Blind system identification: instantaneous mixtures of<i>n</i>sources

Kofidis, Nikos; Margaris, Athanasios; Diamantaras, Konstantinos I.; Roumeliotis, Μanos

doi:10.1080/00207160701534755

Cited by 3 publications

(11 citation statements)

References 8 publications

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“…Consequently, (62) follows. Furthermore, as n < δ(a 2 − a 1 )/(2m(a k − a 1 )) for all n > N (see (42)), Theorem 1.4 implies that…”

Section: Supplement To Multiscale Blind Source Separationmentioning

confidence: 97%

“…Let I, I ∈ I 2 be the constant parts of g left and right of this change point and I 1 , I 1 be those sub-intervals which include the largest constant piece of g (see green lines in Figure S1.1), with g| I 1 ≡ g I 1 and g| I 1 ≡ g I 1 . As n < δ/2 for all n > N (see (42)) g I 1 − g I 1 > 0 (see the vertical distance between the left and the right green line in Figure S1.1), such that g has at least one jump in a 2d n -neighborhood of a jump ofĝ. Conversely, as 2d n < λ for all n > N (see (42)) g has at most one jump in a 2d n -neighborhood of a jump ofĝ.…”

Section: Supplement To Multiscale Blind Source Separationmentioning

confidence: 99%

“…Then, Theorem 2.5 is still valid forH(β) replaced by H(β). Further, a careful modification of the proof of Theorem 2.7 shows that the assertions in Theorem 2.7 hold for a possibly smaller N in (41) and (42) and for c 1 replaced by 75m 2 (a k − a 1 ) 2 c 1 /(a 2 − a 1 ) 2 . We stress that the finite alphabet assumption is still required and the corresponding identifiability assumption ASB(ω) ≥ δ must be valid.…”

Section: 4mentioning

confidence: 99%

“…Every interval I ∈ I 1 includes a sub-interval I , which is the union of two constant pieces of g and, as 2d n < λ for all n > N (see (42)), I ∈ I 3 .…”

Section: Supplement To Multiscale Blind Source Separationmentioning

confidence: 99%

“…Before we introduce estimators for ω and f , we need to discuss identifiability of these parameters in the SBSSRmodel, that is, conditions when g determines them uniquely via g = m i=1 ω i f i . Although, deterministic finite alphabet instantaneous (linear) mixtures, i.e., σ = 0 in the SBSSR-model (4), received a lot of attention in the literature [66,53,72,21,42,36,58], a complete characterization of identifiability remained elusive and has been recently provided in [5], which will be briefly reviewed here as far as it is required for our purposes. Obviously, not every mixture g ∈ M in (2) is identifiable.…”

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confidence: 99%

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Multiscale blind source separation

Behr¹,

Holmes²,

Munk³

2018

Ann. Statist.

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We provide a new methodology for statistical recovery of single linear mixtures of piecewise constant signals (sources) with unknown mixing weights and change points in a multiscale fashion. We show exact recovery within an -neighborhood of the mixture when the sources take only values in a known finite alphabet. Based on this we provide the SLAM (Separates Linear Alphabet Mixtures) estimators for the mixing weights and sources. For Gaussian error, we obtain uniform confidence sets and optimal rates (up to log-factors) for all quantities. SLAM is efficiently computed as a nonconvex optimization problem by a dynamic program tailored to the finite alphabet assumption. Its performance is investigated in a simulation study. Finally, it is applied to assign copy-number aberrations from genetic sequencing data to different clones and to estimate their proportions. * Merle Behr acknowledges support of DFG RTG 2088 and CRC 803 Z.

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“…Consequently, (62) follows. Furthermore, as n < δ(a 2 − a 1 )/(2m(a k − a 1 )) for all n > N (see (42)), Theorem 1.4 implies that…”

Section: Supplement To Multiscale Blind Source Separationmentioning

confidence: 97%

Section: Supplement To Multiscale Blind Source Separationmentioning

confidence: 99%

Section: 4mentioning

confidence: 99%

“…Every interval I ∈ I 1 includes a sub-interval I , which is the union of two constant pieces of g and, as 2d n < λ for all n > N (see (42)), I ∈ I 3 .…”

Section: Supplement To Multiscale Blind Source Separationmentioning

confidence: 99%

mentioning

confidence: 99%

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Multiscale blind source separation

Behr¹,

Holmes²,

Munk³

2018

Ann. Statist.

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Learning and training techniques in fuzzy control for energy efficiency in buildings

Sedano¹,

Villar²,

Curiel³

et al. 2011

Logic Journal of IGPL

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A novel procedure for learning Fuzzy Controllers (FC) is proposed that processes energy efficiency issues and uses them to distribute electrical energy to heaters in an electrical energy heating system. Energy rationalisation together with temperature control can significantly improve energy efficiency, by efficiently controlling electrical heating systems and electrical energy consumption. The novel procedure, which improves the training process, is designed to train the FC, as well as to run the control algorithm and to carry out energy distribution. Firstly, the dynamic thermal performance of different variables is mathematically modelled for each specific building type and climate zone. Secondly, an exploratory projection pursuit method is used to extract the relevant features. Finally, a supervised dynamic neural network model and identification techniques are applied to FC learning and training. The FC rule-set and parameter-set learning process is a multi-objective problem that minimises both the indoor temperature error and the energy deficit in the house. The reliability of the proposed procedure is validated for a city in a winter zone in Spain.

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Independent Vector Analysis: Identification Conditions and Performance Bounds

Anderson

Phlypo

et al. 2014

IEEE Trans. Signal Process.

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Recently, an extension of independent component analysis (ICA) from one to multiple datasets, termed independent vector analysis (IVA), has been the subject of significant research interest. IVA has also been shown to be a generalization of Hotelling's canonical correlation analysis. In this paper, we provide the identification conditions for a general IVA formulation, which accounts for linear, nonlinear, and sample-to-sample dependencies. The identification conditions are a generalization of previous results for ICA and for IVA when samples are independently and identically distributed. Furthermore, a principal aim of IVA is the identification of dependent sources between datasets. Thus, we provide the additional conditions for when the arbitrary ordering of the sources within each dataset is common. Performance bounds in terms of the Cramér-Rao lower bound are also provided for the demixing matrices and interference to source ratio. The performance of two IVA algorithms are compared to the theoretical bounds.

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Blind system identification: instantaneous mixtures ofnsources

Cited by 3 publications

References 8 publications

Multiscale blind source separation

Multiscale blind source separation

Learning and training techniques in fuzzy control for energy efficiency in buildings

Independent Vector Analysis: Identification Conditions and Performance Bounds

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