A Computational Approach to Edge Detection
IEEE Transactions on Pattern Analysis and Machine Intelligence
Matrix computations (3rd ed.)
Authoritative sources in a hyperlinked environment
Journal of the ACM (JACM)
Support vector machine active learning for image retrieval
MULTIMEDIA '01 Proceedings of the ninth ACM international conference on Multimedia
Distortion Invariant Object Recognition in the Dynamic Link Architecture
IEEE Transactions on Computers
The CMU Pose, Illumination, and Expression Database
IEEE Transactions on Pattern Analysis and Machine Intelligence
Manifold-ranking based image retrieval
Proceedings of the 12th annual ACM international conference on Multimedia
ICML '06 Proceedings of the 23rd international conference on Machine learning
Manifold-ranking based video concept detection on large database and feature pool
MULTIMEDIA '06 Proceedings of the 14th annual ACM international conference on Multimedia
Introduction to Information Retrieval
Introduction to Information Retrieval
Geometric Mean for Subspace Selection
IEEE Transactions on Pattern Analysis and Machine Intelligence
Proceedings of the 18th international conference on World wide web
Personalized tag recommendation using graph-based ranking on multi-type interrelated objects
Proceedings of the 32nd international ACM SIGIR conference on Research and development in information retrieval
Manifold-ranking based topic-focused multi-document summarization
IJCAI'07 Proceedings of the 20th international joint conference on Artifical intelligence
LIBSVM: A library for support vector machines
ACM Transactions on Intelligent Systems and Technology (TIST)
Efficient manifold ranking for image retrieval
Proceedings of the 34th international ACM SIGIR conference on Research and development in Information Retrieval
Semi-supervised ranking on very large graphs with rich metadata
Proceedings of the 17th ACM SIGKDD international conference on Knowledge discovery and data mining
An iterated graph laplacian approach for ranking on manifolds
Proceedings of the 17th ACM SIGKDD international conference on Knowledge discovery and data mining
IEEE Transactions on Multimedia
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Recently, ranking data with respect to the intrinsic geometric structure (manifold ranking) has received considerable attentions, with encouraging performance in many applications in pattern recognition, information retrieval and recommendation systems. Most of the existing manifold ranking methods focus on learning a ranking function that varies smoothly along the data manifold. However, beyond smoothness, a desirable ranking function should vary monotonically along the geodesics of the data manifold, such that the ranking order along the geodesics is preserved. In this article, we aim to learn a ranking function that varies linearly and therefore monotonically along the geodesics of the data manifold. Recent theoretical work shows that the gradient field of a linear function on the manifold has to be a parallel vector field. Therefore, we propose a novel ranking algorithm on the data manifolds, called Parallel Field Ranking. Specifically, we try to learn a ranking function and a vector field simultaneously. We require the vector field to be close to the gradient field of the ranking function, and the vector field to be as parallel as possible. Moreover, we require the value of the ranking function at the query point to be the highest, and then decrease linearly along the manifold. Experimental results on both synthetic data and real data demonstrate the effectiveness of our proposed algorithm.