Proximally Sensitive Error for Anomaly Detection and Feature Learning

Mean squared error (MSE) is one of the most widely used metrics to expression differences between multi-dimensional entities, including images. However, MSE is not locally sensitive as it does not take into account the spatial arrangement of the (pixel) differences, which matters for structured data types like images. Such spatial arrangements carry information about the source of the differences; therefore, an error function that also incorporates the location of errors can lead to a more meaningful distance measure. We introduce Proximally Sensitive Error (PSE), through which we suggest that a regional emphasis in the error measure can 'highlight' semantic differences between images over syntactic/random deviations. We demonstrate that this emphasis can be leveraged upon for the task of anomaly/occlusion detection. We further explore its utility as a loss function to help a model focus on learning representations of semantic objects instead of minimizing syntactic reconstruction noise.