Adaptive graph weighting for multi-view dimensionality reduction

Abstract Multi-view learning has become a flourishing topic in recent years since it can discover various informative structures with respect to disparate statistical properties. However, multi-view data fusion remains challenging when exploring a proper way to find shared while complementary information. In this paper, we present an adaptive graph weighting scheme to conduct semi-supervised multi-view dimensional reduction. Particularly, we construct a Laplacian graph for each view, and thus the final graph is approximately regarded as a centroid of these single view graphs with different weights. Based on the learned graph, a simple yet effective linear regression function is employed to project data into a low-dimensional space. In addition, our proposed scheme can be well extended to an unsupervised version within a unified framework. Extensive experiments on varying benchmark datasets illustrate that our proposed scheme is superior to several state-of-the-art semi-supervised/unsupervised multi-view dimensionality reduction methods. Last but not least, we demonstrate that our proposed scheme provides a unified view to explain and understand a family of traditional schemes.

[1]  Johan A. K. Suykens,et al.  Least Squares Support Vector Machines , 2002 .

[2]  Wei-Yun Yau,et al.  Structured AutoEncoders for Subspace Clustering , 2018, IEEE Transactions on Image Processing.

[3]  Terence Sim,et al.  The CMU Pose, Illumination, and Expression Database , 2003, IEEE Trans. Pattern Anal. Mach. Intell..

[4]  Mikhail Belkin,et al.  Laplacian Eigenmaps and Spectral Techniques for Embedding and Clustering , 2001, NIPS.

[5]  Masashi Sugiyama,et al.  Dimensionality Reduction of Multimodal Labeled Data by Local Fisher Discriminant Analysis , 2007, J. Mach. Learn. Res..

[6]  Ion Muslea,et al.  Active Learning with Multiple Views , 2009, Encyclopedia of Data Warehousing and Mining.

[7]  Tao Jiang,et al.  Efficient and robust feature extraction by maximum margin criterion , 2003, IEEE Transactions on Neural Networks.

[8]  Jiawei Han,et al.  Spectral Regression for Efficient Regularized Subspace Learning , 2007, 2007 IEEE 11th International Conference on Computer Vision.

[9]  Ulf Brefeld,et al.  Co-EM support vector learning , 2004, ICML.

[10]  Jieping Ye,et al.  Multi-class Discriminant Kernel Learning via Convex Programming , 2008, J. Mach. Learn. Res..

[11]  Stephen Lin,et al.  Graph Embedding and Extensions: A General Framework for Dimensionality Reduction , 2007, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[12]  Ivor W. Tsang,et al.  Flexible Manifold Embedding: A Framework for Semi-Supervised and Unsupervised Dimension Reduction , 2010, IEEE Transactions on Image Processing.

[13]  Xuelong Li,et al.  Parameter-Free Auto-Weighted Multiple Graph Learning: A Framework for Multiview Clustering and Semi-Supervised Classification , 2016, IJCAI.

[14]  Yoram Singer,et al.  Efficient projections onto the l1-ball for learning in high dimensions , 2008, ICML '08.

[15]  Avrim Blum,et al.  The Bottleneck , 2021, Monopsony Capitalism.

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

[17]  Shiliang Sun,et al.  Robust Co-Training , 2011, Int. J. Pattern Recognit. Artif. Intell..

[18]  R. Shah,et al.  Least Squares Support Vector Machines , 2022 .

[19]  Wei Liu,et al.  Transductive Component Analysis , 2008, 2008 Eighth IEEE International Conference on Data Mining.

[20]  Daoqiang Zhang,et al.  Semi-Supervised Dimensionality Reduction ∗ , 2007 .

[21]  Shuicheng Yan,et al.  Neighborhood preserving embedding , 2005, Tenth IEEE International Conference on Computer Vision (ICCV'05) Volume 1.

[22]  Yuxiao Hu,et al.  Face recognition using Laplacianfaces , 2005, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[23]  Feiping Nie,et al.  Re-Weighted Discriminatively Embedded $K$ -Means for Multi-View Clustering , 2017, IEEE Transactions on Image Processing.

[24]  Xuelong Li,et al.  Multi-View Clustering and Semi-Supervised Classification with Adaptive Neighbours , 2017, AAAI.

[25]  Zhenyu Huang,et al.  Multiple Marginal Fisher Analysis , 2019, IEEE Transactions on Industrial Electronics.

[26]  Shuicheng Yan,et al.  Graph Embedding and Extensions: A General Framework for Dimensionality Reduction , 2007 .

[27]  Derek Hoiem,et al.  Indoor Segmentation and Support Inference from RGBD Images , 2012, ECCV.

[28]  Lei Huang,et al.  Multi-View Complementary Hash Tables for Nearest Neighbor Search , 2015, 2015 IEEE International Conference on Computer Vision (ICCV).

[29]  David J. Kriegman,et al.  Eigenfaces vs. Fisherfaces: Recognition Using Class Specific Linear Projection , 1996, ECCV.

[30]  Mikhail Belkin,et al.  Manifold Regularization: A Geometric Framework for Learning from Labeled and Unlabeled Examples , 2006, J. Mach. Learn. Res..

[31]  Paul Geladi,et al.  Principal Component Analysis , 1987, Comprehensive Chemometrics.

[32]  Lei Huang,et al.  Query-Adaptive Hash Code Ranking for Large-Scale Multi-View Visual Search , 2016, IEEE Transactions on Image Processing.

[33]  Wei Liu,et al.  Semantic Structure-based Unsupervised Deep Hashing , 2018, IJCAI.

[34]  David G. Lowe,et al.  Distinctive Image Features from Scale-Invariant Keypoints , 2004, International Journal of Computer Vision.

[35]  Weiwei Liu,et al.  Making Decision Trees Feasible in Ultrahigh Feature and Label Dimensions , 2017, J. Mach. Learn. Res..

[36]  Xiaoyang Tan,et al.  Pattern Recognition , 2016, Communications in Computer and Information Science.

[37]  J. Lafferty,et al.  Combining active learning and semi-supervised learning using Gaussian fields and harmonic functions , 2003, ICML 2003.

[38]  Johan A. K. Suykens,et al.  L2-norm multiple kernel learning and its application to biomedical data fusion , 2010, BMC Bioinformatics.

[39]  Rama Chellappa,et al.  Hierarchical Multimodal Metric Learning for Multimodal Classification , 2017, 2017 IEEE Conference on Computer Vision and Pattern Recognition (CVPR).

[40]  H. Hotelling.  Relations Between Two Sets of Variates , 1936 .

[41]  Rongrong Ji,et al.  Visual Reranking through Weakly Supervised Multi-graph Learning , 2013, 2013 IEEE International Conference on Computer Vision.

[42]  G LoweDavid,et al.  Distinctive Image Features from Scale-Invariant Keypoints , 2004 .

[43]  David J. Kriegman,et al.  From Few to Many: Illumination Cone Models for Face Recognition under Variable Lighting and Pose , 2001, IEEE Trans. Pattern Anal. Mach. Intell..

[44]  Feiping Nie,et al.  Efficient and Robust Feature Selection via Joint ℓ2, 1-Norms Minimization , 2010, NIPS.

[45]  D. B. Graham,et al.  Characterising Virtual Eigensignatures for General Purpose Face Recognition , 1998 .

[46]  Antonio Torralba,et al.  Modeling the Shape of the Scene: A Holistic Representation of the Spatial Envelope , 2001, International Journal of Computer Vision.

[47]  Feiping Nie,et al.  Adaptive-weighting discriminative regression for multi-view classification , 2019, Pattern Recognit..

[48]  Heng Tao Shen,et al.  Principal Component Analysis , 2009, Encyclopedia of Biometrics.

[49]  Shinichi Nakajima,et al.  Semi-supervised local Fisher discriminant analysis for dimensionality reduction , 2009, Machine Learning.

[50]  Jiawei Han,et al.  Semi-supervised Discriminant Analysis , 2007, 2007 IEEE 11th International Conference on Computer Vision.

[51]  Weiwei Liu,et al.  Metric Learning for Multi-Output Tasks , 2019, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[52]  Daoqiang Zhang,et al.  Efficient and robust feature extraction by maximum margin criterion , 2003, IEEE Transactions on Neural Networks.

[53]  Jianxiong Xiao,et al.  SUN RGB-D: A RGB-D scene understanding benchmark suite , 2015, 2015 IEEE Conference on Computer Vision and Pattern Recognition (CVPR).

[54]  Weiwei Liu,et al.  An Easy-to-hard Learning Paradigm for Multiple Classes and Multiple Labels , 2017, J. Mach. Learn. Res..

[55]  Mikhail Belkin,et al.  Linear Manifold Regularization for Large Scale Semi-supervised Learning , 2005 .