Introduction to Algorithms
Convex Optimization
Feature selection, L1 vs. L2 regularization, and rotational invariance
ICML '04 Proceedings of the twenty-first international conference on Machine learning
Efficient Learning of Label Ranking by Soft Projections onto Polyhedra
The Journal of Machine Learning Research
An Interior-Point Method for Large-Scale l1-Regularized Logistic Regression
The Journal of Machine Learning Research
Efficient projections onto the l1-ball for learning in high dimensions
Proceedings of the 25th international conference on Machine learning
IEEE Transactions on Information Theory
Large-scale sparse logistic regression
Proceedings of the 15th ACM SIGKDD international conference on Knowledge discovery and data mining
Multi-task feature learning via efficient l2, 1-norm minimization
UAI '09 Proceedings of the Twenty-Fifth Conference on Uncertainty in Artificial Intelligence
Learning incoherent sparse and low-rank patterns from multiple tasks
Proceedings of the 16th ACM SIGKDD international conference on Knowledge discovery and data mining
Distance metric learning from uncertain side information for automated photo tagging
ACM Transactions on Intelligent Systems and Technology (TIST)
The Journal of Machine Learning Research
Mining weakly labeled web facial images for search-based face annotation
Proceedings of the 34th international ACM SIGIR conference on Research and development in Information Retrieval
Fast Projections onto l1,q-norm balls for grouped feature selection
ECML PKDD'11 Proceedings of the 2011 European conference on Machine learning and knowledge discovery in databases - Volume Part III
Retrieval-based face annotation by weak label regularized local coordinate coding
MM '11 Proceedings of the 19th ACM international conference on Multimedia
Learning Incoherent Sparse and Low-Rank Patterns from Multiple Tasks
ACM Transactions on Knowledge Discovery from Data (TKDD)
New approximation algorithms for minimum enclosing convex shapes
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Simultaneous clustering and classification over cluster structure representation
Pattern Recognition
A continuous max-flow approach to minimal partitions with label cost prior
SSVM'11 Proceedings of the Third international conference on Scale Space and Variational Methods in Computer Vision
Statistical Analysis and Data Mining
Stochastic coordinate descent methods for regularized smooth and nonsmooth losses
ECML PKDD'12 Proceedings of the 2012 European conference on Machine Learning and Knowledge Discovery in Databases - Volume Part I
Supervised patient similarity measure of heterogeneous patient records
ACM SIGKDD Explorations Newsletter
Guided learning for role discovery (GLRD): framework, algorithms, and applications
Proceedings of the 19th ACM SIGKDD international conference on Knowledge discovery and data mining
FeaFiner: biomarker identification from medical data through feature generalization and selection
Proceedings of the 19th ACM SIGKDD international conference on Knowledge discovery and data mining
Towards efficient sparse coding for scalable image annotation
Proceedings of the 21st ACM international conference on Multimedia
Sparse activity and sparse connectivity in supervised learning
The Journal of Machine Learning Research
Trading regret for efficiency: online convex optimization with long term constraints
The Journal of Machine Learning Research
Lead-lag analysis via sparse co-projection in correlated text streams
Proceedings of the 22nd ACM international conference on Conference on information & knowledge management
Social trust prediction using rank-k matrix recovery
IJCAI'13 Proceedings of the Twenty-Third international joint conference on Artificial Intelligence
Bilinear discriminative dictionary learning for face recognition
Pattern Recognition
Shape from Sharp and Motion-Blurred Image Pair
International Journal of Computer Vision
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We consider the problem of computing the Euclidean projection of a vector of length n onto a closed convex set including the l1 ball and the specialized polyhedra employed in (Shalev-Shwartz & Singer, 2006). These problems have played building block roles in solving several l1-norm based sparse learning problems. Existing methods have a worst-case time complexity of O(n log n). In this paper, we propose to cast both Euclidean projections as root finding problems associated with specific auxiliary functions, which can be solved in linear time via bisection. We further make use of the special structure of the auxiliary functions, and propose an improved bisection algorithm. Empirical studies demonstrate that the proposed algorithms are much more efficient than the competing ones for computing the projections.