{"type":"ScholarlyArticle","title":"Locality Preserving Projections for Grassmann manifold","authors":[{"name":"Boyue Wang","slug":"boyue-wang","given":"Boyue","family":"Wang","affiliation":"Beijing Key Laboratory of Multimedia and Intelligent Software Technology , Faculty of Information Technology , Beijing University of Technology , Beijing , China"},{"name":"Yongli Hu","slug":"yongli-hu","given":"Yongli","family":"Hu","affiliation":"Beijing Key Laboratory of Multimedia and Intelligent Software Technology , Faculty of Information Technology , Beijing University of Technology , Beijing , China"},{"name":"Junbin Gao","slug":"junbin-gao","given":"Junbin","family":"Gao","affiliation":"Discipline of Business Analytics . The University of Sydney Business School ,"},{"name":"Yanfeng Sun","slug":"yanfeng-sun","given":"Yanfeng","family":"Sun","affiliation":"Beijing Key Laboratory of Multimedia and Intelligent Software Technology , Faculty of Information Technology , Beijing University of Technology , Beijing , China"},{"name":"Haoran Chen","slug":"haoran-chen","given":"Haoran","family":"Chen","affiliation":"Beijing Key Laboratory of Multimedia and Intelligent Software Technology , Faculty of Information Technology , Beijing University of Technology , Beijing , China; Beijing Ad- vanced Innovation Center for Future Internet Technology. Muham- mad Ali is with Charles Sturt University , Bathurst , Australia."},{"name":"Muhammad Ali","slug":"muhammad-ali","given":"Muhammad","family":"Ali","affiliation":"University of Sydney , NSW 2006 , Australia"},{"name":"Baocai Yin","slug":"baocai-yin","given":"Baocai","family":"Yin","affiliation":"Faculty of Electronic Information and Electrical Engineering , Dalian University of Technology , China; Beijing Key Laboratory of Multimedia and Intelligent Software Technology , Faculty of Information Technology , Beijing University of Technology , Beijing , China"}],"abstract":"Learning on Grassmann manifold has become popular in many computer vision tasks, with the strong capability to extract discriminative information for imagesets and videos. However, such learning algorithms particularly on high-dimensional Grassmann manifold always involve with significantly high computational cost, which seriously limits the applicability of learning on Grassmann manifold in more wide areas. In this research, we propose an unsupervised dimensionality reduction algorithm on Grassmann manifold based on the Locality Preserving Projections (LPP) criterion. LPP is a commonly used dimensionality reduction algorithm for vector-valued data, aiming to preserve local structure of data in the dimension-reduced space. The strategy is to construct a mapping from higher dimensional Grassmann manifold into the one in a relative low-dimensional with more discriminative capability.  The proposed method can be optimized as a basic eigenvalue problem. The performance of our proposed method is assessed on several classification and clustering tasks and the experimental results show show its clear advantages over other Grassmann based algorithms.","doi":"10.24963/ijcai.2017/403","url":"https://ijcai.org/proceedings/2017/403","pdf":"https://ijcai.org/proceedings/2017/0403.pdf","markdown":"https://ijcai.org/proceedings/2017/403.md","bibtex":"https://ijcai.org/proceedings/2017/bibtex/403","volume":{"slug":"2017","title":"Proceedings of the Twenty-Sixth International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2017","url":"https://ijcai.org/proceedings/2017/","year":2017,"location":"Melbourne, Australia","dates":"19-25 August 2017","editors":"Carles Sierra","isbn":"978-0-9992411-0-3","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2017"},"section":"Machine Learning S-Z","track":"Main track","number":403,"pages":{"first":2893,"last":2900},"keywords":["Machine Learning: Unsupervised Learning","Machine Learning: Machine Learning"],"videos":[],"references":[{"position":1,"raw":"[Absil et al., 2008] P.-A. Absil, Robert Mahony, and Rodolphe Sepulchre. Optimization Algorithms on Matrix Manifolds. Princeton University Press, 2008.","title":"Optimization Algorithms on Matrix Manifolds","authors":"P.-A Absil, Robert Mahony, Rodolphe Sepulchre","year":"2008","venue":null,"doi":null,"url":null,"internal_url":null},{"position":2,"raw":"[Bishop, 2006] Christopher M. Bishop. Pattern Recognition and Machine Learning (Information Science and Statis- tics). Springer-Verlag New York, Inc., Secaucus, NJ, USA, 2006.","title":"Pattern Recognition and Machine Learning (Information Science and Statistics)","authors":"Christopher M Bishop","year":"2006","venue":null,"doi":null,"url":null,"internal_url":null},{"position":3,"raw":"[Chen et al., 2007] Sibao Chen, Haifeng Zhao, Min Kong, and Bin Luo. 2D-LPP: A two-dimensional extension of locality preserving projections. Neurocomputing, 70:912- 921, 2007.","title":"2D-LPP: A two-dimensional extension of locality preserving projections","authors":"Chen","year":"2007","venue":"Neurocomputing","doi":null,"url":null,"internal_url":null},{"position":4,"raw":"[Comon, 1994] Pierre Comon. Independent component anal- ysis, a new concept? Signal Processing, 36(3):287-314, 1994.","title":"Pierre Comon. Independent component analysis, a new concept?","authors":"Comon","year":"1994","venue":"Signal Processing","doi":null,"url":null,"internal_url":null},{"position":5,"raw":"[Faraki et al., 2015] Masoud Faraki, Mehrtash T. Harandi, and Fatih. Porikli. More about VLAD: A leap from Eu- clidean to Riemannian manifolds. In CVPR, 2015.","title":"More about VLAD: A leap from Euclidean to Riemannian manifolds","authors":"Masoud Faraki, T Mehrtash, Fatih Harandi, Porikli","year":"2015","venue":"CVPR","doi":null,"url":null,"internal_url":null},{"position":6,"raw":"[Hamm and Lee, 2008] Jihun Hamm and Daniel D. Lee. Grassmann discriminant analysis: a unifying view on sub- space-based learning. In ICML, 2008.","title":"Grassmann discriminant analysis: a unifying view on subspace-based learning","authors":"Jihun Hamm, Daniel D Lee","year":"2008","venue":"ICML","doi":null,"url":null,"internal_url":null},{"position":7,"raw":"[Harandi et al., 2011] Mehrtash T. Harandi, Conrad Sander- son, Sareh Shirazi, and Brian C. Lovell. Graph embedding discriminant analysis on Grassmannian manifolds for im- proved image set matching. In CVPR, 2011.","title":"Graph embedding discriminant analysis on Grassmannian manifolds for improved image set matching","authors":"T Mehrtash, Conrad Harandi, Sareh Sanderson, Brian C Shirazi, Lovell","year":"2011","venue":"CVPR","doi":null,"url":null,"internal_url":null},{"position":8,"raw":"[Harandi et al., 2013] Mehrtash T. Harandi, Conrad Sander- son, Chunhua Shen, and Brain C. Lovell. Dictionary learn- ing and sparse coding on Grassmann manifolds: An extrin- sic solution. In ICCV, 2013.","title":"Dictionary learning and sparse coding on Grassmann manifolds: An extrinsic solution","authors":"Harandi","year":"2013","venue":"ICCV","doi":null,"url":null,"internal_url":null},{"position":9,"raw":"[Harandi et al., 2014] Mehrtash T. Harandi, Mathieu Salz- mann, and Richard Hartley. From manifold to manifold: Geometry-aware dimensionality reduction for SPD matri- ces. In ECCV, 2014.","title":"From manifold to manifold: Geometry-aware dimensionality reduction for SPD matrices","authors":"T Mehrtash, Harandi, Richard Mathieu Salzmann, Hartley","year":"2014","venue":"ECCV","doi":null,"url":null,"internal_url":null},{"position":10,"raw":"[Harandi et al., 2015] Mehrtash T. Harandi, Richard Hartley, Brian Lovell, and Conrad Sanderson. Sparse coding on symmetric positive definite manifolds using Bregman di- vergences. IEEE TNNLS, 27(6):1294-1306, 2015.","title":"Sparse coding on symmetric positive definite manifolds using Bregman divergences","authors":"T Mehrtash, Richard Harandi, Brian Hartley, Conrad Lovell, Sanderson","year":"2015","venue":"IEEE TNNLS","doi":null,"url":null,"internal_url":null},{"position":11,"raw":"[He and Niyogi, 2003] Xiaofei He and Partha Niyogi. Lo- cality preserving projections. In NIPS, 2003.","title":"Locality preserving projections","authors":"Xiaofei He, Partha Niyogi","year":"2003","venue":"NIPS","doi":null,"url":null,"internal_url":null},{"position":12,"raw":"[He et al., 2005] Xiaofei He, Deng Cai, Shuicheng Yan, and Hongjiang Zhang. Neighborhood preserving embedding. In ICCV, 2005.","title":"Neighborhood preserving embedding","authors":"Xiaofei He, Deng Cai, Shuicheng Yan, Hongjiang Zhang","year":"2005","venue":"ICCV","doi":null,"url":null,"internal_url":null},{"position":13,"raw":"[Huang et al., 2014] Zhiwu Huang, Ruiping Wang, Shiguang Shan, and Xilin Chen. Learning Euclidean- to-Riemannian metric for point-to-set classification. In CVPR, 2014.","title":"Learning Euclideanto-Riemannian metric for point-to-set classification","authors":"Zhiwu Huang, Ruiping Wang, Shiguang Shan, Xilin Chen","year":"2014","venue":"CVPR","doi":null,"url":null,"internal_url":null},{"position":14,"raw":"[Huang et al., 2015] Zhiwu Huang, Ruiping Wang, Shiguang Shan, and Xilin Chen. Projection metric learning on Grassmann manifold with application to video based face recognition. In CVPR, 2015.","title":"Projection metric learning on Grassmann manifold with application to video based face recognition","authors":"Zhiwu Huang, Ruiping Wang, Shiguang Shan, Xilin Chen","year":"2015","venue":"CVPR","doi":null,"url":null,"internal_url":null},{"position":15,"raw":"[Jayasumana et al., 2015] Sadeep Jayasumana, Richard Hartley, Mathieu Salzmann, Hongdong Li, and Mehrtash T. Harandi. Kernel methods on Riemannian manifolds with Gaussian RBF kernels. IEEE PAMI, 37(12):2464-2477, 2015.","title":"Kernel methods on Riemannian manifolds with Gaussian RBF kernels","authors":"Jayasumana","year":"2015","venue":"IEEE PAMI","doi":null,"url":null,"internal_url":null},{"position":16,"raw":"[Ju et al., 2015] Fujiao Ju, Yanfeng Sun, Junbin Gao, Yongli Hu, and Baocai Yin. Image outlier detection and feature extraction via L1-norm based 2D probabilis- tic PCA. IEEE TIP, 24(12):4834-4846, 2015.","title":"Image outlier detection and feature extraction via L1-norm based 2D probabilistic PCA","authors":"Ju","year":"2015","venue":"IEEE TIP","doi":null,"url":null,"internal_url":null},{"position":17,"raw":"[Kvalseth, 1987] Tarald O. Kvalseth. Entropy and correla- tion : Some comments. IEEE TSMC Part C, 17(3):517- 519, 1987.","title":"Entropy and correlation : Some comments","authors":"O Tarald, Kvalseth","year":"1987","venue":"IEEE TSMC Part C","doi":null,"url":null,"internal_url":null},{"position":18,"raw":"[Luo et al., 2016] Minnan Luo, Feiping Nie, Xiaojun Chang, Yi Yang, Alexander Hauptmann, and Qinghua Zheng. Avoiding optimal mean robust PCA/2DPCA with non- greedy ℓ 1 -norm maximization. In IJCAI, 2016.","title":"Avoiding optimal mean robust PCA/2DPCA with nongreedy ℓ 1 -norm maximization","authors":"Luo","year":"2016","venue":"IJCAI","doi":null,"url":null,"internal_url":null},{"position":19,"raw":"[Nguyen et al., 2008] Nam Nguyen, Wanquan Liu, and Svetha Venkatesh. Ridge regression for two dimensional locality preserving projection. In ICPR, 2008.","title":"Ridge regression for two dimensional locality preserving projection","authors":"Nguyen","year":"2008","venue":"ICPR","doi":null,"url":null,"internal_url":null},{"position":20,"raw":"[Pennec et al., 2006] Xavier Pennec, Pierre Fillard, and Nicholas Ayache. A Riemannian framework for tensor computing. IJCV, 66(1):41-66, 2006.","title":"A Riemannian framework for tensor computing","authors":"Xavier Pennec, Pierre Fillard, Nicholas Ayache","year":"2006","venue":"IJCV","doi":null,"url":null,"internal_url":null},{"position":21,"raw":"[Sun et al., 2010] Liang Sun, Betul Ceran, and Jieping Ye. A scalable two-stage approach for a class of dimensionality reduction techniques. In KDD, 2010.","title":"A scalable two-stage approach for a class of dimensionality reduction techniques","authors":"Liang Sun, Betul Ceran, Jieping Ye","year":"2010","venue":"KDD","doi":null,"url":null,"internal_url":null},{"position":22,"raw":"[Turaga et al., 2011] Pavan Turaga, Ashok Veeraraghavan, Anuj Srivastava, and Rama Chellappa. Statistical com- putations on Grassmann and Stiefel manifolds for image and video-based recognition. IEEE TPAMI, 33(11):2273- 2286, 2011.","title":"Statistical computations on Grassmann and Stiefel manifolds for image and video-based recognition","authors":"Pavan Turaga, Ashok Veeraraghavan, Anuj Srivastava, Rama Chellappa","year":"2011","venue":"IEEE TPAMI","doi":null,"url":null,"internal_url":null},{"position":23,"raw":"[Wang and Gao, 2016] Qianqian Wang and Quanxue Gao. Robust 2DPCA and its application. In CVPR, 2016.","title":"Robust 2DPCA and its application","authors":"Qianqian Wang, Quanxue Gao","year":"2016","venue":"CVPR","doi":null,"url":null,"internal_url":null},{"position":24,"raw":"[Wang et al., 2008] Haixian Wang, Sibao Chen, Zilan Hu, and Bin Luo. Probabilistic two-dimensional principal component analysis and its mixture model for face recog- nition. Neural Computing and Applications, 17(5-6):541- 547, 2008.","title":"Probabilistic two-dimensional principal component analysis and its mixture model for face recognition","authors":"Wang","year":"2008","venue":"Neural Computing and Applications","doi":null,"url":null,"internal_url":null},{"position":25,"raw":"[Wang et al., 2012] Rruiping Wang, Huimin Guo, LArry S. Davis, and Qionghai Dai. Covariance dis- criminative learning: A natural and efficient approach to image set classification. In CVPR, 2012.","title":"Covariance discriminative learning: A natural and efficient approach to image set classification","authors":"Rruiping Wang, Huimin Guo, Larry S Davis, Qionghai Dai","year":"2012","venue":"CVPR","doi":null,"url":null,"internal_url":null},{"position":26,"raw":"[Wang et al., 2016] Boyue Wang, Yongli Hu, Junbin Gao, Yanfeng Sun, and Baocai Yin. Product Grassmann mani- fold representation and its LRR models. In AAAI, 2016.","title":"Product Grassmann manifold representation and its LRR models","authors":"Wang","year":"2016","venue":"AAAI","doi":null,"url":null,"internal_url":null},{"position":27,"raw":"[Xie et al., 2016] Liping Xie, Dacheng Tao, and Haikun Wei. Multi-view exclusive unsupervised dimension reduction for video-based facial expression recognition. In IJCAI, 2016.","title":"Multi-view exclusive unsupervised dimension reduction for video-based facial expression recognition","authors":"Liping Xie, Dacheng Tao, Haikun Wei","year":"2016","venue":"IJCAI","doi":null,"url":null,"internal_url":"/proceedings/2016/316"},{"position":28,"raw":"[Xu et al., 2009] Yong Xu, Ge Feng, and Yingnan Zhao. One improvement to two-dimensional locality preserving pro- jection method for use with face recognition. Neurocom- puting, 73(2009):245-249, 2009.","title":"One improvement to two-dimensional locality preserving projection method for use with face recognition","authors":"Yong Xu, Ge Feng, Yingnan Zhao","year":"2009","venue":"Neurocomputing","doi":null,"url":null,"internal_url":null},{"position":29,"raw":"[Yang et al., 2004] Jian Yang, David Zhang, Alejandro F. Frangi, and Jing-yu. Yang. Two dimensional PCA: A new approach to appearance-based face representation and recognition. IEEE TPAMI, 26(1):131-137, 2004.","title":"Two dimensional PCA: A new approach to appearance-based face representation and recognition","authors":"Jian Yang, David Zhang, Alejandro F Frangi, Jing-Yu Yang","year":"2004","venue":"IEEE TPAMI","doi":null,"url":null,"internal_url":null}],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}