Digital staining for the automated annotation of mass spectrometry imaging (MSI) data has previously been achieved using state-of-the-art classifiers such as random forests or support vector machines (SVMs). However, the training of such classifiers requires an expert to label exemplary data in advance. This process is time-consuming and hence costly, especially if the tissue is heterogeneous. In theory, it may be sufficient to only label a few highly representative pixels of an MS image, but it is not known a priori which pixels to select. This motivates active learning strategies in which the algorithm itself queries the expert by automatically suggesting promising candidate pixels of an MS image for labeling. Given a suitable querying strategy, the number of required training labels can be significantly reduced while maintaining classification accuracy. In this work, we propose active learning for convenient annotation of MSI data. We generalize a recently proposed active learning method to the multiclass case and combine it with the random forest classifier. Its superior performance over random sampling is demonstrated on secondary ion mass spectrometry data, making it an interesting approach for the classification of MS images.

The aim of this paper is to compare four different methods for binary classification with an underlying Gaussian process with respect to theoretical consistency and practical performance. Two of the inference schemes, namely classical indicator kriging and simplicial indicator kriging, are analytically tractable and fast. However, these methods rely on simplifying assumptions which are inappropriate for categorical class labels. A consistent and previously described model extension involves a doubly stochastic process. There, the unknown posterior class probability f(Á) is considered a realization of a spatially correlated Gaussian process that has been squashed to the unit interval, and a label at position x is considered an independent Bernoulli realization with success parameter f(x). Unfortunately, inference for this model is not known to be analytically tractable. In this paper, we propose two new computational schemes for the inference in this doubly stochastic model, namely the ''Aitchison Maximum Posterior'' and the ''Doubly Stochastic Gaussian Quadrature''. Both methods are analytical up to a final step where optimization or integration must be carried out numerically. For the comparison of practical performance, the methods are applied to storm forecasts for the Spanish coast based on wave heights in the Mediterranean Sea. While the error rate of the doubly stochastic models is slightly lower, their computational cost is much higher.Keywords Model-based geostatistics Á Logistic transformation Á Classical indicator kriging Á Simplicial indicator kriging Á Doubly stochastic process Aitchison maximum posterior Á Doubly stochastic Gaussian quadrature 1 Introduction

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