Analyzing neuroimaging data with subclasses: A shrinkage approach.

Among the numerous methods used to analyze neuroimaging data, Linear Discriminant Analysis (LDA) is commonly applied for binary classification problems. LDAs popularity derives from its simplicity and its competitive classification performance, which has been reported for various types of neuroimaging data. Yet the standard LDA approach proves less than optimal for binary classification problems when additional label information (i.e. subclass labels) is present. Subclass labels allow to model structure in the data, which can be used to facilitate the classification task. In this paper, we illustrate how neuroimaging data exhibit subclass labels that may contain valuable information. We also show that the standard LDA classifier is unable to exploit subclass labels. We introduce a novel method that allows subclass labels to be incorporated efficiently into the classifier. The novel method, which we call Relevance Subclass LDA (RSLDA), computes an individual classification hyperplane for each subclass. It is based on regularized estimators of the subclass mean and uses other subclasses as regularization targets. We demonstrate the applicability and performance of our method on data drawn from two different neuroimaging modalities: (I) EEG data from brain-computer interfacing with event-related potentials, and (II) fMRI data in response to different levels of visual motion. We show that RSLDA outperforms the standard LDA approach for both types of datasets. These findings illustrate the benefits of exploiting subclass structure in neuroimaging data. Finally, we show that our classifier also outputs regularization profiles, enabling researchers to interpret the subclass structure in a meaningful way. RSLDA therefore yields increased classification accuracy as well as a better interpretation of neuroimaging data. Since both results are highly favorable, we suggest to apply RSLDA for various classification problems within neuroimaging and beyond.

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.