An Extension of Slow Feature Analysis for Nonlinear Blind Source Separation
Authors: Henning Sprekeler, Tiziano Zito, Laurenz Wiskott
JMLR 2014 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | We present and test an extension of slow feature analysis as a novel approach to nonlinear blind source separation. The algorithm relies on temporal correlations and iteratively reconstructs a set of statistically independent sources from arbitrary nonlinear instantaneous mixtures. Simulations show that it is able to invert a complicated nonlinear mixture of two audio signals with a high reliability. |
| Researcher Affiliation | Academia | Henning Sprekeler EMAIL Tiziano Zito EMAIL Laurenz Wiskott EMAIL Institute for Theoretical Biology and Bernstein Center for Computational Neuroscience Berlin Humboldt-Universit at zu Berlin Unter den Linden 6 10099 Berlin, Germany . H.S. is now also at the Computational and Biological Learning Laboratory, Department of Engineering, University of Cambridge, UK. . L.W. is now at the Institut f ur Neuroinformatik, Ruhr-Universit at Bochum, Germany. |
| Pseudocode | Yes | The structure of the algorithm is the following (see also Figure 2): 1. Start with the first source: i = 1. 2. Apply a polynomial expansion of degree NSFA to the mixture to obtain the expanded mixture z. 3. Apply linear SFA to the expanded mixture z and store the slowest output signal as an estimate si of source i. 4. Stop if the desired number of sources has been extracted (i = S). 5. Apply a polynomial expansion of degree Nnl to the estimated sources s1,...,i and whiten the resulting signals. We refer to the resulting nonlinear versions of the first sources as nk, k {1, ..., Nexp}, where Nexp denotes the dimension of a polynomial expansion of degree Nnl of i signals. 6. Remove the nonlinear versions of the first i sources from the expanded mixture z zj(t) zj(t) k=1 cov(zj, nk) nk(t) 7. To extract the next source, increase i by one and go to step 2, using the new expanded signals z. |
| Open Source Code | Yes | The simulations were done in Python using the modular toolkit for data processing (MDP) developed by Zito et al. (2008). The x SFA algorithm is included in the current version of MDP (http://mdp-toolkit.sourceforge.net). |
| Open Datasets | No | Audio signals: We first evaluated the performance of the algorithm on two different test sets of audio signals. Data set A consists of excerpts from 14 string quartets by Béla Bartók. ... Data set B consists of 20 excerpts from popular music pieces from various genres, ranging from classical music over rock to electronic music. The paper describes the audio datasets but does not provide concrete access information (e.g., a link, DOI, or specific citation for public availability) for these specific excerpts used in the experiments. |
| Dataset Splits | No | Figure 4 shows the performance of the algorithm depending on the duration of the training data. To provide an idea of the statistics of the performance, we plot the median as well as the 25th and 75th percentile of the distribution of the correlation coefficient and the signal-to-noise ratio. For data set A, the algorithm requires on the order of 0.5s of training data to extract the first source... The paper discusses the 'duration of the training data' but does not specify explicit training/test/validation splits (e.g., percentages, sample counts, or methodology for partitioning data into distinct sets). |
| Hardware Specification | Yes | The algorithm is relatively fast: On a notebook with 1.7GHz, the simulation of the 182 source pairs for data set A with 0.2s training sequences takes about 380 seconds... |
| Software Dependencies | No | The simulations were done in Python using the modular toolkit for data processing (MDP) developed by Zito et al. (2008). The paper mentions 'Python' and 'modular toolkit for data processing (MDP)' but does not provide specific version numbers for either. |
| Experiment Setup | Yes | Degree of the expansion in the first SFA step: For the simulations with two sources, we used a polynomial expansion of degree NSFA = 7... For the simulations with more than two sources, we used a polynomial expansion of degree NSFA = 3. Degree of the expansion for source removal: For the simulations with two sources, we expanded the estimate for the first source in polynomials of degree Nnl = 20... For the separation of more than two sources, all polynomials of degree Nnl = 4 of the already estimated sources were projected out. Variance threshold: After the removal of the nonlinear versions of the first source, there is at least one direction with vanishing variance. To avoid numerical problems caused by singularities in the covariance matrices, directions with variance below ϵ = 10 7 were removed. |