Source Number Estimation and Effective Channel Order Determination Based on Higher-Order Tensors

Source number estimation is an essential task in underdetermined convolutive blind source separation, and effective channel order determination is also a challenging issue. For solving the two problems, the classical methods are based on information theoretic criteria. However, these are prone to the underestimation and overestimation of the number of sources in the underdetermined case. To compensate for this shortcoming, in this paper we propose two algorithms based on higher-order tensors. First, an improved algorithm is presented to estimate the number of sources. By transforming the tensor into a matrix, the eigenvalues of the resultant matrices are used to estimate the number of sources. Additionally, we employ higher-order tensors to detect the effective channel order and confirm the relationship between the number of sources and the effective channel order in the convolutive mixture model. Finally, a series of simulation experiments demonstrate that the proposed algorithms have an advantage over the conventional methods.

[1]  L. T. DeCarlo.  On the meaning and use of kurtosis. , 1997 .

[2]  Hongjing Liang,et al.  Adaptive Event-Triggered Output Feedback Fuzzy Control for Nonlinear Networked Systems With Packet Dropouts and Actuator Failure , 2019, IEEE Transactions on Fuzzy Systems.

[3]  Vincent Y. F. Tan,et al.  Automatic Relevance Determination in Nonnegative Matrix Factorization with the /spl beta/-Divergence , 2011, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[4]  Kyuwan Choi,et al.  Detecting the Number of Clusters in n-Way Probabilistic Clustering , 2010, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[5]  Lieven De Lathauwer,et al.  Fourth-Order Cumulant-Based Blind Identification of Underdetermined Mixtures , 2007, IEEE Transactions on Signal Processing.

[6]  Thomas Kailath,et al.  Detection of signals by information theoretic criteria , 1985, IEEE Trans. Acoust. Speech Signal Process..

[7]  Yong Xiang,et al.  Non-Negative Matrix Factorization With Dual Constraints for Image Clustering , 2020, IEEE Transactions on Systems, Man, and Cybernetics: Systems.

[8]  Junjie Yang,et al.  Underdetermined Blind Source Separation Combining Tensor Decomposition and Nonnegative Matrix Factorization , 2018, Symmetry.

[9]  G. Kitagawa,et al.  Generalised information criteria in model selection , 1996 .

[10]  H. Kiers.  Towards a standardized notation and terminology in multiway analysis , 2000 .

[11]  A. G. Farashahi.  Wave packet transforms over finite cyclic groups , 2016 .

[12]  Yong Xiang,et al.  Adaptive Method for Nonsmooth Nonnegative Matrix Factorization , 2017, IEEE Transactions on Neural Networks and Learning Systems.

[13]  Boaz Nadler,et al.  Non-Parametric Detection of the Number of Signals: Hypothesis Testing and Random Matrix Theory , 2009, IEEE Transactions on Signal Processing.

[14]  Andrzej Cichocki,et al.  Nonnegative Matrix and Tensor Factorizations : An algorithmic perspective , 2014, IEEE Signal Processing Magazine.

[15]  Kon Max Wong,et al.  On information theoretic criteria for determining the number of signals in high resolution array processing , 1990, IEEE Trans. Acoust. Speech Signal Process..

[16]  A. G. Farashahi,et al.  A UNIFIED THEORETICAL HARMONIC ANALYSIS APPROACH TO THE CYCLIC WAVELET TRANSFORM (CWT) FOR PERIODIC SIGNALS OF PRIME DIMENSIONS , 2014 .

[17]  Shengli Xie,et al.  Underdetermined convolutive blind separation of sources integrating tensor factorization and expectation maximization , 2019, Digit. Signal Process..

[18]  Hongjing Liang,et al.  Adaptive Distributed Observer Approach for Cooperative Containment Control of Nonidentical Networks , 2019, IEEE Transactions on Systems, Man, and Cybernetics: Systems.

[19]  G. Schwarz.  Estimating the Dimension of a Model , 1978 .

[20]  Frank L. Lewis,et al.  Fully Distributed Resilience for Adaptive Exponential Synchronization of Heterogeneous Multiagent Systems Against Actuator Faults , 2019, IEEE Transactions on Automatic Control.

[21]  Jean Pierre Delmas,et al.  Blind channel approximation: effective channel order determination , 1998, Conference Record of Thirty-Second Asilomar Conference on Signals, Systems and Computers (Cat. No.98CH36284).

[22]  Junbin Gao,et al.  Multiview Subspace Clustering via Tensorial t-Product Representation , 2019, IEEE Transactions on Neural Networks and Learning Systems.

[23]  Zongze Wu,et al.  Learning Graph Similarity With Large Spectral Gap , 2021, IEEE Transactions on Systems, Man, and Cybernetics: Systems.

[24]  Min Han,et al.  Nonnegative Mixture for Underdetermined Blind Source Separation Based on a Tensor Algorithm , 2015, Circuits, Systems, and Signal Processing.

[25]  Zongze Wu,et al.  Underdetermined Reverberant Audio-Source Separation Through Improved Expectation–Maximization Algorithm , 2019, Circuits Syst. Signal Process..

[26]  Zhe Wang,et al.  A Source Counting Method Using Acoustic Vector Sensor Based on Sparse Modeling of DOA Histogram , 2019, IEEE Signal Processing Letters.

[27]  Shengli Xie,et al.  Computing Resource Trading for Edge-Cloud-Assisted Internet of Things , 2019, IEEE Transactions on Industrial Informatics.

[28]  Yujie Li,et al.  Manifold optimization-based analysis dictionary learning with an ℓ1∕2-norm regularizer , 2018, Neural Networks.

[29]  Michael L. Donnell,et al.  Fuzzy Decision Analysis , 1979, IEEE Transactions on Systems, Man, and Cybernetics.

[30]  Alan Edelman,et al.  Sample Eigenvalue Based Detection of High-Dimensional Signals in White Noise Using Relatively Few Samples , 2007, IEEE Transactions on Signal Processing.

[31]  Junjie Yang,et al.  Under-Determined Convolutive Blind Source Separation Combining Density-Based Clustering and Sparse Reconstruction in Time-Frequency Domain , 2019, IEEE Transactions on Circuits and Systems I: Regular Papers.

[32]  Adam W. Bojanczyk,et al.  Effective Channel Order Estimation Based on Nullspace Structure and Exponential Fit , 2010, IEEE Transactions on Signal Processing.

[33]  Thai Quang Vinh,et al.  Demand-Side Management in Microgrids with the Presence of Renewable Sources in Vietnam , 2019 .

[34]  Zhaoshui He,et al.  Eliminating the Permutation Ambiguity of Convolutive Blind Source Separation by Using Coupled Frequency Bins , 2020, IEEE Transactions on Neural Networks and Learning Systems.

[35]  Andrzej Cichocki,et al.  Tensor Decompositions for Signal Processing Applications: From two-way to multiway component analysis , 2014, IEEE Signal Processing Magazine.

[36]  Andrzej Cichocki,et al.  Robust Multilinear Tensor Rank Estimation Using Higher Order Singular Value Decomposition and Information Criteria , 2017, IEEE Transactions on Signal Processing.

[37]  Arash Ghaani Farashahi,et al.  Cyclic wave packet transform on finite Abelian groups of prime order , 2014, Int. J. Wavelets Multiresolution Inf. Process..

[38]  Sharon Gannot,et al.  Source Counting and Separation Based on Simplex Analysis , 2018, IEEE Transactions on Signal Processing.

[39]  H. Akaike.  A new look at the statistical model identification , 1974 .

[40]  Zhaoshui He,et al.  Symmetric Nonnegative Matrix Factorization: Algorithms and Applications to Probabilistic Clustering , 2011, IEEE Transactions on Neural Networks.

[41]  Paul D. Gader.  Guest editorial- foreword to the special issue on recognition technology , 2001, IEEE Trans. Fuzzy Syst..

[42]  Xuelong Li,et al.  Flexible Affinity Matrix Learning for Unsupervised and Semisupervised Classification , 2019, IEEE Transactions on Neural Networks and Learning Systems.