An iterated graph laplacian approach for ranking on manifolds
Xueyuan Zhou,Mikhail Belkin,Nathan Srebro +2 more
- pp 877-885
Reads0
Chats0
TLDR
This paper proposes an improved ranking algorithm on manifolds using Green's function of an iterated unnormalized graph Laplacian, which is more robust and density adaptive, as well as pointwise continuous in the limit of infinite samples.Abstract:
Ranking is one of the key problems in information retrieval. Recently, there has been significant interest in a class of ranking algorithms based on the assumption that data is sampled from a low dimensional manifold embedded in a higher dimensional Euclidean space.In this paper, we study a popular graph Laplacian based ranking algorithm [23] using an analytical method, which provides theoretical insights into the ranking algorithm going beyond the intuitive idea of "diffusion." Our analysis shows that the algorithm is sensitive to a commonly used parameter due to the use of symmetric normalized graph Laplacian. We also show that the ranking function may diverge to infinity at the query point in the limit of infinite samples. To address these issues, we propose an improved ranking algorithm on manifolds using Green's function of an iterated unnormalized graph Laplacian, which is more robust and density adaptive, as well as pointwise continuous in the limit of infinite samples.We also for the first time in the ranking literature empirically explore two variants from a family of twice normalized graph Laplacians. Experimental results on text and image data support our analysis, which also suggest the potential value of twice normalized graph Laplacians in practice.read more
Citations
More filters
Proceedings ArticleDOI
Person re-identification by manifold ranking
TL;DR: This study shows that it is possible to propagate the query information along the unlabelled data manifold in an unsupervised way to obtain robust ranking results, and demonstrates that the performance of existing supervised metric learning methods can be significantly boosted once integrated into the proposed manifold ranking-based framework.
Proceedings ArticleDOI
SHREC'12 track: generic 3D shape retrieval
Bo Li,Afzal Godil,Masaki Aono,X. Bai,Takahiko Furuya,L. Li,Roberto J. López-Sastre,Henry Johan,Ryutarou Ohbuchi,Carolina Redondo-Cabrera,Atsushi Tatsuma,T. Yanagimachi,Shixiong Zhang +12 more
TL;DR: The aim of this track is to measure and compare the performance of generic 3D shape retrieval methods implemented by different participants over the world and their retrieval accuracies were evaluated using 7 commonly used performance metrics.
Proceedings Article
SHREC'14 Track: Shape retrieval of non-rigid 3D human models
David Pickup,Ralph R. Martin,Paul L. Rosin,Xianfang Sun,Zhi-Quan Cheng,Zhouhui Lian,Masaki Aono,A. Ben Hamza,Alexander M. Bronstein,Michael M. Bronstein,Shuhui Bu,Umberto Castellani,Sheng Cheng,Valeria Garro,Andrea Giachetti,Afzal Godil,Junwei Han,Henry Johan,L. Lai,Bo Li,Chenfeng Li,Haisheng Li,Roee Litman,Xin-Bi Liu,Z. Liu,Yijuan Lu,Atsushi Tatsuma,Jianbo Ye +27 more
TL;DR: In this article, the authors created a new benchmarking dataset for testing non-rigid 3D shape retrieval algorithms, one that is much more challenging than existing datasets and features exclusively human models, in a variety of body shapes and poses.
Proceedings ArticleDOI
Shape retrieval of non-rigid 3D human models
David Pickup,Xianfang Sun,Paul L. Rosin,Ralph R. Martin,Zhi-Quan Cheng,Zhouhui Lian,Masaki Aono,A. Ben Hamza,Alexander M. Bronstein,Michael M. Bronstein,Shuhui Bu,Umberto Castellani,S. Cheng,Valeria Garro,Andrea Giachetti,Afzal Godil,Junwei Han,Henry Johan,L. Lai,Bo Li,Chunyuan Li,Haisheng Li,Roee Litman,X. Liu,Z. Liu,Yijuan Lu,Atsushi Tatsuma,Jianbo Ye +27 more
TL;DR: In this article, the authors have created a new benchmarking dataset for testing non-rigid 3D shape retrieval algorithms, one that is much more challenging than existing datasets and features exclusively human models, in a variety of body shapes and poses.
Journal ArticleDOI
Shape Retrieval of Non-rigid 3D Human Models
David Pickup,Xianfang Sun,Paul L. Rosin,Ralph R. Martin,Zhi-Quan Cheng,Zhouhui Lian,Masaki Aono,A. Ben Hamza,Alexander M. Bronstein,Michael M. Bronstein,Shuhui Bu,Umberto Castellani,Sheng Cheng,Valeria Garro,Andrea Giachetti,Afzal Godil,Luca Isaia,Junwei Han,Henry Johan,L. Lai,Bo Li,Chunyuan Li,Haisheng Li,Roee Litman,X. Liu,Z. Liu,Yijuan Lu,L. Sun,Gary K. L. Tam,Atsushi Tatsuma,Jianbo Ye +30 more
TL;DR: In this paper, the FAUST dataset was used as a benchmark for testing non-rigid 3D shape retrieval algorithms on 3D human models, with 145 new models for use as a separate training set, to standardise the training data used and provide a fairer comparison.
References
More filters
Journal ArticleDOI
A tutorial on spectral clustering
TL;DR: In this article, the authors present the most common spectral clustering algorithms, and derive those algorithms from scratch by several different approaches, and discuss the advantages and disadvantages of these algorithms.
Journal ArticleDOI
Laplacian Eigenmaps for dimensionality reduction and data representation
Mikhail Belkin,Partha Niyogi +1 more
TL;DR: In this article, the authors proposed a geometrically motivated algorithm for representing high-dimensional data, based on the correspondence between the graph Laplacian, the Laplace Beltrami operator on the manifold and the connections to the heat equation.
Journal ArticleDOI
Modeling the Shape of the Scene: A Holistic Representation of the Spatial Envelope
Aude Oliva,Antonio Torralba +1 more
TL;DR: The performance of the spatial envelope model shows that specific information about object shape or identity is not a requirement for scene categorization and that modeling a holistic representation of the scene informs about its probable semantic category.
Book
Spline models for observational data
TL;DR: In this paper, a theory and practice for the estimation of functions from noisy data on functionals is developed, where convergence properties, data based smoothing parameter selection, confidence intervals, and numerical methods are established which are appropriate to a number of problems within this framework.
Proceedings Article
Learning with Local and Global Consistency
TL;DR: A principled approach to semi-supervised learning is to design a classifying function which is sufficiently smooth with respect to the intrinsic structure collectively revealed by known labeled and unlabeled points.