Kernel-Based Nonlinear Blind Source Separation

By Stefan Harmeling, Andreas Ziehe, Motoaki Kawanabe, K. Müller. 2003

149 citations recorded by the source corpus.

Subfields: Analytical Chemistry, Signal Processing

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Analytical Chemistry

1. Aapo Hyvärinen
2. Hiroshi Morioka
3. Hermanni Hälvä
4. Richard E. Turner
5. Hiroaki Sasaki
6. Yash Sharma
7. Henning Sprekeler
8. Wieland Brendel

In Signal Processing

1. Aapo Hyvärinen
2. Hermanni Hälvä
3. Hiroshi Morioka
4. Yash Sharma
5. Richard E. Turner
6. Wieland Brendel
7. Matthias Bethge
8. Hiroaki Sasaki

Citations in the corpus

• Hidden Markov Nonlinear ICA: Unsupervised Learning from Nonstationary Time Series (2020, background): “, 1991), and extensions to the nonlinear case have been also been proposed in earlier work (Harmeling et al., 2003; Sprekeler et al., 2014).”
• Unsupervised Feature Extraction by Time-Contrastive Learning and Nonlinear ICA (2016, methodology): “For comparison, we also applied a linear ICA method based on nonstationarity of variance (NSVICA) [16], a kernel-based nonlinear ICA method (kTDSEP) [12], and a denoising autoencoder (DAE) [31] to the observed data.”
• Nonlinear ICA Using Auxiliary Variables and Generalized Contrastive Learning (2018, methodology): “Fortunately, a solution to non-identifiability in non-linear ICA can be found by utilizing temporal structure in the data (Harmeling et al., 2003; Sprekeler et al., 2014; Hyv¨arinen and Morioka, 2017b,a).”
• An extension of slow feature analysis for nonlinear blind source separation (2014, methodology): “Moreover, SFA is intimately related to ICA techniques like TDSEP (Ziehe and Müller, 1998; Blaschke et al., 2006) and differential decorrelation (Choi, 2006) and is therefore an interesting starting point for developing nonlinear BSS techniques.”
• Variational Approach for Learning Markov Processes from Time Series Data (2017, background): “2016b) and corresponding kernel embeddings (Harmeling et al. 2003; Song et al. 2013; Schwantes and Pande 2015) and tensor formulations (Nüske et al.”
• Nonlinear ICA of Temporally Dependent Stationary Sources (2017, methodology): “This is to be contrasted to kTDSEP (Harmeling et al., 2003) and xSFA (Sprekeler et al.”
• Linear-Time Computation of Similarity Measures for Sequential Data (2008, methodology): “Following the seminal work of Boser et al. (1992), various learning methods have been re-formulated in terms of kernels, such as PCA (Schölkopf et al., 1998b), ridge regression (Cherkassky et al., 1999), ICA (Harmeling et al., 2003) and many others.”
• Support vector machines (2008, unknown): “, 1998b), Kernel ICA (Harmeling et al., 2003), temporal Kernel CCA (Bießmann et al.”
• Contrastive Learning Inverts the Data Generating Process (2021, background): “In the spirit of existing literature on nonlinear ICA (Hyvärinen & Pajunen, 1999; Harmeling et al., 2003; Sprekeler et al., 2014; Hyvärinen & Morioka, 2016; 2017; Gutmann & Hyvärinen, 2012; Hyvärinen et al., 2019; Khemakhem et al., 2020a), we assume that the observations x ∈ X are generated by a”