The Experts below are selected from a list of 160908 Experts worldwide ranked by ideXlab platform
Ichiro Takeuchi - One of the best experts on this subject based on the ideXlab platform.
-
Multi-parametric solution-Path Algorithm for instance-weighted support vector machines
Machine Learning, 2012Co-Authors: Masayuki Karasuyama, Masashi Sugiyama, Naoyuki Harada, Ichiro TakeuchiAbstract:An instance-weighted variant of the support vector machine (SVM) has attracted considerable attention recently since they are useful in various machine learning tasks such as non-stationary data analysis, heteroscedastic data modeling, transfer learning, learning to rank, and transduction. An important challenge in these scenarios is to overcome the computational bottleneck—instance weights often change dynamically or adaptively, and thus the weighted SVM solutions must be repeatedly computed. In this paper, we develop an Algorithm that can efficiently and exactly update the weighted SVM solutions for arbitrary change of instance weights. Technically, this contribution can be regarded as an extension of the conventional solution-Path Algorithm for a single regularization parameter to multiple instance-weight parameters. However, this extension gives rise to a significant problem that breakpoints (at which the solution Path turns) have to be identified in high-dimensional space. To facilitate this, we introduce a parametric representation of instance weights. We also provide a geometric interpretation in weight space using a notion of critical region : a polyhedron in which the current affine solution remains to be optimal. Then we find breakpoints at intersections of the solution Path and boundaries of polyhedrons. Through extensive experiments on various practical applications, we demonstrate the usefulness of the proposed Algorithm.
Peter Sanders - One of the best experts on this subject based on the ideXlab platform.
-
δ stepping a parallelizable shortest Path Algorithm
European Symposium on Algorithms, 2003Co-Authors: Ulrich Meyer, Peter SandersAbstract:The single source shortest Path problem for arbitrary directed graphs with n nodes, m edges and nonnegative edge weights can sequentially be solved using O(n.log n + m) operations. However, no work-efficient parallel Algorithm is known that runs in sublinear time for arbitrary graphs. In this paper we present a rather simple Algorithm for the single source shortest Path problem. Our new Algorithm, which we call Delta-stepping, can be implemented very efficiently in sequential and parallel setting for a large class of graphs. For random edge weights and arbitrary graphs with maximum node degree d, sequential Δ-stepping needs O(n + m + d.L) total average-case time, where L denotes the maximum shortest Path weight from the source node s to any node reachable from s. For example, this means linear time on directed graphs with constant maximum degree. Our best parallel version for a PRAM takes O(d.L.log n + log 2 n) time and O(n + m + d L.log n) work on average. For random graphs, even O(log 2 n) time and O(n + m) work on average can be achieved. We also discuss how the Algorithm can be adapted to work with nonrandom edge weights and how it can be implemented on distributed memory machines. Experiments indicate that already a simple implementation of the Algorithm achieves significant speedup on real machines.
Masayuki Karasuyama - One of the best experts on this subject based on the ideXlab platform.
-
Multi-parametric solution-Path Algorithm for instance-weighted support vector machines
Machine Learning, 2012Co-Authors: Masayuki Karasuyama, Masashi Sugiyama, Naoyuki Harada, Ichiro TakeuchiAbstract:An instance-weighted variant of the support vector machine (SVM) has attracted considerable attention recently since they are useful in various machine learning tasks such as non-stationary data analysis, heteroscedastic data modeling, transfer learning, learning to rank, and transduction. An important challenge in these scenarios is to overcome the computational bottleneck—instance weights often change dynamically or adaptively, and thus the weighted SVM solutions must be repeatedly computed. In this paper, we develop an Algorithm that can efficiently and exactly update the weighted SVM solutions for arbitrary change of instance weights. Technically, this contribution can be regarded as an extension of the conventional solution-Path Algorithm for a single regularization parameter to multiple instance-weight parameters. However, this extension gives rise to a significant problem that breakpoints (at which the solution Path turns) have to be identified in high-dimensional space. To facilitate this, we introduce a parametric representation of instance weights. We also provide a geometric interpretation in weight space using a notion of critical region : a polyhedron in which the current affine solution remains to be optimal. Then we find breakpoints at intersections of the solution Path and boundaries of polyhedrons. Through extensive experiments on various practical applications, we demonstrate the usefulness of the proposed Algorithm.
Tang Zhuo - One of the best experts on this subject based on the ideXlab platform.
-
Research on the Single Source Shortest Path Algorithm Using MapReduce
Microcomputer Information, 2011Co-Authors: Tang ZhuoAbstract:Via the analysis to implementation process of mapreduce, aimming at the problem that single source shortest Path Algorithm is hard to be used with the appearance and development of cloud computing and the problem of searching efficiency,a parallel single source shortest Path Algorithm based on mapreduce framework is designed and implemented .research and experiment are done based on hadoop platform.As shown by the experimental results,the proposed Algorithm can search the single source shortest Path efficiently in the whole graphic structure,and its good performance is testified.
Trevor Hastie - One of the best experts on this subject based on the ideXlab platform.
-
l1 regularization Path Algorithm for generalized linear models
Journal of The Royal Statistical Society Series B-statistical Methodology, 2007Co-Authors: Mee Young Park, Trevor HastieAbstract:Summary. We introduce a Path following Algorithm for L1‐regularized generalized linear models. The L1‐regularization procedure is useful especially because it, in effect, selects variables according to the amount of penalization on the L1‐norm of the coefficients, in a manner that is less greedy than forward selection–backward deletion. The generalized linear model Path Algorithm efficiently computes solutions along the entire regularization Path by using the predictor–corrector method of convex optimization. Selecting the step length of the regularization parameter is critical in controlling the overall accuracy of the Paths; we suggest intuitive and flexible strategies for choosing appropriate values. We demonstrate the implementation with several simulated and real data sets.
