A Bregman Divergence Optimization Framework for Ranking on Data Manifold and Its New Extensions

Recently, graph-based ranking algorithms have received considerable interests in machine learning, computer vision and information retrieval communities. Ranking on data manifold (or manifold ranking, MR) is one of the representative approaches. One of the limitations of manifold ranking is its high computational complexity (O(n3), where n is the number of samples in database). In this paper, we cast the manifold ranking into a Bregman divergence optimization framework under which we transform the original MR to an equivalent optimal kernel matrix learning problem.With this new formulation, two effective and efficient extensions are proposed to enhance the ranking performance. Extensive experimental results on two real world image databases show the effectiveness of the proposed approach.

[1]  Yixin Chen,et al.  Ranking on Data Manifold with Sink Points , 2013, IEEE Transactions on Knowledge and Data Engineering.

[2]  Nicolas Le Roux,et al.  Out-of-Sample Extensions for LLE, Isomap, MDS, Eigenmaps, and Spectral Clustering , 2003, NIPS.

[3]  Shuicheng Yan,et al.  Near-duplicate keyframe retrieval by nonrigid image matching , 2008, ACM Multimedia.

[4]  Michael I. Jordan,et al.  Distance Metric Learning with Application to Clustering with Side-Information , 2002, NIPS.

[5]  Chun Chen,et al.  Efficient manifold ranking for image retrieval , 2011, SIGIR.

[6]  Xiaofei He,et al.  Laplacian Regularized D-Optimal Design for Active Learning and Its Application to Image Retrieval , 2010, IEEE Transactions on Image Processing.

[7]  Bernhard Schölkopf,et al.  Learning with Local and Global Consistency , 2003, NIPS.

[8]  Hinrich Schütze,et al.  Introduction to information retrieval , 2008 .

[9]  Jiawei Han,et al.  Learning a Maximum Margin Subspace for Image Retrieval , 2008, IEEE Transactions on Knowledge and Data Engineering.

[10]  Joachim M. Buhmann,et al.  Distortion Invariant Object Recognition in the Dynamic Link Architecture , 1993, IEEE Trans. Computers.

[11]  Tie-Yan Liu,et al.  Learning to rank for information retrieval , 2009, SIGIR.

[12]  Matti Pietikäinen,et al.  A comparative study of texture measures with classification based on featured distributions , 1996, Pattern Recognit..

[13]  Meng Wang,et al.  Manifold-ranking based video concept detection on large database and feature pool , 2006, MM '06.

[14]  Xiaojun Wan,et al.  Manifold-Ranking Based Topic-Focused Multi-Document Summarization , 2007, IJCAI.

[15]  Jiawei Han,et al.  Regularized regression on image manifold for retrieval , 2007, MIR '07.

[16]  Jonathon Shlens,et al.  A Tutorial on Principal Component Analysis , 2014, ArXiv.

[17]  Luo Si,et al.  Collaborative image retrieval via regularized metric learning , 2006, Multimedia Systems.

[18]  LiuWei,et al.  Semi-supervised distance metric learning for collaborative image retrieval and clustering , 2010 .

[19]  Jingrui He,et al.  Generalized Manifold-Ranking-Based Image Retrieval , 2006, IEEE Transactions on Image Processing.

[20]  Wei Liu,et al.  Semi-supervised distance metric learning for collaborative image retrieval and clustering , 2010, ACM Trans. Multim. Comput. Commun. Appl..

[21]  Jiawei Han,et al.  Spectral regression: a unified subspace learning framework for content-based image retrieval , 2007, ACM Multimedia.

[22]  John F. Canny,et al.  A Computational Approach to Edge Detection , 1986, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[23]  L. Bregman.  The relaxation method of finding the common point of convex sets and its application to the solution of problems in convex programming , 1967 .

[24]  Inderjit S. Dhillon,et al.  Information-theoretic metric learning , 2006, ICML '07.

[25]  Fan Chung,et al.  Spectral Graph Theory , 1996 .

[26]  Jingrui He,et al.  Manifold-ranking based image retrieval , 2004, MULTIMEDIA '04.

[27]  Kun Zhou,et al.  Laplacian optimal design for image retrieval , 2007, SIGIR.

[28]  Bernhard Schölkopf,et al.  Ranking on Data Manifolds , 2003, NIPS.

[29]  Yi Liu,et al.  An Efficient Algorithm for Local Distance Metric Learning , 2006, AAAI.

[30]  Inderjit S. Dhillon,et al.  Learning low-rank kernel matrices , 2006, ICML.

[31]  Sergey Brin,et al.  The Anatomy of a Large-Scale Hypertextual Web Search Engine , 1998, Comput. Networks.