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Most connectivity metrics in neuroimaging research reduce multivariate activity patterns in regions-of-interests (ROIs) to one dimension, which leads to a loss of information. Importantly, it prevents us from investigating the transformations between patterns in different ROIs. Here, we applied linear estimation theory in order to robustly estimate the linear transformations between multivariate fMRI patterns with a cross-validated ridge regression approach. We used three functional connectivity metrics that describe different features of these voxel-by-voxel mappings: goodness-of-fit, sparsity and pattern deformation. The goodness-of-fit describes the degree to which the patterns in an input region can be described as a linear transformation of patterns in an output region. The sparsity metric, which relies on a Monte Carlo procedure, was introduced in order to test whether the transformation mostly consists of one-to-one mappings between voxels in different regions. Furthermore, we defined a metric for pattern deformation, i.e. the degree to which the transformation rotates or rescales the input patterns. As a proof of concept, we applied these metrics to an event-related fMRI data set consisting of four subjects that has been used in previous studies. We focused on the transformations from early visual cortex (EVC) to inferior temporal cortex (ITC), fusiform face area (FFA) and parahippocampal place area (PPA). Our results suggest that the estimated linear mappings explain a significant amount of response variance in the three output ROIs. The transformation from EVC to ITC shows the highest goodness-of-fit, and those from EVC to FFA and PPA show …