Directional variance adjustment: bias reduction in covariance matrices based on factor analysis with an application to portfolio optimization.

Robust and reliable covariance estimates play a decisive role in financial and many other applications. An important class of estimators is based on factor models. Here, we show by extensive Monte Carlo simulations that covariance matrices derived from the statistical Factor Analysis model exhibit a systematic error, which is similar to the well-known systematic error of the spectrum of the sample covariance matrix. Moreover, we introduce the Directional Variance Adjustment (DVA) algorithm, which diminishes the systematic error. In a thorough empirical study for the US, European, and Hong Kong stock market we show that our proposed method leads to improved portfolio allocation.

Semi-blind identification of movement-related magnetoencephalogram components using a classification approach.

Many biomedical signal processing applications involving the analysis of multi-channel electrophysiological recordings, such as the magnetoencephalogram (MEG) and electroencephalogram (EEG), increasingly employ blind source separation (BSS) techniques to estimate signal components reflecting artifacts and neurophysiological activity. While much research focuses on developing methods for automatic removal of artefact sources, comparatively little effort has been spent on trying to identify neurophysiological sources of interest, which is especially challenging in the absence of prior knowledge about their spatial or time-freqency characteristics. This work presents a method for identifying source signals exhibiting systematic and reliable time-frequency differences over clearly defined epochs associated with different 'system-states'. The proposed method uses annotated data and a classification approach to identify those sources which individually reflect significant differences between epochs (classes). Applied to segments of 275-channel MEG data from a visuo-motor task in which left, right or no finger movements occurred, the method selects only a small number of sources whose scalp topographies are consistent with primary sensorimotor cortical areas.

Model order estimation for blind source separation of multichannel magnetoencephalogram and electroencephalogram signals.

Most blind source separation (BSS) approaches - especially independent component analysis (ICA) - assume a noiseless mixture of the same number of sources as sensors. It is doubtful, however, whether this assumption actually holds for multichannel magnetoencephalogram (MEG) and electroencephalogram (EEG) measurements comprising a large number of channels. Corroborating and extending previous results, this work further examines the utility of second-order statistical methods based on probabilistic principal component analysis (PPCA) and factor analysis (FA) models for estimating the number of underlying sources in multichannel MEG and EEG. Compared with conventional PCA-based eigenvalue thresholding, both PPCA and FA approaches yield stable model order estimates which are almost independent of total signal power. The FA model provides a more optimal description of both MEG and EEG data than PPCA, in terms of balancing goodness-of-fit and parsimony. These findings add to the growing evidence that anisotropic 'sensor noise' may be a statistically robust characteristic of both the EEG and MEG, which most BSS algorithms and applications do not address.

On estimating the signal subspace dimension of high-density multichannel magnetoencephalogram measurements.

Accurate estimates of the dimension and an (orthogonal) basis of the signal subspace of noise corrupted multi-channel measurements are essential for accurate identification and extraction of any signals of interest within that subspace. For most biomedical signals comprising very large numbers of channels, including the magnetoencephalogram (MEG), the "true" number of underlying signals ¿ although ultimately unknown ¿ is unlikely to be of the same order as the number of measurements, and has to be estimated from the available data. This work examines several second-order statistical approaches to signal subspace (dimension) estimation with respect to their underlying assumptions and their performance in high-dimensional measurement spaces using 151-channel MEG data. The purpose is to identify which of these methods might be most appropriate for modeling the signal subspace structure of high-density MEG data recorded under controlled conditions, and what are the practical consequences with regard to the subsequent application of biophysical modeling and statistical source separation techniques.

On semi-blind source separation using spatial constraints with applications in EEG analysis.

Blind source separation (BSS) techniques, such as independent component analysis (ICA), are increasingly being used in biomedical signal processing applications, including the analysis of multichannel electroencephalogram (EEG) and magnetoencephalogram (MEG) signals. These methods estimate a set of sources from the observed data, which reflect the underlying physiological signal generating and mixing processes, noise and artifacts. In practice, BSS methods are often applied in the context of additional information and expectations regarding the spatial or temporal characteristics of some sources of interest, whose identification requires complicated post-hoc analysis or, more commonly, manual selection by human experts. An alternative would be to incorporate any available prior knowledge about the source signals or locations into a semi-blind source separation (SBSS) approach, effectively by imposing temporal or spatial constraints on the underlying source mixture model. This work is concerned with biomedical applications of SBSS using spatial constraints, particularly for artifact removal and source tracking in EEG analysis, and provides definitions of different types of spatial constraint along with general guidelines on how these can be implemented in conjunction with conventional BSS methods.

Independent component analysis for biomedical signals.

Independent component analysis (ICA) is increasing in popularity in the field of biomedical signal processing. It is generally used when it is required to separate measured multi-channel biomedical signals into their constituent underlying components. The use of ICA has been facilitated in part by the free availability of toolboxes that implement popular flavours of the techniques. Fundamentally ICA in biomedicine involves the extraction and separation of statistically independent sources underlying multiple measurements of biomedical signals. Technical advances in algorithmic developments implementing ICA are reviewed along with new directions in the field. These advances are specifically summarized with applications to biomedical signals in mind. The basic assumptions that are made when applying ICA are discussed, along with their implications when applied particularly to biomedical signals. ICA as a specific embodiment of blind source separation (BSS) is also discussed, and as a consequence the criterion used for establishing independence between sources is reviewed and this leads to the introduction of ICA/BSS techniques based on time, frequency and joint time-frequency decomposition of the data. Finally, advanced implementations of ICA are illustrated as applied to neurophysiologic signals in the form of electro-magnetic brain signals data.