Tensor completion via adaptive sampling of tensor fibers: Application to efficient indoor RF fingerprinting

In this paper, we consider tensor completion under adaptive sampling of tensor (a multidimensional array) fibers. Tensor fibers or tubes are vectors obtained by fixing all but one index of the array. This sampling is in contrast to the cases considered so far where one performs an adaptive element-wise sampling. In this context we exploit a recently proposed algebraic framework to model tensor data [1] and model the underlying data as a tensor with low tensor tubal-rank. Under this model we then present an algorithm for adaptive sampling and recovery, which is shown to be nearly optimal in terms of sampling complexity. We apply this algorithm for robust estimation of RF fingerprints for accurate indoor localization. We show the performance on real and synthetic data sets. Compared to existing methods, that are primarily based on non-adaptive matrix completion methods, adaptive tensor completion achieves significantly better performance.

[1]  Emmanuel J. Candès,et al.  A Singular Value Thresholding Algorithm for Matrix Completion , 2008, SIAM J. Optim..

[2]  Jieping Ye,et al.  Tensor Completion for Estimating Missing Values in Visual Data , 2009, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[3]  Akshay Krishnamurthy,et al.  Low-Rank Matrix and Tensor Completion via Adaptive Sampling , 2013, NIPS.

[4]  Santosh S. Vempala,et al.  Matrix approximation and projective clustering via volume sampling , 2006, SODA '06.

[5]  Yanfeng Sun,et al.  Efficient Radio Map Construction Based on Low-Rank Approximation for Indoor Positioning , 2013 .

[6]  Tamara G. Kolda,et al.  Tensor Decompositions and Applications , 2009, SIAM Rev..

[7]  Yehuda Koren,et al.  Matrix Factorization Techniques for Recommender Systems , 2009, Computer.

[8]  Panagiotis Tsakalides,et al.  Efficient training for fingerprint based positioning using matrix completion , 2012, 2012 Proceedings of the 20th European Signal Processing Conference (EUSIPCO).

[9]  Prateek Jain,et al.  Low-rank matrix completion using alternating minimization , 2012, STOC '13.

[10]  Xue Liu,et al.  Data loss and reconstruction in sensor networks , 2013, 2013 Proceedings IEEE INFOCOM.

[11]  Aarti Singh,et al.  Column Subset Selection with Missing Data via Active Sampling , 2015, AISTATS.

[12]  Panagiotis Tsakalides,et al.  Efficient Multi-Channel Signal Strength Based Localization via Matrix Completion and Bayesian Sparse Learning , 2015, IEEE Transactions on Mobile Computing.

[13]  Misha Elena Kilmer,et al.  Third-Order Tensors as Operators on Matrices: A Theoretical and Computational Framework with Applications in Imaging , 2013, SIAM J. Matrix Anal. Appl..

[14]  Zemin Zhang,et al.  Exact Tensor Completion Using t-SVD , 2015, IEEE Transactions on Signal Processing.

[15]  Robert D. Nowak,et al.  High-dimensional Matched Subspace Detection when data are missing , 2010, 2010 IEEE International Symposium on Information Theory.

[16]  B. Recht,et al.  Tensor completion and low-n-rank tensor recovery via convex optimization , 2011 .

[17]  Larry J. Greenstein,et al.  Characterizing indoor wireless channels via ray tracing combined with stochastic modeling , 2009, IEEE Transactions on Wireless Communications.

[18]  Misha Elena Kilmer,et al.  Novel Methods for Multilinear Data Completion and De-noising Based on Tensor-SVD , 2014, 2014 IEEE Conference on Computer Vision and Pattern Recognition.

[19]  Shuchin Aeron,et al.  5D and 4D pre-stack seismic data completion using tensor nuclear norm (TNN) , 2013, SEG Technical Program Expanded Abstracts 2013.

[20]  Panagiotis Tsakalides,et al.  Efficient recalibration via Dynamic Matrix Completion , 2013, 2013 IEEE International Workshop on Machine Learning for Signal Processing (MLSP).

[21]  Sujay Sanghavi,et al.  A New Sampling Technique for Tensors , 2015, ArXiv.

[22]  Ying Zhu,et al.  Using compressive sensing to reduce fingerprint collection for indoor localization , 2013, 2013 IEEE Wireless Communications and Networking Conference (WCNC).

[23]  Xiaodong Wang,et al.  Adaptive Sampling of RF Fingerprints for Fine-Grained Indoor Localization , 2015, IEEE Transactions on Mobile Computing.

[24]  Xiaodong Wang,et al.  Fine-grained Indoor Localization with Adaptively Sampled RF Fingerprints , 2015, ArXiv.