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Feature Robust Optimal Transport for High-dimensional Data [article]

Mathis Petrovich and Chao Liang and Ryoma Sato and Yanbin Liu and Yao-Hung Hubert Tsai and Linchao Zhu and Yi Yang and Ruslan Salakhutdinov and Makoto Yamada
2020 arXiv   pre-print
In this paper, we propose feature-robust optimal transport (FROT) for high-dimensional data, which solves high-dimensional OT problems using feature selection to avoid the curse of dimensionality.  ...  Since FROT finds the transport plan from selected features, it is robust to noise features.  ...  However, the optimal transport problem for high-dimensional data has remained unsolved for many years.  ... 
arXiv:2005.12123v4 fatcat:b2veo5yxk5cmblxbgiy3iqwurm

Optimal Transport Classifier: Defending Against Adversarial Attacks by Regularized Deep Embedding [article]

Yao Li, Martin Renqiang Min, Wenchao Yu, Cho-Jui Hsieh, Thomas C.M. Lee, Erik Kruus
2018 arXiv   pre-print
to embed high-dimensional input images into a low-dimensional space to perform classification.  ...  Leveraging optimal transport theory, we propose a new framework, Optimal Transport Classifier (OT-Classifier), and derive an objective that minimizes the discrepancy between the distribution of the true  ...  This is the core idea of the paper, summarizing the high-dimensional data in a space of much lower dimension without losing important features for classification.  ... 
arXiv:1811.07950v2 fatcat:lrtksdog2zayxgnujmsxowxoie

Robust Shape Reconstruction and Optimal Transportation

Pierre Alliez, Simon Giraudot, David Cohen-Steiner
2013 Actes des rencontres du CIRM  
cedram Texte mis en ligne dans le cadre du Centre de diffusion des revues académiques de mathématiques Abstract We describe a framework for robust shape reconstruction from raw point sets, based on optimal  ...  transportation between measures, where the input point sets are seen as distribution of masses.  ...  In addition to being symmetric, this distortion measure is by construction noise and outlier robust, a highly desirable feature when seeking robustness to defect-laden data.  ... 
doi:10.5802/acirm.57 fatcat:6mfjsh5ydzg7haltejd2bauyx4

Efficient Robust Optimal Transport with Application to Multi-Label Classification [article]

Pratik Jawanpuria, N T V Satyadev, Bamdev Mishra
2021 arXiv   pre-print
For high-dimensional data, we additionally propose suitable low-dimensional modeling of the Mahalanobis metric.  ...  Optimal transport (OT) is a powerful geometric tool for comparing two distributions and has been employed in various machine learning applications.  ...  Saketha Nath for insightful discussions on the topic.  ... 
arXiv:2010.11852v2 fatcat:yhxtklttvja2fbmaaewga6wj3m

Intelligent computational techniques for multimodal data

Shishir Kumar, Prabhat Mahanti, Su-Jing Wang
2019 Multimedia tools and applications  
The special issue touched different hot topics related to Computer Vision, Computational Biology, Multimedia data mining, High-dimensional multimedia data, Deep convolution network, Deep semantic preserving  ...  hashing, High-dimensional multimedia classification, Deep CNN and extended residual units, particle swarm optimization, Cyberbullying detection on social multimedia, Multimedia detection algorithm of  ...  Conclusion We hope these contributions will be of interest and value to readers from a wide range of subject areas and form a reference for future development.  ... 
doi:10.1007/s11042-019-07936-z fatcat:icmwanpmgbd77cdv47nminn4ee

Group-Structured Adversarial Training [article]

Farzan Farnia, Amirali Aghazadeh, James Zou, David Tse
2021 arXiv   pre-print
We formulate GSAT as a non-convex concave minimax optimization problem which minimizes a group-structured optimal transport cost.  ...  Robust training methods against perturbations to the input data have received great attention in the machine learning literature.  ...  A GSAT for Robust Feature and Basis Selection Feature selection is a basic task to extract knowledge from high-dimensional datasets by selecting a subset of features which properly model the output label  ... 
arXiv:2106.10324v1 fatcat:3emsct4kg5chvc3cottai3avqu

Intelligent Face Recognition based on Manifold Learning and Genetic-Chaos Algorithm Optimized Kernel Extreme Learning Machine

Wei He, Enjun Wang, Ting Xiong
2013 Journal of Communications  
In order to extract sensitive features of face images from high dimensional image data and facilitate the recognition speed, this paper has proposed a novel method based on the manifold learning and genetic-chaos  ...  Hence, the genetic-chaos algorithm was used for the first time to optimize the KELM parameter in this paper. A robust KELM structure may be attained after the genetic-chaos optimization.  ...  ACKNOWLEDGMENT The authors wish to thank the Editors and reviewers for their valuable comments on this work.  ... 
doi:10.12720/jcm.8.10.658-664 fatcat:phhnefghrzexvm6vrh6p64poue

Optimal Transport with Dimensionality Reduction for Domain Adaptation

Ping Li, Zhiwei Ni, Xuhui Zhu, Juan Song, Wenying Wu
2020 Symmetry  
To address this problem, this paper proposes a two-stage feature-based adaptation approach, referred to as optimal transport with dimensionality reduction (OTDR).  ...  To bridge distribution shift between the two domains, most of previous works aim to align their feature distributions through feature transformation, of which optimal transport for domain adaptation has  ...  However, high-dimensional source and target data usually leads to irregularities in the OTP and incorrect transport of instances.  ... 
doi:10.3390/sym12121994 fatcat:25hwkwcfsradhgnuobpbjpqj2e

Swarm Intelligence in Big Data Analytics [chapter]

Shi Cheng, Yuhui Shi, Quande Qin, Ruibin Bai
2013 Lecture Notes in Computer Science  
In this paper, the other three properties of big data analytics, which include the high dimensionality of data, the dynamical change of data, and the multi-objective of problems, are discussed.  ...  big data analytics problems.  ...  Handling High Dimensional Data The "curse of dimensionality" also happens on the high dimensional data mining problems [11, 12, 18] .  ... 
doi:10.1007/978-3-642-41278-3_51 fatcat:kcvmhmfjdjadre7kb5f34kh52q

Transfer Learning from an Auxiliary Discriminative Task for Unsupervised Anomaly Detection [article]

Urwa Muaz, Stanislav Sobolevsky
2019 arXiv   pre-print
Study of different approaches of feature engineering from such high dimensional data have been a focus of research in this field.  ...  Unsupervised anomaly detection from high dimensional data like mobility networks is a challenging task.  ...  However complexity and dimensionality of the data along with sparsity of available measurements at the local scale and resulting high noise-to-signal ratio challenges our ability of detecting robust and  ... 
arXiv:1912.02864v1 fatcat:kuzbwcfcfbaqbdlkjpnb233g3q

Gaussian Mixture Model and Deep Neural Network based Vehicle Detection and Classification

S Sri, K. R.
2016 International Journal of Advanced Computer Science and Applications  
Similar to AlexNet features, SIFT as SIFT feature descriptors retrieved 4096-dimensional features has been processed for dimensional reduction using features for each image  ...  To enable ROI data for feature extraction with single lane has been taken into consideration.  ... 
doi:10.14569/ijacsa.2016.070903 fatcat:ti4lbwvf3bhcxmxuaxmapslzii

Audio Fingerprint Retrieval Method Based on Feature Dimension Reduction and Feature Combination

2021 KSII Transactions on Internet and Information Systems  
accuracy and efficiency, a robust audio fingerprint retrieval method based on feature dimension reduction and feature combination is proposed.  ...  Secondly, the feature dimension reduction method based on information entropy is used for column dimension reduction, and the feature matrix after dimension reduction is used for row dimension reduction  ...  and data when searching for similar fingerprints in high dimensions due to the dimensionality disaster [2] .  ... 
doi:10.3837/tiis.2021.02.008 fatcat:plevwqtsgfgkpi5uxcm4ohxjyq

Complexity and robustness [chapter]

2000 Uncertainty and Feedback  
Highly Optimized Tolerance (HOT) was recently introduced as a conceptual framework to study fundamental aspects of complexity.  ...  HOT claims these are the most important features of complexity and are not accidents of evolution or artifices of engineering design, but are inevitably intertwined and mutually reinforcing.  ...  Because HOT and Data turn out to be identical for these features, we can collapse the Table as shown.  ... 
doi:10.1142/9781848160453_0005 fatcat:pr3kixdknfewfafemqdaktm27y

IEEE Access Special Section Editorial: Data Mining and Granular Computing in Big Data and Knowledge Processing

Weiping Ding, Gary G. Yen, Gleb Beliakov, Isaac Triguero, Mahardhika Pratama, Xiangliang Zhang, Hongjun Li
2019 IEEE Access  
To deal with the high-dimensional D-optimal design challenge, Xu, et al., in the invited article entitled ''Finding high-dimensional D-optimal designs for logistic models via differential evolution,''  ...  This data mining technology in evolutionary computation can find a highly efficient D-optimal design for high-dimensional real-world applications.  ... 
doi:10.1109/access.2019.2908776 fatcat:7km2edtcuzeutnwy3pjbvg264e

Wasserstein discriminant analysis

Rémi Flamary, Marco Cuturi, Nicolas Courty, Alain Rakotomamonjy
2018 Machine Learning  
Wasserstein Discriminant Analysis (WDA) is a new supervised method that can improve classification of high-dimensional data by computing a suitable linear map onto a lower dimensional subspace.  ...  Thanks to the the underlying principles of optimal transport, WDA is able to capture both global (at distribution scale) and local (at samples scale) interactions between classes.  ...  Introduction Dimensionality reduction techniques can convert high-dimensional data with potentially redundant features into low-dimensional vectors [1, 2] .  ... 
doi:10.1007/s10994-018-5717-1 fatcat:lku64gfoljfm3g2voxiopgicpu
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