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- Aapo Hyvärinen
- IEEE Transactions on Neural Networks
- 2004

A long-standing problem in statistics and related areas is how to find a suitable representation of multivariate data. Representation here means that we somehow transform the data so that its essential structure is made more visible or accessible. In neural computation, this fundamental problem belongs to the area of unsupervised learning, since the… (More)

- Aapo Hyvärinen
- IEEE Trans. Neural Networks
- 1999

Independent component analysis (ICA) is a statistical method for transforming an observed multidimensional random vector into components that are statistically as independent from each other as possible. In this paper, we use a combination of two different approaches for linear ICA: Comon's information-theoretic approach and the projection pursuit approach.… (More)

- Aapo Hyvärinen, Erkki Oja
- Neural Networks
- 2000

A fundamental problem in neural network research, as well as in many other disciplines, is finding a suitable representation of multivariate data, i.e. random vectors. For reasons of computational and conceptual simplicity, the representation is often sought as a linear transformation of the original data. In other words, each component of the… (More)

- Aapo Hyvärinen, Erkki Oja
- Neural Computation
- 1997

We introduce a novel fast algorithm for Independent Component Analysis, which can be used for blind source separation and feature extraction. It is shown how a neural network learning rule can be transformed into a xed-point iteration, which provides an algorithm that is very simple, does not depend on any user-deened parameters, and is fast to converge to… (More)

- Aapo Hyvärinen
- 1999

A common problem encountered in such disciplines as statistics, data analysis, signal processing, and neural network research, is nding a suitable representation of multivariate data. For computational and conceptual simplicity, such a representation is often sought as a linear transformation of the original data. Well-known linear transformation methods… (More)

- Johan Himberg, Aapo Hyvärinen, Fabrizio Esposito
- NeuroImage
- 2004

Recently, independent component analysis (ICA) has been widely used in the analysis of brain imaging data. An important problem with most ICA algorithms is, however, that they are stochastic; that is, their results may be somewhat different in different runs of the algorithm. Thus, the outputs of a single run of an ICA algorithm should be interpreted with… (More)

- Ella Bingham, Aapo Hyvärinen
- Int. J. Neural Syst.
- 2000

Separation of complex valued signals is a frequently arising problem in signal processing. For example, separation of convolutively mixed source signals involves computations on complex valued signals. In this article, it is assumed that the original, complex valued source signals are mutually statistically independent, and the problem is solved by the… (More)

- Aapo Hyvärinen, Patrik O. Hoyer
- Neural Computation
- 2000

Olshausen and Field (1996) applied the principle of independence maximization by sparse coding to extract features from natural images. This leads to the emergence of oriented linear filters that have simultaneous localization in space and in frequency, thus resembling Gabor functions and simple cell receptive fields. In this article, we show that the same… (More)

- Aapo Hyvärinen
- Encyclopedia of Computational Neuroscience
- 2001

In ordinary independent component analysis, the components are assumed to be completely independent, and they do not necessarily have any meaningful order relationships. In practice, however, the estimated "independent" components are often not at all independent. We propose that this residual dependence structure could be used to define a topographic order… (More)

- Shohei Shimizu, Patrik O. Hoyer, Aapo Hyvärinen, Antti J. Kerminen
- Journal of Machine Learning Research
- 2006

In recent years, several methods have been proposed for the discovery of causal structure from non-experimental data. Such methods make various assumptions on the data generating process to facilitate its identification from purely observational data. Continuing this line of research, we show how to discover the complete causal structure of… (More)