully combinatorial algorithm for submodular function minimization. The algorithm is based on the parametric search method proposed by Megiddo. 1
Submodularity cuts and applications
 In Adv. NIPS 22
, 2009
"... Several key problems in machine learning, such as feature selection and active learning, can be formulated as submodular set function maximization. We present herein a novel algorithm for maximizing a submodular set function under a cardinality constraint — the algorithm is based on a cuttingplane ..."
Abstract

Cited by 9 (3 self)
 Add to MetaCart
Several key problems in machine learning, such as feature selection and active learning, can be formulated as submodular set function maximization. We present herein a novel algorithm for maximizing a submodular set function under a cardinality constraint — the algorithm is based on a cuttingplane method and is implemented as an iterative smallscale binaryinteger linear programming procedure. It is well known that this problem is NPhard, and the approximation factor achieved by the greedy algorithm is the theoretical limit for polynomial time. As for (nonpolynomial time) exact algorithms that perform reasonably in practice, there has been very little in the literature although the problem is quite important for many applications. Our algorithm is guaranteed to find the exact solution finitely many iterations, and it converges fast in practice due to the efficiency of the cuttingplane mechanism. Moreover, we also provide a method that produces successively decreasing upperbounds of the optimal solution, while our algorithm provides successively increasing lowerbounds. Thus, the accuracy of the current solution can be estimated at any point, and the algorithm can be stopped early once a desired degree of tolerance is met. We evaluate our algorithm on sensor placement and feature selection applications showing good performance. 1
Minimum average cost clustering
 In Advances in Neural Information Processing Systems 23
, 2010
"... A number of objective functions in clustering problems can be described with submodular functions. In this paper, we introduce the minimum average cost criterion, and show that the theory of intersecting submodular functions can be used for clustering with submodular objective functions. The propose ..."
Abstract

Cited by 8 (2 self)
 Add to MetaCart
A number of objective functions in clustering problems can be described with submodular functions. In this paper, we introduce the minimum average cost criterion, and show that the theory of intersecting submodular functions can be used for clustering with submodular objective functions. The proposed algorithm does not require the number of clusters in advance, and it will be determined by the property of a given set of data points. The minimum average cost clustering problem is parameterized with a real variable, and surprisingly, we show that all information about optimal clusterings for all parameters can be computed in polynomial time in total. Additionally, we evaluate the performance of the proposed algorithm through computational experiments. 1
The algebraic combinatorial approach for lowrank matrix completion
 CoRR
"... We present a novel algebraic combinatorial view on lowrank matrix completion based on studying relations between a few entries with tools from algebraic geometry and matroid theory. The intrinsic locality of the approach allows for the treatment of single entries in a closed theoretical and practic ..."
Abstract

Cited by 10 (2 self)
 Add to MetaCart
We present a novel algebraic combinatorial view on lowrank matrix completion based on studying relations between a few entries with tools from algebraic geometry and matroid theory. The intrinsic locality of the approach allows for the treatment of single entries in a closed theoretical and practical framework. More specifically, apart from introducing an algebraic combinatorial theory of lowrank matrix completion, we present probabilityone algorithms to decide whether a particular entry of the matrix can be completed. We also describe methods to complete that entry from a few others, and to estimate the error which is incurred by any method completing that entry. Furthermore, we show how known results on matrix completion and their sampling assumptions can be related to our new perspective and interpreted in terms of a completability phase transition. On this revision This revision version 4 is both abridged and extended in terms of exposition and results, as compared to version 3 Király et al. (2013). The theoretical foundations are developed in a more adhoc way which allow to reach the main statements and algorithmic implications more quickly. Version 3 contains a more principled derivation of the theory, more related results (e.g., estimation of missing entries and its consistency, representations for the determinantal matroid, detailed examples), but a focus which is further away from applications. A reader who is interested in both is invited to read the main parts of version 4 first, then go through version 3 for a more detailed view on the theory. 1.
L Balanced Clustering via Discrete DC Programming
, 1
"... c©The author(s) of this report reserves all the rights. We address the balanced clustering problem where cluster sizes are regularized with submodular functions. The objective function for balanced clustering is the ratio of two submodular functions, and thus includes the wellknown ratio cut and n ..."
Abstract
 Add to MetaCart
c©The author(s) of this report reserves all the rights. We address the balanced clustering problem where cluster sizes are regularized with submodular functions. The objective function for balanced clustering is the ratio of two submodular functions, and thus includes the wellknown ratio cut and normalized cut as special cases. We present a novel algorithm for this problem using recent submodular optimization techniques. The main idea is to utilize an algorithm to minimize the difference of two submodular functions (discrete DC programming), combined with the discrete Newton method. Thus, it can be applied to the objective function involving any submodular functions in both the numerator and the denominator, which enables us to design flexible clustering setups. We also give theoretical analysis on the algorithm, and evaluate the performance through comparative experiments with conventional algorithms by artificial and realworld datasets. 1
Results 1  10
of
17