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Generalized RBF kernel for incomplete data [article]

Łukasz Struski, Marek Śmieja, Jacek Tabor
2016 arXiv   pre-print
We construct genRBF kernel, which generalizes the classical Gaussian RBF kernel to the case of incomplete data.  ...  This allows to embed incomplete data into the function space and to define a kernel between two missing data points based on scalar product in L_2.  ...  Let us observe that the above scalar product generalizes the classical RBF kernel to incomplete data.  ... 
arXiv:1612.01480v1 fatcat:uiu2pxw5i5hovfyftcx5r5y7ke

Clustering Incomplete Data Using Kernel-Based Fuzzy C-means Algorithm

Dao-Qiang Zhang, Song-Can Chen
2003 Neural Processing Letters  
Chen). one real datasets show that KFCM has better clustering performance and more robust than several modifications of FCM for incomplete data clustering.  ...  KFCM adopts a new kernel-induced metric in the data space to replace the original Euclidean norm metric in FCM and the clustered prototypes still lie in the data space so that the clustering results can  ...  Acknowledgements The authors are grateful to the anonymous reviewers for their comments and suggestions to improve the presentation of this paper.  ... 
doi:10.1023/b:nepl.0000011135.19145.1b fatcat:kmf5edoc4vevtgwnh37ni4xcfq

Privacy-Preserved Big Data Analysis Based on Asymmetric Imputation Kernels and Multiside Similarities [article]

Bo-Wei Chen
2016 arXiv   pre-print
To deal with these incomplete data, a new kernel function with asymmetric intrinsic mappings is proposed in this study. Such a new kernel uses three-side similarities for kernel matrix formation.  ...  This study presents an efficient approach for incomplete data classification, where the entries of samples are missing or masked due to privacy preservation.  ...  Sun-Yuan Kung for his supervision and teaching when Dr. Chen worked as a postdoctoral fellow at Princeton University, USA.  ... 
arXiv:1603.07828v2 fatcat:kqqldprhurhnbassdkkbfaw77q

Spectral Clustering Using PCKID – A Probabilistic Cluster Kernel for Incomplete Data [chapter]

Sigurd Løkse, Filippo M. Bianchi, Arnt-Børre Salberg, Robert Jenssen
2017 Lecture Notes in Computer Science  
By combining posterior distributions of Gaussian Mixture Models for incomplete data on different scales, we are able to learn a kernel for incomplete data that does not depend on any critical hyperparameters  ...  , unlike the commonly used RBF kernel.  ...  Acknowledgments This work was partially funded by the Norwegian Research Council FRIPRO grant no. 239844 on developing the Next Generation Learning Machines.  ... 
doi:10.1007/978-3-319-59126-1_36 fatcat:aanysgfqifdqnbcztxpkpujasa

Spectral Clustering using PCKID - A Probabilistic Cluster Kernel for Incomplete Data [article]

Sigurd Løkse, Filippo Maria Bianchi, Arnt-Børre Salberg, Robert Jenssen
2017 arXiv   pre-print
By combining posterior distributions of Gaussian Mixture Models for incomplete data on different scales, we are able to learn a kernel for incomplete data that does not depend on any critical hyperparameters  ...  , unlike the commonly used RBF kernel.  ...  Acknowledgments This work was partially funded by the Norwegian Research Council FRIPRO grant no. 239844 on developing the Next Generation Learning Machines.  ... 
arXiv:1702.07190v1 fatcat:mlyme7425jgedem4nebs5vyj5e

Regression SVM for Incomplete Data

2017 Schedae Informaticae  
This representation allows to construct an analogue of RBF kernel for incomplete data. We show that such a kernel can be successfully used in regression SVM.  ...  Although this methodology is very common, it produces less informative data, because artificially generated values are treated in the same way as the known ones.  ...  This is visually confirmed by the results in Figure 2 Conclusion We have presented a method that constructs an analogue of classical RBF kernel for incomplete data.  ... 
doi:10.4467/20838476si.17.001.6807 fatcat:mcayvpe3uff53at6pfsoofctby

Online High Rank Matrix Completion

Jicong Fan, Madeleine Udell
2019 2019 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR)  
The method works by (implicitly) mapping the data into a high dimensional polynomial feature space using the kernel trick; importantly, the data occupies a low dimensional subspace in this feature space  ...  We also provide guidance on sampling rate required for these methods to succeed. Experimental results on synthetic data and motion data validate the performance of the proposed methods.  ...  For the RBF kernel, q = ∞, so the condition (36) is vacuous. However, the RBF kernel can be well approximated by a polynomial kernel and we have φ i (x) =φ i (x) + O( c q+1 (q+1)!  ... 
doi:10.1109/cvpr.2019.00889 dblp:conf/cvpr/FanU19 fatcat:h2ih5rvjvvf55gr4i6szef7yvi

Deep RBFNet: Point Cloud Feature Learning using Radial Basis Functions [article]

Weikai Chen, Xiaoguang Han, Guanbin Li, Chao Chen, Jun Xing, Yajie Zhao, Hao Li
2019 arXiv   pre-print
In this paper, we propose a simple yet effective framework for point set feature learning by leveraging a nonlinear activation layer encoded by Radial Basis Function (RBF) kernels.  ...  We demonstrate that the proposed network with a single RBF layer can outperform the state-of-the-art Pointnet++ in terms of classification accuracy for 3D object recognition tasks.  ...  Therefore, for N input points, the RBF layer will generate a feature map with dimension N × M .  ... 
arXiv:1812.04302v2 fatcat:ma3vjx47mbcsnjoje3tljrdpq4

Online high rank matrix completion [article]

Jicong Fan, Madeleine Udell
2020 arXiv   pre-print
The method works by (implicitly) mapping the data into a high dimensional polynomial feature space using the kernel trick; importantly, the data occupies a low dimensional subspace in this feature space  ...  In this paper, we develop a new model for high rank matrix completion (HRMC), together with batch and online methods to fit the model and out-of-sample extension to complete new data.  ...  For the RBF kernel, q = ∞, so the condition (36) is vacuous. However, the RBF kernel can be well approximated by a polynomial kernel and we have φ i (x) =φ i (x) + O( c q+1 (q+1)!  ... 
arXiv:2002.08934v1 fatcat:w3j5c4qxtrfyrd2qmoqssiznom

Shared kernel models for class conditional density estimation

M.K. Titsias, A.C. Likas
2001 IEEE Transactions on Neural Networks  
We present a general model that allows for the expression of intermediate cases where the degree of kernel sharing can be specified through an extra model parameter.  ...  We present probabilistic models which are suitable for class conditional density estimation and can be regarded as shared kernel models where sharing means that each kernel may contribute to the estimation  ...  ACKNOWLEDGMENT The authors would like to thank the anonymous referees for their useful suggestions.  ... 
doi:10.1109/72.950129 pmid:18249927 fatcat:e6g6vsuf65bqvgokfwmla6m2fy

Educational Data Classification using Data Mining and Kernel Ensemble Classifier

2019 VOLUME-8 ISSUE-10, AUGUST 2019, REGULAR ISSUE  
The SVM kernels like linear, polynomial, quadratic and radial basis function based ensemble classifier is used for classification of student's data.  ...  and Radial Basis Function (RBF) is discussed.  ...  The SVM kernel functions like linear, polynomial, quadratic and RBF is used for ensemble classification of student's data.  ... 
doi:10.35940/ijitee.b1238.1292s419 fatcat:6ioa7jcvyverjoyif6vh45pa2i

Smooth surface reconstruction from noisy range data

J. C. Carr, R. K. Beatson, B. C. McCallum, W. R. Fright, T. J. McLennan, T. J. Mitchell
2003 Proceedings of the 1st international conference on Computer graphics and interactive techniques in Austalasia and South East Asia - GRAPHITE '03  
This paper shows that scattered range data can be smoothed at low cost by fitting a Radial Basis Function (RBF) to the data and convolving with a smoothing kernel (low pass filtering).  ...  The RBF exactly describes the range data and interpolates across holes and gaps. The data is smoothed during evaluation of the RBF by simply changing the basic function.  ...  Acknowledgements We are particularly grateful to Allen Instruments and Supplies, USA, for the LIDAR data in Figure 7 , and to Cyra Technologies for the LIDAR data in Figure 1 and Figure 14 .  ... 
doi:10.1145/604492.604495 fatcat:bovnuvv7afaqdktql3lzq63l24

Smooth surface reconstruction from noisy range data

J. C. Carr, R. K. Beatson, B. C. McCallum, W. R. Fright, T. J. McLennan, T. J. Mitchell
2003 Proceedings of the 1st international conference on Computer graphics and interactive techniques in Austalasia and South East Asia - GRAPHITE '03  
This paper shows that scattered range data can be smoothed at low cost by fitting a Radial Basis Function (RBF) to the data and convolving with a smoothing kernel (low pass filtering).  ...  The RBF exactly describes the range data and interpolates across holes and gaps. The data is smoothed during evaluation of the RBF by simply changing the basic function.  ...  Acknowledgements We are particularly grateful to Allen Instruments and Supplies, USA, for the LIDAR data in Figure 7 , and to Cyra Technologies for the LIDAR data in Figure 1 and Figure 14 .  ... 
doi:10.1145/604471.604495 dblp:conf/graphite/CarrBMFMM03 fatcat:rwu2vtow6nf37ajt5pvtvjj7cq

Classification of incomplete feature vectors by radial basis function networks

Richard Dybowski
1998 Pattern Recognition Letters  
The method is discussed in the context of complete and incomplete training sets.  ...  The paper describes the use of radial basis function neural networks with Gaussian basis functions to classify incomplete feature vectors.  ...  If we regard the identity j of the kernel function which generated x as unobserved data, the E-step for mixture model (4) can be written as (Bishop, 1995, pp.69-72] [ ] Q P j C P j C f j C cur n k cur  ... 
doi:10.1016/s0167-8655(98)00096-8 fatcat:wyif4o6m6jemvbgymsx66v23ju

Location Estimation via Support Vector Regression

Zhi-li Wu, Chun-hung Li, Joseph Kee-yin Ng, Karl R.p.h. Leung
2007 IEEE Transactions on Mobile Computing  
Location estimation using the Global System for Mobile communication (GSM) is an emerging application that infers the location of the mobile receiver from multiple signals measurements.  ...  Using support vector regression, we investigate the missing value location estimation problem by providing theoretical and empirical analysis on existing and novel kernels.  ...  Synthetical Data Generator and Experiment Setup The generative propagation model in the STA-EM paper is used by us as a synthetic data generator.  ... 
doi:10.1109/tmc.2007.42 fatcat:cvjfw5ckkfernne3pxozormire
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