Indeterminacy and identifiability of blind identification

By Lang Tong, Raymond Liu, Victor C. Soon, Yih-Fang Huang. 1991

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Citations in the corpus

Hidden Markov Nonlinear ICA: Unsupervised Learning from Nonstationary Time Series (2020, methodology): “For linear ICA this approach has been shown to yield identiﬁable models (Belouchrani et al., 1997; Tong et al., 1991), and extensions to the nonlinear case have been also been proposed in earlier work (Harmel-ing et al., 2003; Sprekeler et al., 2014).”
Nonlinear ICA Using Auxiliary Variables and Generalized Contrastive Learning (2018, background): “As a first attempt, we can assume that the sources si(t) have non-zero autocorrelations, which has a long history in the linear case (Tong et al., 1991; Belouchrani et al., 1997).”
Continuous latent variable models for dimensionality reduction and sequential data reconstruction (2001, background): “Thus, it can be proven that the identifiability of the ICA model (up to reordering and rescaling) is guaranteed if (Tong et al., 1991; Comon, 1994):”
Blind Source Separation and Independent Component Analysis: A Review (2005, methodology): “In mathematical terms these indeterminacies and ambiguities can be expressed as arbitrary scaling, permutation and delay of estimated source signals [138].”
Blind source separation based vibration mode identification (2007, methodology): “To this end various methods have been developed, such as AMUSE [15], SOBI [16], temporal decorrelation separation (TDSEP) [24] or time– frequency blind source separation (TFBSS) [25].”
Fetal electrocardiogram extraction by blind source subspace separation (2000, background): “For non-Gaussian sources, these indeterminacies are the only way in which an ICA-solution is not unique [8], [20].”
Blind Source Separation and Blind Equalization Algorithms for Mechanical Signal Separation and Identification (2006, methodology): “AMUSE uses the sub-optimal time delay p = 1 (Tong et al., 1991).”
Nonlinear ICA of Temporally Dependent Stationary Sources (2017, background): “Gaussian processes in the linear case can be separated only when they have different autocorrelation functions (Tong et al., 1991; Molgedey and Schuster, 1994; Belouchrani et al., 1997); see Section 3.”
A blind source separation technique using second-order statistics (1997, background): “Of course, these indeterminacies do not impede source separation: If the mixture matrix is estimated up to permutation and phase shifts, it is still possible to determine the source signals up to the corresponding fixed permutation and phase shifts (blind identifiability is discussed at length in [1”
Blind Source Separation and Independent Component Analysis : A Review (2004, methodology): “In mathematical terms these indeterminacies and ambiguities can be expressed as arbitrary scaling, permutation and delay of estimated source signals [138].”
Independent component analysis: recent advances (2013, methodology): “…possible to estimate the ICA model even for Gaussian data, based on the time structure (autocorrelations) alone, as initially pointed out by Tong et al. (1991) and further developed by Belouchrani et al. (1997) among others (see Chapter 18 of (Hyvärinen et al., 2001) or (Yeredor, 2010) for…”
Optimization algorithms exploiting unitary constraints (2002, background): “Such symmetries occur in subspace tracking [5], [23], [25] as well as in blind identification [1], [30].”