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Soft and subspace robust multivariate rank tests based on entropy regularized optimal transport [article]

Shoaib Bin Masud, Boyang Lyu, Shuchin Aeron
2021 arXiv   pre-print
In this paper, we extend the recently proposed multivariate rank energy distance, based on the theory of optimal transport, for statistical testing of distributional similarity, to soft rank energy distance  ...  Being differentiable, this in turn allows us to extend the rank energy to a subspace robust rank energy distance, dubbed Projected soft-Rank Energy distance, which can be computed via optimization over  ...  A. Soft Rank Energy Distance To define soft rank energy, we first need to define the notion of a soft rank.  ... 
arXiv:2103.08811v2 fatcat:bmyzohebhnhuhii7qvmft43ldm

Testing using Privileged Information by Adapting Features with Statistical Dependence

Kwang In Kim, James Tompkin
2021 2021 IEEE/CVF International Conference on Computer Vision (ICCV)  
Then, we empirically estimate and strengthen the statistical dependence between the initial noisy predictor and the additional features via manifold denoising.  ...  As an example, we show that this approach leads to improvement in real-world visual attribute ranking.  ...  This material is based on research sponsored by Defense Advanced Research Projects Agency (DARPA) and Air Force Research Laboratory (AFRL) under agreement number FA8750-19-2-1006. The U.S.  ... 
doi:10.1109/iccv48922.2021.00927 fatcat:trcn323uwjb3hlfb2rtoxsi5lu

Support Vector Machines with Manifold Learning and Probabilistic Space Projection for Tourist Expenditure Analysis

Xin Xu, Rob Law, Tao Wu
2009 International Journal of Computational Intelligence Systems  
The first feature projection method is based on ISOMAP (Isometric Feature Mapping), which is a class of manifold learning approaches for dimension reduction.  ...  Experimental results on expenditure data of business travelers show that the proposed method can improve prediction performance both in terms of testing accuracy and statistical coincidence.  ...  Acknowledgements The work described in this paper was fully supported by a grant from the Research Grants Council of the Hong Kong Special Administrative Region, China (Project No. PolyU 4631/06H).  ... 
doi:10.1080/18756891.2009.9727636 fatcat:7nobrzfrlbf4xok7aoqanjm2bi

Support Vector Machines with Manifold Learning and Probabilistic Space Projection for Tourist Expenditure Analysis

Xin Xu, Rob Law, Tao Wu
2009 International Journal of Computational Intelligence Systems  
The first feature projection method is based on ISOMAP (Isometric Feature Mapping), which is a class of manifold learning approaches for dimension reduction.  ...  Experimental results on expenditure data of business travelers show that the proposed method can improve prediction performance both in terms of testing accuracy and statistical coincidence.  ...  Acknowledgements The work described in this paper was fully supported by a grant from the Research Grants Council of the Hong Kong Special Administrative Region, China (Project No. PolyU 4631/06H).  ... 
doi:10.2991/jnmp.2009.2.1.3 fatcat:h5h64gjyb5bv3mgtz2rdaopk4q

Free-breathing and ungated cardiac cine using navigator-less spiral SToRM [article]

Abdul Haseeb Ahmed, Ruixi Zhou, Yang Yang, Prashant Nagpal, Michael Salerno, Mathews Jacob
2020 arXiv   pre-print
Unlike prior work that rely on navigators to estimate the manifold structure, we propose a kernel low-rank matrix completion method to directly fill in the missing k-space data from variable density spiral  ...  We introduce a kernel low-rank algorithm to recover free-breathing and ungated dynamic MRI from spiral acquisitions without explicit k-space navigators.  ...  The framework assumes the images to be on a smooth surface in high dimensions and relies on a kernel low-rank prior to recover the dataset.  ... 
arXiv:1901.05542v3 fatcat:teouvwmaz5gf7lnax3oomba524

Kernel Sparse Subspace Clustering on Symmetric Positive Definite Manifolds [article]

Ming Yin and Yi Guo and Junbin Gao and Zhaoshui He and Shengli Xie
2016 arXiv   pre-print
In this paper, by embedding the SPD matrices into a Reproducing Kernel Hilbert Space (RKHS), a kernel subspace clustering method is constructed on the SPD manifold through an appropriate Log-Euclidean  ...  kernel, termed as kernel sparse subspace clustering on the SPD Riemannian manifold (KSSCR).  ...  Kernel SSC on Euclidean space (KSSCE) [17] , which embeds data onto to a nonlinear manifold by using the kernel trick and then apply SSC based on Euclidean metric.  ... 
arXiv:1601.00414v1 fatcat:kbzuyhabkfabdmagmko4hxomnm

Disturbance Grassmann Kernels for Subspace-Based Learning

Junyuan Hong, Huanhuan Chen, Feng Lin
2018 Proceedings of the 24th ACM SIGKDD International Conference on Knowledge Discovery & Data Mining - KDD '18  
Secondly, we research into two kinds of disturbance, relevant to the subspace matrix and singular values of bases, with which we extend the Projection kernel on Grassmann manifolds to two new kernels.  ...  Experiments on action data indicate that the proposed kernels perform better compared to state-of-the-art subspace-based methods, even in a worse environment.  ...  Priorly, the idea has been applied for statistic estimation on the Grassmann manifold by truncating beyond a radius of π [32] .  ... 
doi:10.1145/3219819.3219959 dblp:conf/kdd/HongCL18 fatcat:3fdt7667onfhba66346flho2e4

Corpus Statistics Empowered Document Classification

Farid Uddin, Yibo Chen, Zuping Zhang, Xin Huang
2022 Electronics  
Using available corpus statistics, WCDV sufficiently handles the data sparsity of short texts without depending on external knowledge sources.  ...  To evaluate the proposed models, we performed a multiclass document classification using standard performance measures (precision, recall, f1-score, and accuracy) on three long- and two short-text benchmark  ...  This conditioning results in a massive expansion of novel kernels in different fields, such as kernels on the statistical manifold [65] , Gapped String Kernels [66] and so on.  ... 
doi:10.3390/electronics11142168 fatcat:yjmkl3zhkjcfhpow7wmanmn5pa

Efficient Pairwise Neuroimage Analysis using the Soft Jaccard Index and 3D Keypoint Sets [article]

Laurent Chauvin, Kuldeep Kumar, Christian Desrosiers, William Wells III, Matthew Toews
2021 arXiv   pre-print
A new kernel is proposed to quantify the variability of keypoint geometry in location and scale.  ...  Our measure generalizes the Jaccard index to account for soft set equivalence (SSE) between keypoint elements, via an adaptive kernel framework modeling uncertainty in keypoint appearance and geometry.  ...  expression for our proposed Jaccard index based on soft set equivalence J SSE (A, B) J SSE (A, B) = µ(A ∩ B) µ(A) + µ(B) − µ(A ∩ B) . (2) In Equation (2) Defining µ(A∩B): The cardinality of the soft  ... 
arXiv:2103.06966v3 fatcat:2l4r56zz65e6nduzzgrav4mksa

Unsupervised dimensionality reduction: Overview and recent advances

John A. Lee, Michel Verleysen
2010 The 2010 International Joint Conference on Neural Networks (IJCNN)  
This paper attempts to give a broad overview of the domain. Past develoments are briefly introduced and pinned up on the time line of the last eleven decades.  ...  Dimensionality reduction can be used for compression or denoising purposes, but data visualization remains one its most prominent applications.  ...  This idea is investigated in [65] , [68] , [37] and a uniform framework for all rank-based criteria is suggested in [38] , [39] .  ... 
doi:10.1109/ijcnn.2010.5596721 dblp:conf/ijcnn/LeeV10a fatcat:6cbvynny4ngmnoxfzjpfmy5g2e

Deep Image Clustering with Tensor Kernels and Unsupervised Companion Objectives [article]

Daniel J. Trosten, Michael C. Kampffmeyer, Robert Jenssen
2020 arXiv   pre-print
These unsupervised companion objectives are constructed based on a proposed generalization of the Cauchy-Schwarz (CS) divergence, from vectors to tensors of arbitrary rank.  ...  In this paper we develop a new model for deep image clustering, using convolutional neural networks and tensor kernels.  ...  We will stick to the Gaussian kernel, but use a distance function on the Grassmann manifold spanned by the respective matricizations (see Figure 2 ).  ... 
arXiv:2001.07026v2 fatcat:ceoyqqy27jbc3cmqpk6ls6nkgm

Adaptive nonlinear manifolds and their applications to pattern recognition

Hujun Yin, Weilin Huang
2010 Information Sciences  
Section 2 provides a review of existing approaches on nonlinearizing PCA. Section 3 describes MDS and related recent approaches in extracting nonlinear manifolds.  ...  Such connections show the advantages of SOM-based methods in dimensionality reduction. A growing variant of the metric preserving ViSOM has been proposed for embedding nonlinear manifolds.  ...  Table 1 1 Error rates of PCA-based methods followed by a NN, soft k-NN or LDA classifier.  ... 
doi:10.1016/j.ins.2010.04.004 fatcat:zhsym3p2nvhszhnsc7rh6h5i4u

Transformed Subspace Clustering [article]

Jyoti Maggu, Angshul Majumdar, Emilie Chouzenoux
2019 arXiv   pre-print
To achieve the intended goal, we embed subspace clustering techniques (locally linear manifold clustering, sparse sub-space clustering and low rank representation) into transform learning.  ...  We assume that, even if the raw data is not separable into subspac-es, one can learn a representation (transform coef-ficients) such that the learnt representation is sep-arable into subspaces.  ...  space clustering and low rank representation) into Our work is based on similar assumptions. Instead of transform learning.  ... 
arXiv:1912.04734v1 fatcat:pfauacjv3zff5mitqo2mc7ew3e

Context-Aware Gaussian Fields for Non-rigid Point Set Registration

Gang Wang, Zhicheng Wang, Yufei Chen, Qiangqiang Zhou, Weidong Zhao
2016 2016 IEEE Conference on Computer Vision and Pattern Recognition (CVPR)  
Experimental results on synthetic and real images reveal that how CA-LapGF outperforms state-of-the-art algorithms for non-rigid PSR.  ...  The CA-LapGF can estimate non-rigid transformations, which are mapped to reproducing kernel Hilbert spaces, accurately and robustly in the presence of degradations.  ...  Registration results on IMM face landmarks under different values of N l for low-rank kernel matrix approximation. (a) Statistics of registration errors. (b) Statistics of registration runtime.  ... 
doi:10.1109/cvpr.2016.626 dblp:conf/cvpr/WangWCZZ16 fatcat:ihywpnrcqfg6pidblhcxwmebve

Esthetic Evaluation of Facial Soft Tissue Based on Nonrigid Image Deformation

Yali He, Yan Yang, Abdelrahman Mohamed, Genmiao Qi, Xiaojie Guo
2020 Mathematical Problems in Engineering  
However, related research is mostly in the stage of qualitative evaluation without clinical reference of specific soft tissue data.  ...  Therefore, by collecting the pre- and post-treatment photographs of 26 adult female patients, this study used image deformation technology to process the photos of a 23-year-old female patient, and two  ...  aging changes on facial soft tissues).  ... 
doi:10.1155/2020/2526542 fatcat:zbuunhn4ffct7c5tahxcl72r4e
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