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Erkki Oja

Publications and source records attributed to Erkki Oja.

6 recordsLinked to original sources
PubMed2004

A "nonnegative PCA" algorithm for independent component analysis.

We consider the task of independent component analysis when the independent sources are known to be nonnegative and well-grounded, so that they have a nonzero probability density function (pdf) in the region of zero. We propose the use of a "nonnegative principal component analysis (nonnegative PCA)" algorithm, which is a special case of the nonlinear PCA algorithm, but with a rectification nonlinearity, and we conjecture that this algorithm will find such nonnegative well-grounded independent sources, under reasonable initial conditions. While the algorithm has proved difficult to analyze in the general case, we give some analytical results that are consistent with this conjecture and some numerical simulations that illustrate its operation.

Algorithms↗
PubMed2004

Nonlinear dynamical factor analysis for state change detection.

Changes in a dynamical process are often detected by monitoring selected indicators directly obtained from the process observations, such as the mean values or variances. Standard change detection algorithms such as the Shewhart control charts or the cumulative sum (CUSUM) algorithm are often based on such first- and second-order statistics. Much better results can be obtained if the dynamical process is properly modeled, for example by a nonlinear state-space model, and then the accuracy of the model is monitored over time. The success of the latter approach depends largely on the quality of the model. In practical applications like industrial processes, the state variables, dynamics, and observation mapping are rarely known accurately. Learning from data must be used; however, methods for the simultaneous estimation of the state and the unknown nonlinear mappings are very limited. We use a novel method of learning a nonlinear state-space model, the nonlinear dynamical factor analysis (NDFA) algorithm. It takes a set of multivariate observations over time and fits blindly a generative dynamical latent variable model, resembling nonlinear independent component analysis. We compare the performance of the model in process change detection to various traditional methods. It is shown that NDFA outperforms the classical methods by a wide margin in a variety of cases where the underlying process dynamics changes.

Factor Analysis, Statistical↗
PubMed2004

Blind separation of positive sources by globally convergent gradient search.

The instantaneous noise-free linear mixing model in independent component analysis is largely a solved problem under the usual assumption of independent nongaussian sources and full column rank mixing matrix. However, with some prior information on the sources, like positivity, new analysis and perhaps simplified solution methods may yet become possible. In this letter, we consider the task of independent component analysis when the independent sources are known to be nonnegative and well grounded, which means that they have a nonzero pdf in the region of zero. It can be shown that in this case, the solution method is basically very simple: an orthogonal rotation of the whitened observation vector into nonnegative outputs will give a positive permutation of the original sources. We propose a cost function whose minimum coincides with nonnegativity and derive the gradient algorithm under the whitening constraint, under which the separating matrix is orthogonal. We further prove that in the Stiefel manifold of orthogonal matrices, the cost function is a Lyapunov function for the matrix gradient flow, implying global convergence. Thus, this algorithm is guaranteed to find the nonnegative well-grounded independent sources. The analysis is complemented by a numerical simulation, which illustrates the algorithm.

Algorithms↗
PubMedDate not supplied

Class distributions on SOM surfaces for feature extraction and object retrieval.

A Self-Organizing Map (SOM) is typically trained in unsupervised mode, using a large batch of training data. If the data contain semantically related object groupings or classes, subsets of vectors belonging to such user-defined classes can be mapped on the SOM by finding the best matching unit for each vector in the set. The distribution of the data vectors over the map forms a two-dimensional discrete probability density. Even from the same data, qualitatively different distributions can be obtained by using different feature extraction techniques. We used such feature distributions for comparing different classes and different feature representations of the data in the context of our content-based image retrieval system PicSOM. The information-theoretic measures of entropy and mutual information are suggested to evaluate the compactness of a distribution and the independence of two distributions. Also, the effect of low-pass filtering the SOM surfaces prior to the calculation of the entropy is studied.

Artificial Intelligence↗
PubMedDate not supplied

Independent component analysis for artefact separation in astrophysical images.

In this paper, we demonstrate that independent component analysis, a novel signal processing technique, is a powerful method for separating artefacts from astrophysical image data. When studying far-out galaxies from a series of consequent telescope images, there are several sources for artefacts that influence all the images, such as camera noise, atmospheric fluctuations and disturbances, cosmic rays, and stars in our own galaxy. In the analysis of astrophysical image data it is very important to implement techniques which are able to detect them with great accuracy, to avoid the possible physical events from being eliminated from the data along with the artefacts. For this problem, the linear ICA model holds very accurately because such artefacts are all theoretically independent of each other and of the physical events. Using image data on the M31 Galaxy, it is shown that several artefacts can be detected and recognized based on their temporal pixel luminosity profiles and independent component images. The obtained separation is good and the method is very fast. It is also shown that ICA outperforms principal component analysis in this task. For these reasons, ICA might provide a very useful pre-processing technique for the large amounts of available telescope image data.

Artifacts↗